U.S. patent application number 12/421943 was filed with the patent office on 2009-09-24 for apparatuses and processes for calculating options.
Invention is credited to Vergil L. Daughtery, III.
Application Number | 20090240535 12/421943 |
Document ID | / |
Family ID | 27395779 |
Filed Date | 2009-09-24 |
United States Patent
Application |
20090240535 |
Kind Code |
A1 |
Daughtery, III; Vergil L. |
September 24, 2009 |
APPARATUSES AND PROCESSES FOR CALCULATING OPTIONS
Abstract
The present invention introduces an apparatus and process which
may be implemented on a vast variety of computer systems. The
apparatus and process of the present invention use a computer
system to receive and store data representative of a particular
asset, a type of option (call or put), requested exercise price and
a multitude of other variables related to the asset. The apparatus
and process then generate data representative of an option premium.
The data representative of the option may then be used for
transacting an option, as the basis for determining a correlated
expiring option premium, or to determine the premium of an asset
relatable to a corresponding option. Other embodiments are also
claimed and described.
Inventors: |
Daughtery, III; Vergil L.;
(Waynesville, NC) |
Correspondence
Address: |
SMITH HOPEN, PA
180 PINE AVENUE NORTH
OLDSMAR
FL
34677
US
|
Family ID: |
27395779 |
Appl. No.: |
12/421943 |
Filed: |
April 10, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11276293 |
Feb 22, 2006 |
7536334 |
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12421943 |
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09906305 |
Jul 16, 2001 |
7024384 |
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11276293 |
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09262663 |
Mar 4, 1999 |
6263321 |
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09906305 |
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08718630 |
Sep 17, 1996 |
5884286 |
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09262663 |
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08282717 |
Jul 29, 1994 |
5557517 |
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08718630 |
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Current U.S.
Class: |
705/4 ; 705/35;
705/36R |
Current CPC
Class: |
G06Q 90/00 20130101;
G06Q 40/04 20130101; G06Q 40/08 20130101; G06Q 40/06 20130101; G06Q
30/00 20130101; G06Q 40/00 20130101; G06Q 30/08 20130101 |
Class at
Publication: |
705/4 ; 705/36.R;
705/35 |
International
Class: |
G06Q 40/00 20060101
G06Q040/00 |
Claims
1. An apparatus for transacting an expirationless option contract
comprising: an interface for receiving data representative of an
option on an asset, wherein the data includes the value of the
underlying asset; a storage medium in communication with the
interface to store the data received by the interface and an option
pricing algorithm; and a processor in communication with the
storage medium configured to compute an option premium on an
expirationless option contract using the value of an underlying
asset of the option and an option pricing algorithm, wherein the
option contract grants the owner of the option contract a right to
sell or buy the underlying asset at a predetermined price.
2. The apparatus of claim 1 wherein the data representative of an
option on an asset further includes data selected from the group
consisting of an option type, an exercise price for the particular
asset, the historic price volatility of the particular asset and
the margin requirement for the particular asset and combinations
thereof.
3. The apparatus of claim 1 wherein the asset is a security.
4. The apparatus of claim 3 wherein the data representative of an
option on an asset further includes data selected from the group
consisting of the current market price for the security, an
exercise price for the security, the margin price for the security
and combinations thereof.
5. The apparatus of claim 1 wherein the interface is configured to
receive a signal representative of a request to transact an option
on an asset.
6. The apparatus of claim 1 wherein the option pricing algorithm is
selected from the group consisting of the Black-Scholes, the
Binomial Pricing, the Finite Difference and the Analytic
Approximation algorithms.
7. The apparatus of claim 1 wherein said asset is an option
selected from the group consisting of: vanilla options; Asian
options; barrier options; binary options; chooser options; compound
options; crack/spread options; currency translated options; jump
options; lookback options; rainbow options; options on U.S. or
foreign "stripped" government securities divided into two or more
instruments of principal and interest or price and dividend;
options on stripped corporate, agency, and municipal securities,
notes, bills and certificates of deposit; options on callables; and
options on odd-first, -last, -middle, or securities with varying
coupon/dividend periods.
8. The apparatus of claim 1 wherein said asset is selected from the
group consisting of: equity, bonds, loans, private placements,
forward contracts, futures contracts, swaps, forward swaps/delayed
start swaps, break forwards, straddles/strangles/butterflies,
reverse floating rate loan/bull floating rate notes, dual currency
bonds, callable/puttable bonds, puttable stock, bond with warrant,
convertible bonds, liquid yield option notes, commodity-linked
bonds, auction rate notes/debentures, collaterallized mortgage
obligations/real estate mortgage investment conduits, commercial
real-estate backed bonds, credit enhanced debt securities, dollar
bills, foreign exchange paper, floating/bate sensitive notes,
floating rate tax-exempt revenue bonds, increasing rate notes,
indexed currency option notes or principal exchange rate linked
securities, caps/floors/collars, interest rate reset notes,
mortgage pass-through certificates, negotiable certificates of
deposit, adjustable tender securities, puttable/extendable notes,
real yield securities, receivable pay-through securities,
remarketed reset notes, stripped mortgage backed securities,
stripped treasuries/municipals, variable coupon renewable notes,
variable rate renewable notes, yield curve/maximum rate notes,
adjustable rate preferred stock, auction rate preferred stock,
convertible adjustable preferred stock, remarketed preferred stock,
single point adjustable rate stock, state rate auction preferred
stock, variable cumulative preferred stock, adjustable rate
convertible debt, convertible exchangeable preferred stock,
convertible reset debentures, debt with mandatory common stock
purchase contracts, exchangeable preferred stock, synthetic
convertible debt, zero coupon convertible debt, puttable common
stock.
9. The apparatus of claim 1 wherein the processor is further
configured to compute an implied time using an option pricing
algorithm, the current price of the particular asset, and the
margin requirement for the particular asset, the margin requirement
substituted for the option premium and the current price
substituted for the exercise price in the calculation of implied
time using the option pricing algorithm, and wherein the implied
time is used as the time value in the computation of the option
premium on an expirationless option contract.
10. An apparatus for transacting an expirationless option contract
comprising: an interface for receiving data representative of an
option on an asset, wherein the data includes the value of the
underlying asset; a storage medium in communication with the
interface to store the data received by the interface and an
expirationless option algorithm; and a processor in communication
with the storage medium configured to compute a price on an
expirationless option contract using the value of an underlying
asset of the option and an option pricing algorithm, wherein the
option contract grants the owner of the option contract a right to
sell or buy the underlying asset at a predetermined price and
wherein the option contract is associated with a guarantor, the
guarantor providing a guarantee of performance of the
expirationless options contract by a party other than the issuer of
the underlying asset.
11. The apparatus of claim 10 wherein the data representative of an
option on an asset further includes data selected from the group
consisting of an option type, an exercise price for the particular
asset, the historic price volatility of the particular asset and
the margin requirement for the particular asset and combinations
thereof.
12. The apparatus of claim 10 wherein the asset is a security.
13. The apparatus of claim 12 wherein the data representative of an
option on an asset further includes data selected from the group
consisting of the current market price for the security, an
exercise price for the security, the margin price for the security
and combinations thereof.
14. The apparatus of claim 10 wherein the interface is configured
to receive a signal representative of a request to transact an
option on an asset.
15. The apparatus of claim 10 wherein the option pricing algorithm
is selected from the group consisting of the Black-Scholes, the
Binomial Pricing, the Finite Difference and the Analytic
Approximation algorithms.
16. The apparatus of claim 10 wherein the processor is further
configured to compute an implied time using an option pricing
algorithm, the current price of the particular asset, and the
margin requirement for the particular asset, the margin requirement
substituted for the option premium and the current price
substituted for the exercise price in the calculation of implied
time using the option pricing algorithm, and wherein the implied
time is used as the time value in the computation of the option
premium on an expirationless option contract.
17. An apparatus for transacting an expirationless option contract
comprising: an interface for receiving data representative of an
option on an asset, wherein the data includes the value of the
underlying asset; a storage medium in communication with the
interface to store the data received by the interface and an
expirationless option algorithm; and a processor in communication
with the storage medium configured to compute a price on an
expirationless option contract using the value of an underlying
asset of the option and an option pricing algorithm, wherein the
option contract grants the owner of the option contract a right to
sell or buy the underlying asset at a predetermined price, said
option contractually coupled to a guarantor, the guarantor
providing a guarantee of performance of the expirationless options
contract by a party other than the issuer of the underlying
asset.
18. The apparatus of claim 17 wherein the data representative of an
option on an asset further includes data selected from the group
consisting of an option type, an exercise price for the particular
asset, the historic price volatility of the particular asset and
the margin requirement for the particular asset and combinations
thereof.
19. The apparatus of claim 17 wherein the asset is a security.
20. The apparatus of claim 19 wherein the data representative of an
option on an asset further includes data selected from the group
consisting of the current market price for the security, an
exercise price for the security, the margin price for the security
and combinations thereof.
21. The apparatus of claim 17 wherein the interface is configured
to receive a signal representative of a request to transact an
option on an asset.
22. The apparatus of claim 17 wherein the option pricing algorithm
is selected from the group consisting of the Black-Scholes, the
Binomial Pricing, the Finite Difference and the Analytic
Approximation algorithms.
23. The apparatus of claim 17 wherein the processor is further
configured to compute an implied time using an option pricing
algorithm, the current price of the particular asset, and the
margin requirement for the particular asset, the margin requirement
substituted for the option premium and the current price
substituted for the exercise price in the calculation of implied
time using the option pricing algorithm, and wherein the implied
time is used as the time value in the computation of the option
premium on an expirationless option contract.
24. A automated method for transacting an expiring financial
instrument comprising the steps of: receiving data representative
of an asset value for an asset; determining an expirationless
option value for the asset using a computer, the expirationless
option value having a value less than the asset value; computing a
premium for the expiring financial instrument using the
expirationless option value; and offering to sell, buy, or trade
said expiring financial instrument at a price calculated utilizing
the computed premium.
25. The method of claim 24, further comprising providing a
guarantee of performance of said expiring financial instrument,
said guarantee insuring against loss by one party to an options
transaction resulting from nonperformance of another party to the
options transaction.
26. The method of claim 24, wherein said expiring financial
instrument is characterized by being limited to contingent
claims.
27. The method of claim 24, wherein said expiring financial
instrument is an American options contract.
28. The method of claim 24, wherein the step of determining an
expirationless option value for an asset comprises: generating an
implied time to expiration using data representative of the asset
value; and generating a premium for the expiring financial
instrument using the implied time to expiration.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 11/276,293, filed 22 Feb. 2006, which is a
continuation of U.S. patent application Ser. No. 09/906,305 filed
16 Jul. 2001, now U.S. Pat. No. 7,024,384 B2, which is a
continuation of U.S. patent application Ser. No. 09/262,663 filed 4
Mar. 1999, now U.S. Pat. No. 6,263,321, which is a
continuation-in-part of U.S. patent application Ser. No. 08/718,630
filed Sep. 17, 1996, now U.S. Pat. No. 5,884,286, which is a
continuation-in-part of U.S. patent application Ser. No. 08/282,717
filed 29 Jul. 1994, now U.S. Pat. No. 5,557,517. All of the
above-mentioned patent applications and patents are hereby
incorporated herein by reference as if fully set forth below.
FIELD OF INVENTION
[0002] The present invention relates generally to an apparatus and
process for automatically calculating options for use in a variety
of markets, such as commodities or securities markets.
BACKGROUND OF THE INVENTION
[0003] An "option" is generally used to hedge risk by providing the
right to purchase or sell a commodity or other asset at a later
time at a set price with only limited obligations. An option is
similar to an insurance policy in that it insures that an asset may
be purchased or sold at a later time at a set price in return for a
premium, often referred to as an option premium, which is generally
a relatively small percentage of the current value of the asset.
One type of option is a "call option." A "call" option gives the
purchaser of the option the right, but not the obligation, to buy a
particular asset at a later time at a guaranteed price, often
referred to as the "exercise price." Another type of option is a
"put option". A "put" option gives the purchaser of the option the
right, but not the obligation, to sell a particular asset at a
later time at the exercise price. (The "put" option may be thought
of as giving the owner the right to "put" the security into
another's name at the exercise price.) In either instance, the
seller of the call or put option is obligated to perform the
associated transactions if the purchaser chooses to exercise its
option.
[0004] Options are utilized in a variety of asset-based
transactions. For example, in the commodities market, commodity
producers (e.g., farmers) often enter into option relationships
with commodity users (e.g., manufacturers) and speculators; in the
real estate market, real estate owners often enter into option
relationships with real estate purchasers; and in the securities
market, security holders often enter into option relationships with
security purchasers.
Commodity Market Examples
[0005] A commodity user such as a cereal manufacturer may need a
certain amount of corn and wheat at a future date. The Cereal
manufacturer, rather than purchasing the corn and wheat, may
purchase a "call" option from a speculator by rendering an option
premium. The call option guarantees an exercise price for a set
amount of corn and wheat at a future date. The speculator, in
return for receiving the option premium, agrees to obtain the set
amount of corn and wheat and sell it to the cereal manufacturer at
the exercise price at the future date.
[0006] If the price of the desired commodities increases, then the
cereal manufacturer will likely exercise the "call" option and
obtain the set amount of commodities from the seller at the
guaranteed exercise price. Therefore, by paying the option premium
in advance of knowing the future value of the commodities, the
cereal manufacturer may save itself a substantial amount of money.
If the price of the desired commodities does not reach the exercise
price then the cereal manufacturer will not exercise the call
option and will purchase the commodities on the open market at the
going price.
[0007] A commodity producer, such as a farmer, may plant his fields
many months in advance of having a commodity ready for delivery. To
guarantee a set future price for his commodity, the farmer may
purchase a "put" option from a speculator. Here, if the price of
the farmer's commodities goes down over the set period of time the
farmer is guaranteed to receive a set amount of minimum income for
his efforts from the speculator.
[0008] Prior art systems are only capable of transacting options
which expire after a certain period of "time". The purchaser of a
call or put option using the prior art systems only has the right
to exercise the option before it expires or on the expiration
date.
[0009] As shown in FIGS. 8-11, for a set period of time, an option
transacted using a prior art system has some value associated with
it depending on the type of option, the current value of the asset
relative to the exercise price and other variables. However, the
moment after the option expires, a purchased option, as shown in
FIGS. 8 and 9, is worthless causing an option purchaser who may
have owned a valuable option one day to own a worthless option the
next day. Furthermore, not only is the option worthless, but the
purchaser of the call or put option is no longer protected against
future price fluctuations associated with the asset. On the other
hand, as shown in FIGS. 10 and 11, a sold option, which might be
falling in value, automatically rises to the value of the option
premium and removes all future risks to the option seller the
moment after the option expires.
[0010] Turning to FIG. 8, a call option on shares of Company A is
shown with an option premium of $5 per share and an exercise price
of $55 per share. Ignoring the effect of "time" and other nominal
costs associated with transacting options, the value of the options
on the shares of Company A may increase or decrease based on the
current price of the shares. For example, if the current share
price rose from $50 to $56, then the value of the purchased call
option would increase because it would be more likely to be
exercised at the $55 per share exercise price. Further, if the
current share price rose to $60, then the value of the purchased
call option would increase even more because the owner of the
purchased call option could now purchase shares of Company A at the
exercise price of $55 and sell them for $60 on the open market
resulting in a $5 per share profit. Moreover, the value of the
purchased call option would continue to increase if the current
share-price of the shares of Company A continued to rise higher and
higher. Accordingly, as long as the current price of the asset (the
shares of Company A) continues to increase, the profits associated
with the return on investment for a purchaser of a call option are
unlimited. However, as might be expected, the exact opposite
results for the seller of the call option (see FIG. 10) in that the
losses attributed to the seller of a call option are unlimited.
[0011] On the other hand, continuing to ignore the effect of
"time," if the current share price dropped from $50 to $45, then
the value of the purchased call option would decrease because it
would be less likely to be exercised at the $55 per share exercise
price. Moreover, as the current share price dropped further, the
purchased call option would be even less likely to be exercised.
However, unlike the situation above where the value of the
purchased call option continued to increase as the current share
price increased, for a purchased call option associated with an
asset which decreases in value, the maximum loss associated with
the return on investment is limited to the option premium (for this
example, $5 per share). Again, the exact opposite results for the
seller of the call option in that the profits realized by the
seller of a call option are capped at the option premium.
[0012] Referring to FIGS. 9 and 11, similar yet opposite results
may be realized by the purchaser and seller of a put option,
respectively, using a prior art system for transacting options.
Here, assume that investor P purchases a put option from investors
who sells the put option on the shares of Company A with an
exercise price of $45 in six months in return for an option premium
of $5 per share.
[0013] Here, again ignoring the effect of "time or other nominal
costs," if the value of the shares of Company A fell to $44, then
the value of the purchased put option (FIG. 9) would increase
because it would be more likely to be exercised. Moreover, if the
value of the shares continued to fall to $40, then the value of the
purchased put option would increase even more because the owner of
the purchased put option would be able to obtain shares of Company
A at a price of $40 per share and sell these same shares at $45 per
share by exercising its put option resulting in a $5 per share
profit. Accordingly, as long as the current price of the asset (the
shares of Company A) continue to decrease, the profits associated
with the return on investment for a purchaser of a put option are
limited to the exercise price (less the option premium paid) if the
asset price fell to zero. However, the seller of the put option
(See FIG. 12) realizes potential losses equal to the exercise price
(less the option premium received) if the asset price fell to
zero.
[0014] On the other hand, if the current share price increases,
then the value of the purchased put option would decrease because
it would be less likely to be exercised. However, regardless of how
much the share price increased, the maximum loss associated with
the return on investment that the purchaser of a put option would
realize is limited to the option premium. In contrast, the seller
of the put option realizes a maximum profit of the option
premium.
[0015] Based on the above examples, it should be readily apparent
that, ignoring "time," the purchaser of a call or a put option may
essentially realize an unlimited gain while limiting his or her
potential loss to the amount of the option premium. On the other
hand, the seller of a call or a put option acts as an insurer by
collecting the option premium in return for insuring that the
purchaser of the option will be able to buy or sell the underlying
asset at the exercise price. Thus, the Seller assumes all of the
risks. To reallocate the risks, the element of time is used in
option trading. The purchaser of an option is only allowed to
exercise the option over a preset increment of "time".
[0016] Referring again to FIGS. 8 and 9, even though a purchased
call option may increase in value as the current price of the asset
increases, the value of the call option whose current price has yet
to reach the exercise price must always battle "time." In other
words, the closer that the call option gets to its expiration date,
the more "time" will have a negative effect on the value of the
purchased call option because "time" will be running out for the
current price of the asset to reach the exercise price. If the
current price of the asset on the expiration date is below the
exercise price for the purchased call option the option holder will
(1) be left holding an option worth absolutely nothing and (2) be
left unprotected in its efforts to buy a particular asset at a
later "time." Thus, the purchaser assumes much more of the risk
when options are limited to set times.
[0017] Therefore, there exists a need in the art for a technique to
limit the risk that an option purchaser must assume, which at the
same time, is not unfair to the option seller. More specifically,
there exists a need in the art for an apparatus and process for
calculating an option which is not dependent on "time" and is a
fair value for the option seller. The applicant refers to such an
option as an "expirationless option."
[0018] Current techniques for calculating options are based on
finite times such as 3 months, 6 months, 9 months, and, at the
most, 3 years. In these techniques, the maximum price of an
expiring option is considered to be the underlying security price.
However, in actuality, the maximum price for any expiring option is
its expirationless counter-part which is always less than the
security price. For this reason, the probability space of expiring
options has been incorrectly determined in the current art. This
error helps explain inconsistencies in efficient markets such as
"volatility smiles," where the theoretical price for an
out-of-the-money option is higher than the actual price sellers are
willing to receive. This error in pricing is because the
probability distribution that is assumed in the current art is the
value S, rather than the smaller value for an expirationless
option. Therefore, there exists a need in the art for an apparatus
and process to calculate option prices that are not based on the
maximum price of the underlying security, but rather are based on
the price of an expirationless option that is counterpart to the
expiring option.
[0019] A margin position is a means for an investor to purchase the
right to acquire a particular asset (e.g., security) for an
indefinite (expirationless) amount of time without having to pay
the entire value of the asset at the time of purchase. An investor
purchases the right to acquire the particular asset by opening a
"long" margin position or a "short" margin position. A long margin
position (also referred to as a conditional purchase) is opened
when the investor expects the value of the asset to increase, and a
short margin position (also referred to as a conditional sale) is
opened when the investor expects the value of the asset to
decrease.
[0020] As shown in FIG. 12, a long margin position investor
realizes a Return On Investment ("ROI") equal to the current value
of an asset when the investor closes the margin position less the
value of the asset when he opened the margin positioned. Therefore,
if the value of an asset increases from $20 to $30, then the long
margin position investor realizes a $10 profit when it closes the
margin position. However, if the value of the asset decreases to
$5, then the same investor realizes a $15 loss.
[0021] On the other hand, as shown in FIG. 13, a short margin
position investor realizes a ROI equal to the value of the asset
when the investor opened the margin position less the value of the
asset when it closes the margin position. Therefore, if the value
of an asset decreases from $20 to $5, then the short margin
position investor realizes a $15 profit when it closes the margin
position. However, if the value of the asset increases to $30, then
the same investor realizes a $10 loss. These margin positions, both
long and short, may or may not have an interest cost calculated on
the value of the conditional sale or purchase.
[0022] A margin price in the securities market for an
expirationless option on a particular asset is usually much higher
than an option premium for an expiring option on the same asset.
One reason for the substantial difference between the margin
requirement and the option premium for an expiring option is that
the entity (e.g., exchange or broker) offering the margin position
essentially assumes more risk because, unlike the expiring option,
the margin position does not automatically expire after a preset
period of "time," (unless, of course, the underlying asset expires,
such as a futures or commodity contract). Additionally, while an
option purchaser has the right but not the obligation to execute
the contract, each party in a margin position is obligated to
perform.
[0023] Since any expiring asset must be a derivative of or
represent a contingent claim on a nonexpiring asset, the margin
position is assumed to be on the base of a non-expiring asset. In
the case of a futures contract on corn, though the margin position
is actually for the futures contract which will expire, this margin
requirement can be demonstrated to actually represent the margin
requirement for the corn, or base asset, as well. Using current
techniques, a change in the futures contract is accomplished by
"rolling over", or exchanging one contract for another to maintain
the maximum future date of delivery or sale. The present invention
will make this unnecessary.
[0024] Unlike an option premium, the margin requirement is
essentially refundable to the investor of a margin position. This
refund is realized in that the margin requirement is applied to the
purchase price (current value) at the time the investor of a margin
position closes the margin position. Entities responsible for
regulating margin positions (unscientifically) select a margin
requirement balancing the demand of investors, speculators and
hedgers with the protection of the respective market from default
risk. These entities typically present margin requirements either
as a fixed dollar amount (margin amount) associated with a
particular asset or a fixed percentage (margin percentage) of the
current price (value) of the particular asset.
[0025] A swap is a type of security transaction that is typically
based on large amounts of money or securities wherein the parties
to the swap exchange risks based on a notional amount. For
instance, a swap may include Party A agreeing to pay a fixed
interest rate on a certain amount of money (i.e., 100,000,000) to
Party B, in exchange for Party B agreeing to pay a floating
interest rate based on the same amount of money to Party A.
Generally, the floating interest rate is based on an index, such as
the T-bill rate, plus a fixed offset. As the underlying index
fluctuates, the amount of money exchanged between Party A and Party
B also fluctuates. However, the underlying amount of money, the
$100,000,000, does not exchange hands.
[0026] Expirationless put and call option prices, because they have
to be equal at the money, or where the current security price
equals the exercise price, are arbitrized results. This is because
the value of American options must equal the value of a replicating
portfolio to avoid arbitrage opportunities and be consistent with
economic equilibrium. Expirationless options are equivalent to a
"swap" on the upside potential on the underlying security for the
down side potential on the underlying security, or vice versa.
Expirationless options can be considered a financial swap where the
notional value is the underlying security price. Thus, there exists
a need in the art for an apparatus and a process for calculating
the price of an expirationless option that can be used as the basis
of a swap agreement.
[0027] Experts in the securities market and other markets dealing
with options have concluded for many years that any system for
transacting an option can only generate an option premium, which is
fair to both the purchaser and seller of the option, if data
representing the "time" in which the option expires is input into
the system. More specifically, all algorithms that have been
derived for generating fair option premiums include a variable for
"time". Such algorithms include the Black-Scholes and Binomial
Pricing. While some professionals in the securities markets have
discussed the pricing of expirationless options, they have ignored
the arbitrized requirements that the put and call be equal at the
money and have only focused on when and under what conditions
exercise would be optimal. They have further ignored the equality
of volatility and interest rate costs between expirationless
options and the underlying security. This is a critical omission
since, under the assumptions in the current art concerning rational
expectations and the absence of economic dominance, the interest
rate and volatility assumptions in an option position equivalent to
the underlying security demands equality of volatility and interest
rates between the expirationless option and the underlying
security.
[0028] Moreover, not only is there a need for a system capable of
transacting a fairly calculated premium for an option not dependent
on "time," but there is a further need for such a system to
automatically transact purchases and sales of expirationless
options instantaneously while handling (1) the constantly changing
current asset prices and other variables associated with the option
premium pricing and (2) the high volume (millions) of daily options
transacted in the securities market and other markets.
[0029] The above-referenced shortcomings, and other shortcoming of
the prior art systems for calculating and transacting options that
expire are effectively overcome by the present invention, as
described in further detail below.
SUMMARY OF INVENTION
[0030] The present invention includes an apparatus and a process
for calculating and transacting options. In addition, the present
apparatus and process for calculating option prices may be used in
calculating and transacting any asset which can be constructed as
an individual or series of options, regardless of their expiration
date.
[0031] The present invention may be applied for calculating
expirationless options and option prices in the securities market,
as well as a variety of other asset-based markets. It should be
understood that references to the "present invention" are
references to various embodiments of the present invention.
[0032] The present invention takes advantage of the inefficiency
associated with the unscientifically selected margin requirements.
More specifically, the present invention is able to combine the
expirationless feature of the margin position and the limited risk
of the expiring option by recognizing that, because the margin
requirement is unscientifically selected, a price (an option
premium) exists that would cause many dealing in margin positions
and expiring options to find great benefits in transacting
expiration less options.
[0033] The present invention takes advantage of the
unscientifically selected margin requirements by recognizing a
particular relationship between margin positions and options. As
shown in FIG. 14, a long margin position is equivalent to a
purchased expiring call option and a sold expiring put option when
the effect of "time" is discounted. Additionally, as shown in FIG.
15, a short margin position is equivalent to a sold expiring call
option and a purchased expiring put option. In sum, if the effect
of "time" is discounted, an entity allowing an investor to open a
margin position (e.g., a long margin position), is in the same
position that it would be if it simply allowed an investor to
purchase an expiring option (e.g., a call) and sell an expiring
option (e.g., a put).
[0034] A significant feature of the present invention is that it is
able to discount the effect of "time" to allow a margin position to
be equivalent to a purchased and sold option, as described above.
Specifically, the present invention is able to utilize anyone of
the multitude of expiring option algorithms for determining fair
expiring option premiums, as mentioned in the Background of the
Invention, to discount the effect of "time."
[0035] All expiring option premium algorithms, in addition to
including a "time" variable, include readily observable variables,
such as the current value (price) of the asset, the historic price
volatility of the asset (the standard deviation of the asset's
historic price movement) and the current risk-free interest rate
(the rate of return without default risk, such as a U.S. government
T-Bill rate). Further, all expiring option premium algorithms
include variables for the exercise price.
[0036] Accordingly, the present invention uses the expiring option
premium algorithms to discount the effect of "time" according to
the following process: (1) the exercise price is set equal to the
current price of the asset and (2) the option premium is set equal
to the margin requirement for the asset. The present invention then
uses the expiring option premium algorithm to generate the
anticipated point in "time" (implied time) in which an expiring
option would expire if the purchaser paid an option premium equal
to the unscientifically set margin requirement of the asset and if
the exercise price was equal to the current asset price (as it is
for a margin position at the moment it is opened).
[0037] The present invention utilizes the above process because the
exercise price is always equal to the current asset price at the
moment when the margin position is opened, and this is the point in
time when an investor of a margin position would gladly pay an
inflated option premium equal to the margin position requirement to
limit his risk. Accordingly, the present invention is able to
discount "time" to price a purchased and sold option such that they
are equivalent to a margin position at the point where the asset
price is assumed equal to the exercise price.
[0038] After the implied time value is generated, the present
invention sets the time value in the expiring option premium
algorithm equal to the implied time value. The present invention
then generates an expirationless option premium based on the
particular exercise price selected by the investor.
[0039] The present invention may be implemented on a vast variety
of computer systems. More particularly, the present invention
employs a computer system to receive and store data representative
of the particular asset, a type of option (call or put), a
requested exercise price and the multitude of other variables
related to transacting an expirationless option on the asset. Then,
responsive to the data received, the present invention uses the
computer system to generate data representative of an
expirationless option premium, and to transact the expirationless
option using the expirationless option premium.
[0040] In use, when a user wishes to purchase or sell an
expirationless option, the user is prompted to input data
representative of the asset, the type of option and the requested
exercise price for the asset, into a keyboard or other means of the
computer system. The apparatus and process of the present invention
then prompt the user to enter certain other data related to
transacting an expirationless option on the asset. The certain
other data includes the current price for the asset on the open
market, the historic price volatility of the asset, the current
risk-free interest rate and the margin requirement associated with
the asset. Because this data typically changes frequently, the
present invention may alternatively receive this data from one or
more data source (e.g., a database or real-time quote service such
as S&P CornStock), connected to the computer system of the
present invention. After all of the data is received, it is stored
on a storage medium of the computer system.
[0041] The present invention then uses one of the expiring option
premium algorithms to generate the data representative of the
expirationless option premium. More specifically, the present
invention temporarily sets the option premium variable of these
algorithms to the margin requirement data, temporarily sets the
exercise price variable of these algorithms to the current asset
price data and generates data for the implied time of these
algorithms. The present invention then uses the implied time data
and the exercise price data input by the user to generate the data
for the option premium variable of these algorithms.
[0042] The option premium data generated is the expirationless
option premium used to transact the expirationless option for the
particular asset. Accordingly, the option premium data is output
for use in completing the expirationless option transaction.
[0043] The present invention is particularly important to those who
wish to protect themselves against price swings for indefinite
periods of "time." In other words, individuals and entities may now
concern themselves solely with the future price of an asset, and
cease concerning themselves with the seemingly impossible task of
predicting the "time" in which the asset may hit that price.
[0044] For example, a cereal manufacturer whose cereal prices to
its customers depend significantly on the price in which they are
able to purchase wheat, can now better assure their customers of
steady cereal prices by purchasing an expirationless call option
using the present invention. More specifically, the cereal
manufacturer can now ensure itself that it may continue to purchase
wheat at or below a certain price (the exercise price), regardless
of the "time" in the future when the price of wheat rises above the
exercise price. Referring to FIG. 16, by utilizing the present
invention, in return for the option premium, the cereal
manufacturer is able to purchase an expirationless call option
which has unlimited upside potential, limited downside potential
(the option premium) and never becomes worthless.
[0045] On the other hand, a farmer whose family depends on being
able to sell his entire crop of wheat for a set minimum price would
benefit significantly. Specifically, the farmer who was unable to
predict whether wheat prices might drop next year or in five years
may purchase an expirationless put option using the present
invention to ensure that his wheat will be purchased at a certain
price (the exercise price) regardless of the "time" in the future
when the price of wheat drops below the exercise price. Referring
to FIG. 17, by utilizing the present invention, in return for an
option premium, the farmer is able to purchase an expirationless
put option which has unlimited upside potential, limited downside
potential (the option premium) and never becomes worthless.
[0046] Another aspect of the present invention is that it is
capable of handling constantly changing current asset prices and
other variables associated with generating the option premium price
and transacting the expirationless option. As described above, by
using one or more data source, data from a variety of places,
regardless of location, may be constantly updated and stored for
use in generating the option premium price at any given moment in
time.
[0047] A further aspect of the present invention is that it is
capable of automatically and essentially instantaneously
transacting an expirationless option in the securities market and
other markets throughout the world. This is especially important in
the securities market because millions of option contracts are
typically transacted daily. This feature is also important because
of the volatility of the variables used to generate the option
premium price. This makes the essentially instantaneous transaction
capability imperative, especially in the securities market.
[0048] A yet further aspect of the present invention is that it is
capable of handling extinction bands. An extinction band is a price
higher than the exercise price for a put option and lower than the
exercise price for a call option. The extinction band price is
selected because a particular entity responsible for exchange
management may wish to implement expirationless options without
significantly increasing record-keeping requirements for the
respective exchange. By introducing extinction bands, or forced
closure of an expirationless option based not on time, but on the
distance of the exercise price from the current asset price, an
exchange may retain the aforementioned benefits of expirationless
options for their members without significantly increasing record
keeping requirements. The pricing algorithm for this variant of the
expirationless option assumes that both the band, the maximum
distance of the exercise price from the asset price and the
extinction date (or the effective date of measurement of the
exercise price from the current asset price) for these options is
known. If these variables are not known, then the expirationless
option with extinction bands is priced exactly as the
expirationless option without extinction bands.
[0049] A yet further aspect of the present invention is that it is
capable of facilitating the determination of conventional expiring
option premiums utilizing the expirationless option price as the
maximum price for the expiring option. This allows for more
accurate determination of the option price than is possible using
the underlying security price as the maximum price of an expiring
option.
[0050] Yet another aspect of the present invention is that it is
capable of facilitating the accurate determination of premiums for
any financial instrument which can be expressed in terms of an
option or combination of options. In order to determine a premium
for a financial instrument, the premiums for corresponding option
or options are first determined utilizing the corresponding
expirationless option price. The expiring option premiums are then
relatable to the premiums of the related financial instrument as
appropriate for the instrument type.
[0051] Examples of financial instruments which may be determined
utilizing the present invention include, but are not limited to
equity, bonds, futures, forwards and swaps.
[0052] The aforementioned and other aspects of the present
invention are described in the detailed description and attached
illustrations which follow.
BRIEF DESCRIPTION OF THE DRAWINGS
[0053] For a fuller understanding of the invention, reference
should be made to the following detailed description, taken in
connection with the accompanying drawings, in which:
[0054] FIG. 1 depicts a diagram of an exemplary computer system for
implementing the present invention.
[0055] FIG. 2 depicts components of an end user workstation for the
computer system of FIG. 1 for implementing the present
invention.
[0056] FIG. 3 depicts components of a server for the computer
system of FIG. 1 for implementing the present invention.
[0057] FIG. 4 depicts a flow diagram of an exemplary embodiment for
the Main Module of the present invention.
[0058] FIG. 5 depicts a flow diagram of an exemplary embodiment for
the CALC module of the present invention, which calculates the
expirationless option premium ignoring extinction bands.
[0059] FIG. 6 depicts a flow diagram of an exemplary embodiment for
the DATA_ENTRY module of the present invention, which prompts the
user to enter certain data for transacting the expirationless
option.
[0060] FIG. 7 depicts a flow diagram of an exemplary embodiment for
the CALC_E module of the present invention, which calculates the
expirationless option premium with extinction bands.
[0061] FIG. 8 depicts a graph which illustrates the potential
Return on Investment (ROI) versus the Value of an Asset (Asset
Value) for a purchased expiring option transacted on a prior art
system.
[0062] FIG. 9 depicts a graph which illustrates the potential ROI
versus the Asset Value for a purchased expiring put option
transacted on a prior art system.
[0063] FIG. 10 depicts a graph which illustrates the potential ROI
versus the Asset Value for a sold expiring option transacted on a
prior art system.
[0064] FIG. 11 depicts a graph which illustrates the potential ROI
versus the Asset Value for a sold expiring put option transacted on
a prior art system.
[0065] FIG. 12 depicts a graph which illustrates the potential ROI
versus the Asset Value of a long margin position.
[0066] FIG. 13 depicts a graph which illustrates the potential ROI
versus the Asset Value of a short margin position.
[0067] FIG. 14 illustrates the equivalent relationship between a
long margin is position and a purchased call expirationless option
(expiring option with time discounted) plus a sold put
expirationless option (expiring option with time discounted).
[0068] FIG. 15 illustrates the equivalent relationship between a
short margin position and a sold call expirationless option
(expiring option with time discounted) plus a purchased put
expirationless option (expiring option with time discounted).
[0069] FIG. 16 depicts a graph which illustrates the potential ROI
versus the Asset Value of a purchased call expirationless option
transacted using the apparatus and process of the present
invention.
[0070] FIG. 17 depicts a graph which illustrates the potential ROI
versus the Asset Value of a purchased put expirationless option
transacted using the apparatus and process of the present
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0071] The various aspects of the present invention may be
implemented on numerous types of computer systems, but is
preferably implemented on a client/server network 100 as shown in
FIG. 1. The client/server network 100 includes a server 110
connected to a plurality of clients 120, also known as end-user
workstations, and a data source 130 running on a token ring
environment.
[0072] As shown in FIG. 2, each end user workstation 120 may
include a microprocessor 210, a display 220, a keyboard 230, a
mouse 240, a printer 260, and a storage medium 250 (e.g., a disk
array, tape, optical drive, tape drive or floppy drive).
[0073] As shown in FIG. 3, each server 110 may include a
microprocessor 310 and a storage medium 350. The server may use
Microsoft NT or peer-to-peer with one peer dedicated as a server or
their equivalent.
[0074] Data sources 130 may be a Quotron system or its equivalent,
which may regularly receive data via satellite communications 135,
land line connections (e.g., a modem) 137 or the like. However, any
other source capable of receiving and providing data relevant to
transacting the expirationless option may be used in the present
invention.
[0075] An exemplary client/server network suitable for implementing
aspects of the present invention is a Windows NT PC LAN. These
clients, servers, and client/server networks are mentioned for
illustrative purposes only and, as may be appreciated by one of
ordinary skill in the art, suitable equivalents may be
substituted.
[0076] In an exemplary embodiment, when a user wishes to purchase
or sell an expirationless option related to a particular asset, the
user may view the display 220 of the end user workstation 120 to
obtain instructions on how to transact the expiration less option
contract.
[0077] Referring to FIG. 4, at step 410 of the Main Module, the
display 220 displays a prompt requesting the user to indicate when
the user is ready to transact the expirationless option. By
pressing the ENTER key on the keyboard 230 or clicking on a START
box on the display 220 with the mouse 240, the present invention
starts its operation of transacting the expirationless option by
proceeding to step 420. For simplicity purposes, it may be assumed
that the microprocessor 210 of the end-user workstation 120 and the
microprocessor 310 of the server 110 coordinate all tasks of the
end-user workstation 120 and server 110 of the computer system,
respectively, and all tasks between the two.
[0078] At step 415, the user is prompted to input data
representative of a particular asset. Upon receiving the data
representative of a particular asset, the present invention
proceeds to step 420.
[0079] At step 420, the user is prompted to select which option
pricing algorithm he or she wishes to use to transact the
expirationless option. Such algorithms include, but are not limited
to, the Black-Scholes, the Binomial Pricing, the Finite Difference
and the Analytic Approximation algorithms. These algorithms are
widely used in connection with determining expiring option premiums
and are available in both proprietary and shareware software from
Montgomery Investment Technology. The option prices provided in
this detailed description were determined using this free Internet
service, and demonstrate that any option pricing algorithm may be
used to determine expirationless option prices.
[0080] For example, the Black-Scholes algorithm is:
c = [ j = 0 n ( n ! j ! ( n - j ) ! ) p j ( 1 - p ) n - j max [ 0 ,
u j d n - j S - K ] ] r n ##EQU00001##
[0081] Where: [0082] c=OPT_PREM=the option premium [0083]
S=ASSET_PRICE=the current price for a particular asset [0084]
X=X_PRICE=the exercise price [0085] r=T_BILL=the current risk-free
interest rate [0086] s=VOLATLTY=the standard deviation of the
historic asset price [0087] movement commonly referred to as the
asset's volatility.
[0088] In another example, the Binomial Pricing algorithm is:
c = S .intg. - .infin. ln ( S X ) + [ r + ( .sigma. 2 2 ) ] T
.sigma. T 1 2 .pi. - z 2 2 z - - rT X .intg. - .infin. ln ( S X ) +
[ r - ( .sigma. 2 2 ) ] T .sigma. T 1 2 .pi. - y 2 2 y
##EQU00002##
[0089] Where: [0090] c=OPT_PREM=the option premium [0091]
S=ASSET_PRICE=the current price for a particular asset [0092]
K=X_PRICE=the exercise price [0093] r=T_BILL=the current risk-free
rate [0094] n=the number of periods (the time) until expiration
(for an expiring option)
[0094] p=(r-d)/(u-d) [0095] u=minimum value of an upward movement
in the price of the underlying asset (e.g., $1/8.sup.th in most
stocks), and [0096] d=minimum value of a downward movement in the
price of the underlying asset ($0.0001 in most futures or
commodities) [0097] Note: u and d are generally established by the
exchange and may be [0098] stored in a storage medium for access or
simply input into the system on an as needed basis.
[0099] Further, as one of ordinary skill in the art would readily
appreciate, other related expiring options algorithms may be used
to transact an expirationless option. Upon receiving a number
related to the user's selected algorithm processing continues at
step 430. In an alternative embodiment step 420 may be removed
entirely by only using a single option algorithm.
[0100] At step 430, the user is prompted to input whether or not it
wishes to include extinction bands in the expirationless option
transaction. If the user selects no, then processing continues at
step 500, otherwise processing continues at step 700.
[0101] Referring to FIG. 5, at step 500 the CALC Module is
executed. The CALC Module is used to calculate the expirationless
option premium ignoring extinction bands. Of course, if used
exclusively in markets or on exchanges without extinction bands,
step 430 may be removed entirely.
[0102] Processing then continues at step 600 where the DATA_ENTRY
Module is executed. The DATA_ENTRY Module, as shown in FIG. 6, is
used to prompt the user to input data and to accept the data input
by the user.
[0103] At step 601, the user is prompted to input the current price
for the particular asset. The user may obtain the current price for
the particular asset from a variety of sources, such as the data
source 130. At step 602, it is determined whether the current price
of the asset has been received. If not, then processing returns to
step 601, otherwise the current price of the asset received is
stored in the ASSET_PRICE variable in the storage medium 250 and
processing continues at step 603.
[0104] In another embodiment, steps 601 and 602 may be replaced by
a step which automatically accesses the current price for the
particular asset from the data source 130. In yet another
embodiment, steps 601 and 602 may be replaced by a step which
automatically accesses the current price for the particular asset
from the storage medium 350 of the server 110 which may be updated
automatically by the data source 130 or manually by an
administrator of the network.
[0105] At step 603, the user is prompted to input the current
risk-free interest rate. The user may obtain the current risk-free
interest rate from a variety of sources, such as the data source
130. At step 604, a determination is made as to whether the current
risk-free interest rate has been received. If not, then the
processing continues at step 603, otherwise the current risk-free
interest rate received is stored in the T BILL variable in the
storage medium 250 and processing continues at step 605.
[0106] In another embodiment, steps 603 and 604 may be replaced by
a step which automatically accesses the current risk-free interest
rate from the data source 130. In yet another embodiment, steps 603
and 604 may be replaced by a step which automatically accesses the
current risk-free interest rate from the storage medium 350 of the
server 110 which may be updated automatically by the data source
130 or manually by an administrator of the network.
[0107] At step 605, the user is prompted to input the standard
deviation of the price movement related to the asset known as the
"historic price volatility of the asset." The user may obtain the
historic price volatility of the asset from a variety of sources,
such as the data source 130. At step 606, a determination is made
as to whether the historic price volatility of the asset has been
received. If not, then the processing continues at step 605,
otherwise the historic price volatility of the asset received is
stored in the VOLATLTY variable in the storage medium 250 and
processing continues at step 607.
[0108] In another embodiment, steps 605 and 606 may be replaced by
a step which automatically accesses the historic price volatility
of the asset from the data source] 30. In yet another embodiment,
steps 605 and 606 may be replaced by a step which automatically
accesses the historic price volatility of the asset from the
storage medium 350 of the server 110 which may be updated
automatically by the data source 130 or manually by an
administrator of the network.
[0109] At step 607, the user is prompted to input the exercise
price for the particular asset. At step 608, a determination is
made as to whether the exercise price of the asset has been
received. If not, then processing continues at step 607, otherwise
the exercise price of the asset received is stored in the X_PRICE
variable in the storage medium 250 and processing continues at step
609.
[0110] At step 609, the user is prompted to input the option type
(either a call option or a put option). At step 610, the present
invention then verifies whether the option type has been received.
If not, then the processing returns to step 609, otherwise the
processing stores the option type under the OPT_TYPE variable in
the storage medium 250 and proceeds to step 611.
[0111] At step 611, the user is prompted to input the margin
requirement (margin amount or margin percentage) related to the
particular asset. The user may obtain the margin requirement from a
variety of sources, such as the data source 130. At step 612, a
determination is made as to whether the margin requirement for the
asset has been received. If not, then processing returns to step
611, otherwise the margin requirement for the asset received is
stored in the MARGIN variable in the storage medium 250 and
processing continues at step 699, and then to step 510 of the CALC
Module at FIG. 5.
[0112] In another embodiment, steps 611 and 612 may be replaced by
a step which automatically accesses the margin requirement from the
data source 130. In yet another embodiment, steps 611 and 612 may
be replaced by a step which automatically accesses the margin
requirement from the storage medium 350 of the server 110 which may
be updated automatically by the data source 130 or manually by an
administrator of the network.
[0113] At step 510, the temporary option premium is equated to the
value of the margin requirement (MARGIN) and stored in the
TEMP_OPT_PREM variable in the storage medium 250. Processing then
continues at step 520, where a temporary exercise price is set
equal to the current price of the asset (ASSET_PRICE) and the
temporary exercise price is stored under the TX_PRICE variable in
the storage medium 250. Processing then continues at step 530.
[0114] At step 530, the implied time for the expirationless option
is determined using the option pricing algorithm selected at step
420. The implied time is then stored in the IMPLD_T variable in the
storage medium 250. Processing then continues at step 540.
[0115] At step 540, the actual option premium for the
expirationless option is determined by again using the option
pricing algorithm selected at step 420, the X_PRICE selected at
step 607, and the implied time value (IMPLD_T). Processing then
continues at step 440 of the Main Module at FIG. 4.
[0116] Referring back to step 430, if the user selects to include
extinction bands in the expirationless option transaction,
processing continues at step 700 of the CALC_E module. Referring to
FIG. 7 at step 700 the CALC_E module calculates the expirationless
option premium taking into account extinction bands.
[0117] Processing then continues at step 600 at the DATA_ENTRY
Module. Again, the DATA_ENTRY Module, as shown in FIG. 6, is used
to prompt the user to input data and to accept the data input by
the user.
[0118] At step 601, the user is prompted to input the current price
for the particular asset. The user may obtain the current price for
the particular asset from a variety of sources, such as the data
source 130. At step 602, a determination is made as to whether the
current price of the asset as been received. If not, then
processing returns to step 601, otherwise the current price of the
asset received is stored in the ASSET_PRICE variable in the storage
medium 250 and processing continues at step 603.
[0119] In another embodiment, steps 601 and 602 may be replaced by
a step which automatically accesses the current price from the data
source 130. In yet another embodiment, steps 601 and 602 may be
replaced by a step which automatically accesses the current price
from the storage medium 350 of the server 110 which may be updated
automatically by the data source 130 or manually by an
administrator of the network.
[0120] At step 603, the user is prompted to input the current
risk-free interest rate. The user may obtain the current risk-free
interest rate from a variety of sources, such as the data source
130. At step 604, a determination is made as to whether the current
risk-free interest rate has been received. If not, then processing
returns to step 603, otherwise the current risk-free interest rate
received is stored in the T_BILL variable in the storage medium 250
and processing continues at step 605.
[0121] In another embodiment, steps 603 and 604 may be replaced by
a step which automatically accesses the current risk-free interest
rate from the data source 130. In yet another embodiment, steps 603
and 604 may be replaced by a step which automatically accesses the
current risk-free interest rate from the storage medium 350 of the
server 110 which may be updated automatically by the data source
130 or manually by an administrator of the network.
[0122] At step 605, the user is prompted to input the standard
deviation of the price movement related to the asset known as the
"historic price volatility of the asset." The user may obtain the
historic price volatility of the asset from a variety of sources,
such as the data source 130. At step 606, a determination is made
as to whether the historic price volatility of the asset has been
received. If not, processing returns to step 605, otherwise the
historic price volatility of the asset received is stored in the
VOLATLTY variable in the storage medium 250 and processing
continues at step 607.
[0123] In another embodiment, steps 605 and 606 may be replaced by
a step which automatically accesses the historic price volatility
of the asset from the data source 130. In yet another embodiment,
steps 605 and 606 may be replaced by a step which automatically
accesses the historic price volatility of the asset from the
storage medium 350 of the server 110 which may be updated
automatically by the data source 130 or manually by an
administrator of the network.
[0124] At step 607, the user is prompted to input the exercise
price for the particular asset. At step 608, the processing then
verifies whether the exercise price of the asset has been received.
If not, then the processing returns to step 607, otherwise the
processing stores the exercise price of the asset received under
the X_PRICE variable in the storage medium 250 and proceeds to step
609.
[0125] At step 609, the user is prompted to input the option type
(either a call option or a put option). At step 610, a
determination is made as to whether the option type has been
received. If not, then processing returns to step 609, otherwise
the option type is stored in the OPT_TYPE variable in the storage
medium 250 and processing continues at step 611.
[0126] At step 611, the user is prompted to input the margin
requirement (margin amount or margin percentage) related to the
particular asset. The user may obtain the margin requirement from a
variety of sources, such as the data source 130. At step 612, a
determination is made as to whether the margin requirement for the
asset has been received. If not, then processing returns to step
611, otherwise the margin requirement for the asset received is
stored in the MARGIN variable in the storage medium 250 and
processing continues at step 699, and then to step 510 of the
CALC_E Module at FIG. 7.
[0127] In another embodiment, steps 611 and 612 may be replaced by
a step which automatically accesses the margin requirement from the
data source 130. In yet another embodiment, steps 611 and 612 may
be replaced by a step which automatically accesses the margin
requirement from the storage medium 350 of the server 110 which may
be updated automatically by the data source 130 or manually by an
administrator of the network.
[0128] At step 710, the user is prompted to input whether or not it
wishes to determine the extinction band in percentages or in
dollars. If the user selects percentages, then processing continues
at step 720, otherwise processing continues at step 750.
[0129] At step 720, the user is prompted to input the percentage
price movement to be used to determine the extinction band and the
percentage is stored in the PERCENT variable in the storage medium
250. Processing then continues at step 725, where it determines
whether the expirationless option type (OPTION_TYPE) is a "call" or
a "put". If the expirationless option is a "call," then processing
continues at step 730, otherwise processing continues at step
735.
[0130] At step 730, the current asset price (ASSET_PRICE) for the
"call" option is set to the current asset price (ASSET_PRICE)
multiplied by the value composed of the percentage price movement
(PERCENT) plus one. On the other hand, at step 735, the current
asset price (ASSET_PRICE) for the "put" option is set to the
current asset price (ASSET_PRICE) multiplied by the value composed
of the percentage price movement (PERCENT) minus one.
[0131] Processing then proceeds from step 730 or step 735 to step
775. Processing, at step 775, accesses and receives the extinction
date for the particular asset (EXT_DATE) which has been set by the
exchange and stored by the system administrator from the storage
medium 250 or 350. Of course, the extinction date could also be
manually input by the user of the present invention, who could
manually input the extinction date set by the exchange each time
the system is used. Processing then continues step 780.
[0132] At step 780, processing then determines the option premium
for the expirationless option taking into account the extinction
band by again using the option pricing algorithm selected at step
420 and setting the value of time until expiration in the algorithm
to EXT DATE. Processing then continues at step 799.
[0133] Referring back to step 710, if the user selects to use
dollars to determine the extinction band, then the invention
proceeds to step 750. At step 750, the user is prompted to input
the minimum dollar amount price movement to be used to determine
the extinction band, and the dollar amount price movement is stored
in the TICK variable in the storage medium 250. At step 755,
processing then sets the BAND variable to dollars.
[0134] Processing then continues at step 760, where a determination
is made as to whether the expirationless option type (OPTION_TYPE)
is a "call" or a "put" option. If the expirationless option is a
"call," then processing continues at step 765, otherwise processing
continues at step 770.
[0135] At step 765, the current asset price (ASSET_PRICE) for the
"call" option is set to the current asset price (ASSET_PRICE) plus
the BAND divided by the dollar amount price movement (TICK). On the
other hand, at step 770, the current asset price (ASSET_PRICE) for
the "put" option is set to the current price (ASSET_PRICE) minus
the BAND divided by the dollar amount price movement (TICK).
[0136] Processing then continues at step 765 or step 770 to step
775. Processing continues at step 775, accesses and receives the
extinction date for the particular asset (EXT_DATE) which has been
set by the exchange and stored by the system administrator from the
storage medium 250 or 350. Of course, the extinction date could
also be manually input by the user, who could manually input the
extinction date set by the exchange each time the system is used.
Processing then continues at step 780.
[0137] At step 780, processing then determines the option premium
for the expirationless option taking into account the extinction
band by again using the option pricing algorithm selected at step
420 and setting the value of time until expiration in the algorithm
to EXT_DATE. The present invention then processing continues at
step 799.
[0138] At step 799, the present invention proceeds to step 440 of
the Main Module at FIG. 4, where it stores the expirationless
option premium under the variable OPT_PREM at the storage medium
250. At step 450, the processing may optionally complete the
current financial transaction by issuing a buy or sell hard copy
(ticket) to the user which includes the asset premium and other
pertinent information related to the transaction.
[0139] In another embodiment, rather than issuing a buy or sell
hard copy to the user, the hard copy may be issued by printing a
hard copy to a buyer/seller located in the "trading pit" at the
Chicago Exchange, the "desk" at the New York Exchange, or at any
other similar destination of other exchanges throughout the world.
Once received by a buyer/seller at an exchange, the buyer/seller
may then enter the confirmation order and other information to
effect the transfer of any necessary funds upon the closing of the
market, as is customary. In yet another embodiment, rather than
issuing a buy or sell hard copy to the user, executing the
transaction may include electronically placing or transferring the
transaction information into a queue of a transaction server along
with other transactions. When the queued transaction is removed
from the queue (i.e., by an operator or by a software program), a
search for a matching order is performed (e.g., if the executed
transaction is a buy, the operator or software program searches for
a matching sell transaction). Thus, executing an expirationless
option transaction includes, but is not limited to, issuing a hard
copy to the user, issuing a hard copy to a buyer/seller at the
exchange, or initiating an automatic electronic transaction. The
present invention anticipates the use of these and other similar
methods for executing the transaction and should not be limited to
any particular method.
[0140] The processing then proceeds to step 470, where the user is
prompted to determine whether it wishes to transact another
expirationless option. If yes, then the present invention proceeds
to step 420, where the user is again prompted by the video display
220 to select an option pricing algorithm. If no, then the present
invention proceeds to step 499, where it ends the expiration less
option transactions for the current user.
[0141] Of note, the exemplary embodiment of the present invention
assumes that, even though they may not be in actuality, the
interest rates and dividend yield associated with each particular
asset (e.g., a stock, bond, etc.) are zero. The reason for the
assumption is that algorithms used in connection with pricing the
underlying asset already factor the interest rate and dividend
yield into the asset price. These algorithms may be either
mathematical, inductive or both.
[0142] Accordingly, the present invention for transacting an
expirationless options using the same algorithms used for expiring
options factors the interest rate and dividend yield into the
option premium, but at a value of zero to ensure both the call and
the put option at S=X have a price equal to the margin
requirement.
[0143] The following examples illustrate the time/cost relationship
between expiring options, premiums, expirationless options and
margin requirements.
[0144] Both examples assume a margin requirement of 25%, a current
asset price of $150, a historic price volatility of 35%, and a
current risk-free interest rate of 6%. Thus, using Black-Scholes
algorithm, an implied time of 1210.09 days is derived. The first
example assumes a call option with an exercise price of $60 is
requested by the investor.
TABLE-US-00001 TABLE 1 Time to Expiring Option Expirationless
Margin Expiration Premium Option Premium Requirement Six Months
$2.15 $9.29 $12.5 One Year 4.59 9.29 12.5 Eighteen Months 6.65 9.29
12.5 Two Years 8.56 9.29 12.5 Three Years 11.87 9.29 12.5 Five
Years 16.63 9.29 12.5 Ten Years $27.04 $9.29 $12.5
[0145] The second example assumes a put option with an exercise
price Of $40 is requested by the investor.
TABLE-US-00002 TABLE 2 Time to Expiring Option Expirationless
Margin Expiration Premium Option Premium Requirement Six Months
0.85 6.91 12.5 One Year 1.78 6.91 12.5 Eighteen Months 2.45 6.91
12.5 Two Years 2.96 6.91 12.5 Three Years 3.66 6.91 12.5 Five Years
4.29 6.91 12.5 Ten Years 4.45 6.91 12.5
[0146] In yet another embodiment, the method of the current
invention may be utilized to calculate an expirationless option
premium using a simplified form of an expiring option algorithm.
Typical option pricing calculations require not just a life
expectancy of an expirationless option, but a volatility assumption
over the life of the option as well. This would seem to be
impossible over the undetermined time frame of the expirationless
option. However, if the security price already contains an interest
rate assumption, we can express the volatility portion of the
Black-Scholes algorithm in terms of the current price. If we know
the expirationless put and call must be equal in price, then we can
solve for an implied time to expiration at S=X; and use this
implied time to solve for option prices at exercise prices other
than the current security price.
[0147] For an expirationless option, the Black-Scholes formula
takes the form:
C=e.sup.-dtS N(dl)-E e.sup.-rtN(d2c)
[0148] Where: [0149] C=Option Premium [0150] S=Current stock price
[0151] E=Option exercise price [0152] T=Time to expiration [0153]
d=Dividend yield [0154] r=Risk-free interest rate [0155] v=Stock
volatility
[0155] dl=[ln(S/E)+(r-d+0.5v2)T]/vSQRT(T)
d2=dl-vSQRT(T)
[0156] The expirationless call option price can be calculated by
setting dividends and the risk-free rate to zero, and setting the
exercise price equal to the stock price. An expirationless option
can be calculated under any set of assumptions concerning the
distribution of prices of the underlying security. This method
assumes a log normal price distribution. It is then possible to
calculate the time for which the call price=the put price=0.5 S. It
should be clear that S is the lowest price to buy the security in
the open market. In effect this will be the lower of the actual
price or the margin requirement.
[0157] The Black-Scholes formula reduces to the following. Note
that N is the cumulative normal distribution while NINV is the
inverse cumulative normal distribution. Also, the call price=the
put price=0.5 S, and is referred to as the variable Margin.
C = 0.5 S = SN ( d l ) - SN ( d 2 ) ##EQU00003## 5.0 = N ( d l ) -
N ( d 2 ) ##EQU00003.2## dl = ln ( S / S ) + ( 0 - 0 + 0.5 v 2 ) T
/ vSQRT ( T ) - 0.5 v 2 T / v SQRT ( T ) * SQRT ( T ) = ( 0.5 v 2
TSQRT ( T ) ) / vT = 0.5 vSQRT ( T ) ##EQU00003.3## d 2 = dl -
vSQRT ( T ) = 0.5 vSQRT ( T ) - vSQRT ( T ) = - 0.5 vSQRT ( T )
##EQU00003.4##
[0158] Since:
Margin=N(0.5V SQRT(T))-N(-0.05VSQRT(T))
[0159] And N(0.5v SQRT(T)) and N(-0.5v SQRT(T)) are opposing
numbers around zero, then
Margin/2=N(0.5v SQRT(T))
NINV(Margin/2)=0.5VSQRT(T)
NINV(Margin/2)/0.5V=SQRT(T)
(NINV(Margin/2)/0.5V).sup.2=T
[0160] Now that time is purely a function of volatility it can be
applied back to the Black-Scholes formula as follows:
Allowing x = 2 NINV ( Margin / 2 ) ##EQU00004## and ##EQU00004.2##
T = ( x / v ) 2 = x 2 / v 2 ##EQU00004.3## D 1 = [ ln ( S / E ) + 5
v 2 T ] / vSQRT ( T ) = ln ( S / E ) + 0.5 v 2 ( x 2 / v 2 ) /
vSQRT ( ( x / v ) 2 ) = ( ln ( S / E ) + 0.5 x 2 ) / x = ln ( S / E
) / x + 0.5 x ##EQU00004.4## D 2 = Dl - v ( SQRT ( T ) ) = dl -
vSQRT ( ( xlvl ) = dl - x = ln ( S / E ) / x - 0.5 x
##EQU00004.5##
[0161] From the equation above for the expirationless option we
apply d1 and d2.
EPO=C=SN(ln(S/E)/x+0.5x)-EN(lN(S/E)/x-0.5.times.)
[0162] Therefore, the expirationless option premium can be
calculated purely as a function of the stock price and the exercise
price and x, where x=2 NTNV (Margin/2).
[0163] In yet another embodiment, the method of the present
invention may be utilized to calculate an expirationless option
premium which may then, in turn, be utilized as a basis to
determine a premium for a conventional expiring option. Previous
methods for pricing expiring options have considered the maximum
price of an expiring option to be the price of the underlying
security. However, the maximum price of an expiring option is
actually not the price of the underlying security, but is instead
the price of an otherwise identical expirationless option.
[0164] Accordingly, by utilizing the value for an expirationless
option as determined under the present invention, the price of a
traditional expiring option can be more accurately calculated. The
method for determining an expiring option price utilizing an
expirationless option premium determined according to the method of
the present invention proceeds generally as follows.
[0165] First, data representative of the particular asset
underlying the expiring option, the option type (call or put), an
exercise price for the option, the current price of the particular
asset underlying the option, the historic price volatility of the
particular asset and the margin requirement for the particular
asset are input at step. Then, the current price of the underlying
security is used as the expiration price to solve an expiring
option equation (such as the Black-Scholes, the Binomial Pricing,
the Finite Difference and the Analytic Approximation algorithms)
for an implied time to expiration. Next, the implied time to
expiration is used as the basis for calculating the price for the
corresponding expirationless option. The expirationless option
price is then used as the maximum price of the corresponding
expiring option in determining the premium for the expiring
option.
[0166] In regards to an expiration less option, the present
invention includes any contingent claim upon the assets, promise of
payment, equity, production units or currency of any group,
organization, body, institution or collective over any measure of
time and any measure of value, regardless of whether the claim has
an artificial minimum (floor) or maximum (cap), regardless of
whether the claim is contingent upon unforeseeable or controllable
action, regardless of whether the claim is called by another name,
or is characterized as any product, issue or promise which can be
demonstrated to be an individual or series of options, regardless
of their life span.
[0167] The art has and continues to maintain that the maximum value
of any expiring option is the underlying product, and that such
maximum value is a determinant in pricing said option, when such
statements are clearly false given that expirationless options
exist, since the maximum value of any expiring option is an
otherwise identical non-expiring option. Given that we have a
priority claim on non-expiring options, whose value or price is an
integral component of correctly pricing expiring options, our claim
is expanded to cover not only expiring options, but any financial
product which can be demonstrated to be an individual or series of
options. Expirationless options calculated according to the method
of the present invention may also be used in constructing any
combination or permutation of expiring options currently used. For
example, these options may include but are not limited to:
[0168] Asian options: average price/rate and strike options.
[0169] Barrier options: including knock-out or knock-in, with and
without rebate.
[0170] Binary options: including binary barrier, all-or-none and
gap.
[0171] Chooser options: which are options to choose a put or call
in the future.
[0172] Compound options: which are options where the underlying
security is an option.
[0173] Crack/Spread options: which are options on the distance
between prices of two assets.
[0174] Currency translated options: which are foreign exchange
options translated into another currency.
[0175] Jump options: which are options priced using a jump
diffusion process.
[0176] Lookback options: which are options based on minimum or
maximum price within a certain period.
[0177] Rainbow options: which are options on the minimum or maximum
of two assets.
[0178] Other miscellaneous options: such as options on U.S. or
foreign "stripped" government securities divided into two or more
instruments of principal and interest or price and dividend,
likewise options on stripped corporate, agency, and municipal
securities, notes, bills and Certificates of Deposit; options on
Callables, which are securities callable at premium or discount;
options on Odd-First, -Last, -Middle, or securities with varying
coupon/dividend periods; and Options on Futures, Forwards,
Currencies, Commodities, Swaps, Debt, Metals, Indices or any other
financial instrument not detailed here.
[0179] Even though the present invention has been described
substantially in terms of utilizing the margin requirement of a
margin position in the securities market, equivalents to the margin
requirement in other markets (e.g., earnest money in the real
estate market) may be utilized. Further, even though an exemplary
embodiment of the present invention is described assuming that the
margin requirement on the underlying security is equal for both the
long and short positions, this need not be the case. Specifically,
even in cases where the margin position requirements are different,
it should be obvious to one of the ordinary skill in the art that
the present invention can be used to determine the expirationless
option premiums comprising each respective position by using the
long position margin requirement for purchasing expirationless call
options and selling expirationless put options, while using the
short position margin requirement for purchasing expirationless put
options and selling expirationless call options.
[0180] Furthermore, a variety of other financial instruments have
been shown to be equivalent or relatable to options. Therefore, the
premiums of each of these financial instruments may be determined
utilizing an expiring or expirationless option premium determined
according to the method of the present invention. Examples of these
option relatable financial instruments, provided for example and
not limitation, include:
[0181] Equity: Ownership of a corporation is actually a contingent
claim on the assets of the corporation that does not expire and
only occurs at a zero strike price. Thus, equity can be considered
to be an option.
[0182] Bonds, Loans, Private Placements: These fixed-income
instruments are identical to an individual or series of
cash-settled, "capped" call options--a call option with a maximum
benefit. These options are purchased with the expectation that the
issuer will remain a viable, profitable entity. However, the
maximum return on the call is "capped" at some amount (the coupon
payment and principal payment at the end of the period). One capped
option represents each coupon payment as well as the principal or
notional value repaid. Fixed income instruments may take one of the
following forms:
[0183] Zero Coupon One payment of principal at end of term.
[0184] Floating Rate Coupon: One principal payment at end of term
and coupon payments calculated based on an interest rate calculated
from some external benchmark (90-day Treasury, 90-day LIBOR,
etc.)
[0185] Level Coupon One principal payment at end of term and coupon
payments based on an interest rate agreed at the start of the
term.
[0186] Amortizing: No principal payment is made during the term of
the loan; the principal is repaid over the term as part of the
coupon payments.
[0187] Forward Contracts: A forward contract obligates its owner to
buy a given asset on a specified date at a price (also known as the
exercise price) specified at the origination of the contract This
is identical to a combination of a long call option combined with a
short put option or vice versa.
[0188] Futures Contracts Identical to forward, but typically traded
on an exchange where default risk is eliminated by the exchange's
guarantee of performance.
[0189] Swaps: Two parties exchange ("swap") specified cash flows at
specified intervals, typically "fixed for floating" or vice versa.
A swap contract is really nothing more than a series of forward
contracts.
[0190] Forward Swap/Delayed Start Swap: A combination of a forward
contract and a swap.
[0191] Break Forwards: A forward contract with a floor (or a cap)
in which the contract terminates early if prices fall (rise) to a
certain level.
[0192] Straddles/Strangles/Butterflies: Option combinations that
provide differing payoffs based on price movements, typically
combinations of puts and calls, either both long or both short.
[0193] Reverse Floating Rate Loan/Bull Floating Rate Notes: If the
floating rate rises, the net coupon payment falls.
[0194] Dual Currency Bond: Combination of a standard credit
extension with a forward currency contract.
[0195] Callable/Puttable Bonds: Standard bond and option on
interest rates.
[0196] Extendible Notes Long a standard bond and short a call
option (issuer).
[0197] Puttable Stock Stock issued with puts for investors to
acquire more if the price falls.
[0198] Convertible Bond Bond convertible into shares of the issuing
firm.
[0199] LYON (Liquid Yield Option Notes): Puttable, callable,
convertible, zero coupon bonds.
[0200] Commodity-Linked Bonds: A bond with interest payments linked
to some commodity. Examples include:
[0201] Oil-Indexed Notes: Standard note and options on crude
oil.
[0202] Copper Interest-Indexed Senior Subordinated Notes: Note with
quarterly interest payments determined by the prevailing price of
copper.
[0203] Auction Rate Notes/Debentures: Interest rate reset by Dutch
auction at the end of each interest period.
[0204] Collateralized Mortgage Obligations (CMOs)/Real Estate
Mortgage Investment Conduits (REMICs): Mortgage payment stream
divided into classes prioritized by rights to receive principal
payments.
[0205] Commercial Real-Estate Backed Bonds: Nonrecourse bonds
serviced and backed by a specified piece of real estate.
[0206] Credit Enhanced Debt Securities: Issuer's obligation to pay
is backed by an irrevocable letter of credit or a surety bond.
[0207] Dollar BILS: Floating zero coupon notes with interest rates
figured retrospectively on an index of long-term high-grade
corporate bonds.
[0208] Foreign Exchange Paper: Commercial paper on foreign
companies, usually those operating under a single currency.
[0209] Floating/Rate Sensitive Notes: Coupon rate resets on spread
over T-Bill, LIBOR, etc.
[0210] Floating Rate Tax-Exempt Revenue Bonds: Coupon rate floats
with index (commercial paper, etc.).
[0211] Increasing Rate Notes: Coupon rate note increases by
specified amount at specified intervals.
[0212] Indexed Currency Option Notes or Principal Exchange Rate
Linked Securities: Issuer pays reduced/increased principal based on
appreciation/depreciation of foreign currency.
[0213] Caps/Floors/Collars: Investor who writes a cap
(floor/collar) agrees to make payments when the underlying exceeds
the cap (falls below the floor/outside the collar) or vice
versa.
[0214] Interest Rate Reset Notes: Rate is reset after issuance to
initial rate or some preset rate.
[0215] Mortgage Pass-Through Certificates: Undivided interest in a
pool of mortgages.
[0216] Negotiable Certificates of Deposit: Registered CDs sold on
an agency basis.
[0217] Adjustable Tender Securities: issuer can periodically reset
Terms.
[0218] Puttable/Extendable Notes: At each period, the issuer can
redeem notes at par or extend maturity, notes can be put back to
issuer at option of purchaser.
[0219] Real Yield Securities: Coupon rate resets quarterly,
typically to the Real Yield Spread plus some fixed amount.
[0220] Receivable Pay-Through Securities: Undivided interest m a
pool of receivables.
[0221] Remarketed Reset Notes: Interest rate resets at end of each
period to a rate remarketing agent determines will make the notes
worth par.
[0222] Stripped Mortgage Backed Securities: Coupon payments divided
into interest only and principal only payments to investors.
[0223] Stripped Treasuries/Municipals: Divided into coupon &
principal (creates zero coupon bonds).
[0224] Variable Coupon Renewable Notes: Coupon rate varies based on
T-Bill, renews every 90 days unless terminated.
[0225] Variable Rate Renewable Notes: Coupon rate varies monthly
until investor terminates.
[0226] Yield Curve/Maximum Rate Notes: Rate is specified at level
minus LIBOR (or other standard index/yield).
[0227] Adjustable Rate Preferred Stock: Dividend rate resets based
on index/yield.
[0228] Auction Rate Preferred Stock: Dividend rate resets by Dutch
auction at regular intervals.
[0229] Convertible Adjustable Preferred Stock: Convertible into
common stock at certain dates under certain conditions.
[0230] Remarketed Preferred Stock (SABRES): Dividend rate resets at
the regular intervals to a rate set by the marketing agent to make
the preferred stock worth par.
[0231] Single Point Adjustable Rate Stock: Dividend rate reset
regularly as a fixed percentage of some index/yield.
[0232] State Rate Auction Preferred Stock: Fixed initial dividend
period followed by the issuer's option to convert to a reset by
Dutch auction at periodic intervals.
[0233] Variable Cumulative Preferred Stock: Dividend rate reset at
issuer's option to either auction or remarketing method.
[0234] Adjustable Rate Convertible Debt: Interest rate vanes
directly with the underlying common stock dividend rate.
[0235] Convertible Exchangeable Preferred Stock: Convertible
preferred stock exchangeable at issuer's option for debt with
identical rate and conversion terms.
[0236] Convertible Reset Debentures: Convertible bond with interest
rate reset at a predetermined time to an amount sufficient to give
debentures a market value equal to their face amount.
[0237] Debt with Mandatory Common Stock Purchase Contracts: Notes
that obligate purchasers to buy sufficient stock from the issuer to
retire the issue in full by the scheduled maturity date.
[0238] Exchangeable Preferred Stock: Auction rate preferred stock
exchanged for auction rate notes.
[0239] Synthetic Convertible Debt: Debt and warrants replicating
convertible debt.
[0240] Zero Coupon Convertible Debt: Non-interest bearing
convertible debt.
[0241] Puttable Common Stock: Issue of common stock with the right
to put the stock back to the issuer on a specified date at
specified price.
[0242] Although the present invention has been described in various
embodiments and the various embodiments have been provided as
examples of implementations of the present invention. It should be
understood that the present invention is not limited to any
particular shape, size, embodiment or configuration. On the
contrary, the aspects of the present invention can be embodied in
various manners within the scope and spirit of the invention as
described herein. In addition, the full scope of the various
embodiments is not limited by the above discussion. Instead, the
full scope of the various embodiments of the present invention
shall be measured by the appended claims and all equivalents.
[0243] All references cited in the present application are
incorporated in their entirety herein by reference to the extent
not inconsistent herewith.
[0244] It will be seen that the advantages set forth above, and
those made apparent from the foregoing description, are efficiently
attained and since certain changes may be made in the above
construction without departing from the scope of the invention, it
is intended that all matters contained in the foregoing description
or shown in the accompanying drawings shall be interpreted as
illustrative and not in a limiting sense.
[0245] It is also to be understood that the following claims are
intended to cover all of the generic and specific features of the
invention herein described, and all statements of the scope of the
invention which, as a matter of language, might be said to fall
therebetween. Now that the invention has been described,
* * * * *