U.S. patent application number 14/849283 was filed with the patent office on 2016-08-04 for method of creating and trading derivative investment products based on a statistical property reflecting the variance of an underlying asset.
This patent application is currently assigned to CHICAGO BOARD OPTIONS EXCHANGE, INCORPORATED. The applicant listed for this patent is CHICAGO BOARD OPTIONS EXCHANGE, INCORPORATED. Invention is credited to Lewis Biscamp, Eric Chern, Daniel Feuser, Andrew Hall, John C. Hiatt, JR., Paul Kepes.
Application Number | 20160225083 14/849283 |
Document ID | / |
Family ID | 37395150 |
Filed Date | 2016-08-04 |
United States Patent
Application |
20160225083 |
Kind Code |
A1 |
Feuser; Daniel ; et
al. |
August 4, 2016 |
Method of Creating and Trading Derivative Investment Products Based
on a Statistical Property Reflecting the Variance of an Underlying
Asset
Abstract
A method of creating and trading derivative contracts based on a
statistical property reflecting a variance of an underlying asset
is disclosed. Typically, an underlying asset is chosen to be a base
of a variance derivative and a processor calculates a value of the
statistical property reflecting an average volatility of price
returns of the underlying asset over a predefined period. A trading
facility display device coupled to a trading platform then displays
the variance derivative based on the value of the statistical
property reflecting the volatility of the underlying asset and the
trading facility transmits variance derivative quotes from
liquidity providers over at least one dissemination network.
Inventors: |
Feuser; Daniel; (Chicago,
IL) ; Chern; Eric; (Chicago, IL) ; Kepes;
Paul; (Chicago, IL) ; Hall; Andrew; (Chicago,
IL) ; Biscamp; Lewis; (Santa Fe, NM) ; Hiatt,
JR.; John C.; (Woodbridge, IL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CHICAGO BOARD OPTIONS EXCHANGE, INCORPORATED |
Chicago |
IL |
US |
|
|
Assignee: |
CHICAGO BOARD OPTIONS EXCHANGE,
INCORPORATED
Chicago
IL
|
Family ID: |
37395150 |
Appl. No.: |
14/849283 |
Filed: |
September 9, 2015 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13665381 |
Oct 31, 2012 |
|
|
|
14849283 |
|
|
|
|
11122748 |
May 4, 2005 |
8326715 |
|
|
13665381 |
|
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06Q 40/04 20130101 |
International
Class: |
G06Q 40/04 20060101
G06Q040/04 |
Claims
1. A method of creating derivatives based on a variance of an
underlying asset, comprising: calculating a value for a statistical
property reflecting the variance of the underlying asset on a
processor, the value for the statistical property having a dynamic
value which reflects an average volatility of price returns of the
underlying asset over a predefined time period; displaying at least
one variance derivative based on the statistical property
reflecting variance on a trading facility display device coupled to
a trading platform; and transmitting at least one variance
derivative quote of a liquidity provider from the trading facility
to at least one market participant.
Description
RELATED APPLICATIONS
[0001] The present application is a continuation of U.S. patent
application Ser. No. 13/665,381 (still pending), filed Oct. 31,
2012, which is a continuation of U.S. patent application Ser. No.
11/122,748 (now U.S. Pat. No. 8,326,715), filed May 4, 2005, the
entirety of each of which are hereby incorporated by reference.
FIELD OF THE INVENTION
[0002] The present invention relates to derivative investment
markets. More specifically, this invention relates to aspects of
actively disseminating and trading derivatives.
BACKGROUND
[0003] A derivative is a financial security whose value is derived
in part from a value or characteristic of another security, known
as an underlying asset. Two exemplary, well known derivatives are
options and futures.
[0004] An option is a contract giving a holder of the option a
right, but not an obligation, to buy or sell an underlying asset at
a specific price on or before a certain date. Generally, a party
who purchases an option is referred to as the holder of the option
and a party who sells an option is referred to as the writer of the
option.
[0005] There are generally two types of options: call options and
put options. A holder of a call option receives a right to purchase
an underlying asset at a specific price, known as the "strike
price," such that if the holder exercises the call option, the
writer is obligated to deliver the underlying asset to the holder
at the strike price. Alternatively, the holder of a put option
receives a right to sell an underlying asset at a specific price,
referred to as the strike price, such that if the holder exercises
the put option, the writer is obligated to purchase the underlying
asset at the agreed upon strike price. Thus, the settlement process
for an option involves the transfer of funds from the purchaser of
the underlying asset to the seller, and the transfer of the
underlying asset from the seller of the underlying asset to the
purchaser. This type of settlement may be referred to as "in kind"
settlement. However, an underlying asset of an option does not need
to be tangible, transferable property.
[0006] Options may also be based on more abstract market
indicators, such as stock indices, interest rates, futures
contracts and other derivatives. In these cases, in kind settlement
may not be desired, or in kind settlement may not be possible
because delivering the underlying asset is not possible. Therefore,
cash settlement is employed. Using cash settlement, a holder of an
index call option receives the right to "purchase" not the index
itself, but rather a cash amount equal to the value of the index
multiplied by a multiplier such as $100. Thus, if a holder of an
index call option elects to exercise the option, the writer of the
option is obligated to pay the holder the difference between the
current value of the index and the strike price multiplied by the
multiplier. However, the holder of the index will only realize a
profit if the current value of the index is greater than the strike
price. If the current value of the index is less than or equal to
the strike price, the option is worthless due to the fact the
holder would realize a loss.
[0007] Similar to options contracts, futures contracts may also be
based on abstract market indicators. A future is a contract giving
a buyer of the future a right to receive delivery of an underlying
commodity or asset on a fixed date in the future. Accordingly, a
seller of the future contract agrees to deliver the commodity or
asset on the specified date for a given price. Typically, the
seller will demand a premium over the prevailing market price at
the time the contract is made in order to cover the cost of
carrying the commodity or asset until the delivery date.
[0008] Although futures contracts generally confer an obligation to
deliver an underlying asset on a specified delivery date, the
actual underlying asset need not ever change hands. Instead,
futures contracts may be settled in cash such that to settle a
future, the difference between a market price and a contract price
is paid by one investor to the other. Again, like options, cash
settlement allows futures contracts to be created based on more
abstract "assets" such as market indices. Rather than requiring the
delivery of a market index (a concept that has no real meaning), or
delivery of the individual components that make up the index, at a
set price on a given date, index futures can be settled in cash. In
this case, the difference between the contract price and the price
of the underlying asset (i.e., current value of market index) is
exchanged between the investors to settle the contract.
[0009] Derivatives such as options and futures may be traded
over-the-counter, and/or on other trading facilities such as
organized exchanges. In over-the-counter transactions the
individual parties to a transaction are free to customize each
transaction as they see fit. With trading facility traded
derivatives, a clearing corporation stands between the holders and
writers of derivatives. The clearing corporation matches buyers and
sellers, and settles the trades. Thus, cash or the underlying
assets are delivered, when necessary, to the clearing corporation
and the clearing corporation disperses the assets as necessary as a
consequence of the trades. Typically, such standard derivatives
will be listed as different series expiring each month and
representing a number of different incremental strike prices. The
size of the increment in the strike price will be determined by the
rules of the trading facility, and will typically be related to the
value of the underlying asset.
[0010] While standard derivative contracts may be based on many
different types of market indexes or statistical properties of
underlying assets, current standard derivative contracts do not
provide investors with sufficient tools to hedge against greater
than expected or less than expected volatility in an underlying
asset. Thus, there is a need for a standard derivative contract
based on a statistical property that reflects the volatility of an
underlying asset.
BRIEF SUMMARY
[0011] Accordingly, the present invention relates to a method of
creating and trading derivative contracts based on a statistical
property that reflects variance of an underlying asset. In a first
aspect, the invention relates to a method of creating derivatives
based on the variance of an underlying asset. First, a processor
calculates a dynamic value for a statistical property reflecting an
average volatility of price returns of the underlying asset over a
predefined period. A trading facility display device coupled to a
trading platform then displays at least one quote for the variance
derivative from a liquidity provider and the trading facility
transmits at least one variance derivative quote from the liquidity
provider through a dissemination network to at least one market
participant.
[0012] In a second aspect, the invention relates to a method of
creating derivatives based on the variance of an underlying asset.
First, an underlying asset is chosen to be a base of a variance
derivative. A value for a statistical property reflecting the
variance of the underlying asset is calculated based on an average,
over a variance calculation period, of a summation of a squared
deviation of a daily return of the underlying asset from a previous
daily return of the underlying asset. Each squared deviation of the
daily return of the underlying asset that corresponds to a market
disruption event is removed. Finally, a trading facility display
device coupled to a trading platform displays quotes for the
variance derivative from at least one liquidity provider.
[0013] In a third aspect, the invention relates to a system for
creating and trading derivatives based on the variance of an
underlying asset. Typically, the system comprises a variance
property module coupled with a communications network, a
dissemination module coupled with the variance property module and
the communications network, and a trading module coupled with the
dissemination module and the communications network.
[0014] Generally, the variance property module calculates a
realized variance, cumulative realized variance, and implied
realized variance of the underlying asset. The variance property
module passes the calculated values to the dissemination module,
which transmits the calculated values relating to the variance
derivative to at least one market participant. The trading module
receives buy or sell orders for the variance derivative, executes
the buy or sell orders, and passes the result of the buy or sell
orders to the dissemination module to transmit the result of the
buy or sell order to at least one market participant.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is a flow chart of a method of creating and trading a
variance futures contract;
[0016] FIG. 2 is a diagram showing a listing of a variance futures
contract on a trading facility;
[0017] FIG. 3 is a block diagram of a system for creating and
trading variance futures contracts;
[0018] FIGS. 4a and 4b are a table showing values for a variance
futures contract over a variance calculation period;
[0019] FIG. 5 is a flow chart of a method of creating and trading a
variance option contract;
[0020] FIG. 6 is a diagram showing a listing of a variance options
contract on a trading facility;
[0021] FIG. 7 is a block diagram of a system for creating and
trading variance option contracts; and
[0022] FIGS. 8a and 8b are a table showing values for a variance
option contract over a variance calculation period.
DETAILED DESCRIPTION OF THE DRAWINGS
[0023] Variance derivatives are financial instruments such as
futures and option contracts that trade on trading facilities, such
as exchanges, whose value is based on the volatility of the value
of an underlying asset and not on the return of the underlying
asset. Variance of an underlying asset is a measure of the
statistical dispersion of the value of the underlying asset. Thus,
variance indicates the movement in the value of an underlying asset
from trading day to trading day. Typically, variance is computed as
the average squared deviation of the value of an underlying asset
from an expected value, represented by an average (mean) price
return value.
[0024] Those skilled in the art will recognize that variance
derivatives having features similar to those described herein and
statistical properties which reflect the variance of an underlying
asset, but which are given labels other than variance derivatives,
variance futures, or variance options will nonetheless fall within
the scope of the present invention.
[0025] FIG. 1 is a flow chart of one embodiment of a method for
creating and trading a variance futures contract 100. A variance
futures contract is a financial instrument in which the realized
variance of an underlying asset is calculated at the end of each
trading day over a predefined period, known as the variance
calculation period. Typically, the realized variance of an
underlying asset is calculated using a standardized equation, which
is a function of a daily return of the underlying asset. The daily
return of an underlying asset is typically the natural log of a
final value of the underlying asset over an initial value of the
underlying asset.
[0026] An investor is generally able to purchase a variance futures
contract before a variance calculation period begins, or an
investor may trade into or out of a variance futures contract
during the variance calculation period. To facilitate the purchase
and trading of variance futures contracts, trading facilities such
as exchanges like the CBOE Futures Exchange will calculate and
disseminate cumulative realized variance and implied realized
variance values for a variance futures contract. Cumulative
realized variance and implied realized variance provide tools for
investors to determine when to trade into and out of a variance
futures contract.
[0027] The method for creating and trading a variance futures
contract begins at step 102 by identifying an underlying asset or a
set of underlying assets for the variance futures contract.
Typically, an underlying asset or set of assets is selected based
on trading volume of a prospective underlying asset, the general
level of interest of market participants in a prospective
underlying asset, or for any other reason desired by a trading
facility. The underlying assets for the variance futures contract
may be equity indexes or securities; fixed income indexes or
securities; foreign currency exchange rates; interest rates;
commodity indexes; commodity or structured products traded on a
trading facility or in the over-the-counter ("OTC") market; or any
other type of underlying asset whose value may change from day to
day.
[0028] Once the underlying asset or assets have been selected at
102, a formula is developed at 104 for generating a value for a
statistical property reflecting the realized variance of the
underlying asset or assets over the defined variance calculation
period. In one embodiment, realized variance is calculated using a
standard formula that uses an annualization factor and daily
S&P 500 returns over the variance calculation period, assuming
a mean daily price return of zero. The annualization factor is
normally a number that represents the number of days the underlying
asset will trade in a year. Typically, the annualization factor is
252 to represent the number of trading days an underlying asset is
traded in a year. However, for underlying assets that trade in
international trading facilities or specialized trading facilities,
the annualization factor may be a value other than 252.
[0029] Realized variance is typically calculated according to the
formula:
Realized Variance = AF * i = 1 N a - 1 R i 2 N e - 1 , wherein:
##EQU00001## R i = ln P i + 1 P i . ##EQU00001.2##
P.sub.i is an initial value of the underlying asset used to
calculate a daily return, P.sub.i+1 is a final value of the
underlying asset used to calculate the daily return, N.sub.e is a
number of expected underlying asset values needed to calculate
daily returns during the variance calculation period, N.sub.a is an
actual number of underlying asset values used to calculate daily
returns during the variance calculation period, and AF is the
annualization factor.
[0030] A "daily return" (R.sub.i) is the natural log of a final
value (P.sub.i+1) of an underlying asset over an initial value
(P.sub.i) of the underlying asset. The initial value (P.sub.i) and
the final value (P.sub.i+1) of the underlying asset may be on the
same trading day, consecutive trading days, or non-consecutive
trading days. For example in one embodiment, the daily return may
be the natural log of a closing price of an underlying asset on one
day over the closing price of the underling asset on a previous
trading day. In another embodiment, the daily return may be the
natural log of a closing price of an underlying asset over an
opening price of the underlying asset on the same trading day.
[0031] The initial value (P.sub.i) and final value (P.sub.i+1) of
an underlying asset may be based on a Special Opening Quotation
("SOQ"), closing price, intraday price, or any other price.
Similarly, the final value (P.sub.i+1) of an underlying asset may
be based on a SOQ, closing price, intraday price quote, or any
other price.
[0032] After determining a formula for calculating realized
variance at 104, specific values are defined at 106 for the
variables within the formula for calculating realized variance
during the variance calculation period. Typically, specific values
will be defined for an initial value for the first daily return, a
final value for the first daily return, an initial value for the
last daily return, and the final value of the last daily return. In
one embodiment, the initial value (P.sub.i) for a first daily
return in a variance calculation period is defined to be an initial
value of the underlying asset on a first day of the variance
calculation period; a final value of the underlying asset for the
first daily return is defined to be a closing price value of the
underlying asset on a following trading day; an initial value for a
last daily return in the variance calculation period is defined to
be a closing value of the underlying asset on a trading day
immediately prior to the final settlement date; and a final value
for the last daily return is defined to be a SOQ on the final
settlement date. For all other daily returns, the initial and final
values are defined to be the closing values of the underlying asset
on consecutive trading days.
[0033] Generally, the total number of actual daily returns during
the variance calculation period is defined to be N.sub.a-1, but if
one or more market disruption events occurs during the variance
calculation period, the actual number of underlying asset values
will be less than the expected number of underlying asset values by
an amount equal to the number of market disruption events that
occurred during the variance calculation period.
[0034] A market disruption event generally occurs on a day on which
trading is expected to take place to generate a value for an
underlying asset, but for some reason trading is stopped or a value
for the underlying asset is not available. In one embodiment, a
market disruption event may be defined to be (i) an occurrence or
existence, on any trading day during a one-half period that ends at
the scheduled close of trading, of any suspension of, or limitation
imposed on, trading on the primary trading facility(s) of the
companies comprising the underlying asset in one or more securities
that comprise 20 percent or more of the level of the asset; or (ii)
if on any trading day that one or more primary trading facility(s)
determines to change scheduled close of trading by reducing the
time for trading on such day, and either no public announcement of
such reduction is made by such trading facility or the public
announcement of such change is made less than one hour prior to the
scheduled close of trading; or (iii) if on any trading day one or
more primary trading facility(s) fails to open and if in the case
of either (i) or (ii) above, such suspension, limitation, or
reduction is deemed material. A scheduled close of trading is the
time scheduled by each trading facility, as of the opening for
trading in the underlying asset, as the closing time of the trading
of such asset on the trading day. Examples of market disruption
events include days on which trading is suspended due to a national
day of mourning or days on which trading is suspended for national
security.
[0035] If a trading facility determines that a market disruption
event has occurred on a trading day, the daily return of the
underlying asset on that day will typically be omitted from the
series of daily returns used to calculate the realized variance
over the variance calculation period. For each such market
disruption event, the actual number of underlying asset values used
to calculate daily returns during the settlement calculation,
represented by N.sub.a, will be reduced by one. Typically, if a
market disruption event occurs on a final settlement date of a
variance futures contract, the final settlement date may be
postponed until the next trading day on which a market disruption
event does not occur. Alternatively, any other action may be taken
as agreed upon by a trading facility. These actions will typically
be listed in the Rules and By-Laws of a clearing agent.
[0036] Once the variance calculation period begins for a variance
futures contract, the value represented by N.sub.e will not change
regardless of the number of market disruption events that occur
during the variance calculation period, even if the final
settlement date is postponed. Typically, if the final settlement
date of the expiring variance futures contract is postponed, the
length of the variance calculation period for the next variance
futures contract is shortened by the number of market disruption
events that occur at the beginning of the variance calculation
period. Likewise, the value represented by N.sub.e is reduced by
the number of market disruption events that occur at the beginning
of the variance calculation period.
[0037] Similarly, if a market disruption event occurs at the
beginning of the variance calculation period, the first daily
return of the shortened variance calculation period for the next
variance futures contract will be calculated using the same
procedure as described. For example, if the final settlement date
for the previous variance calculation period of a variance futures
contract is postponed to a Tuesday, the initial value for the first
daily return of the variance calculation period of the next
variance futures contract would be calculated using the SOQ (or
other price designated) of the underlying asset on Tuesday morning
and the closing value of the asset the following Wednesday.
[0038] Once the underlying asset or assets is chosen at 102, the
formula for generating the value of the statistical property
reflecting the variance of the underlying asset or assets is
determined at 104, and the value of the variables within the
variance calculation period are defined at 106, the variance
futures contract based on the chosen underlying asset or assets is
assigned a unique symbol at 108 and listed on a trading platform at
110. Generally, the variance futures contract may be assigned any
unique symbol that serves as a standard identifier for the type of
standardized variance futures contract.
[0039] Generally, a variance futures contract may be listed on an
electronic platform, an open outcry platform, a hybrid environment
that combines the electronic platform and open outcry platform, or
any other type of platform known in the art. One example of a
hybrid exchange environment is disclosed in U.S. patent application
Ser. No. 10/423,201, filed Apr. 24, 2003, the entirety of which is
herein incorporated by reference. Additionally, a trading facility
such as an exchange may transmit variance futures contract quotes
of liquidity providers over dissemination networks 114 to other
market participants. Liquidity providers may include Designated
Primary Market Makers ("DPM"), market makers, locals, specialists,
trading privilege holders, registered traders, members, or any
other entity that may provide a trading facility with a quote for a
variance derivative. Dissemination Networks may include networks
such as the Options Price Reporting Authority ("OPRA"), the CBOE
Futures Network, an interne website or email alerts via email
communication networks. Market participants may include liquidity
providers, brokerage firms, normal investors, or any other entity
that subscribes to a dissemination network.
[0040] As seen in FIG. 2, in one embodiment the variance futures
contracts are listed on a trading platform by displaying the
variance futures contracts on a trading facility display device
coupled with the trading platform. The listing 200 displays the
variance futures contract for purchase in terms of variance points
204 or a square root of variance points 206. A variance point is an
expected realized variance over a variance calculation period
multiplied by a scaling factor such as 10,000. In FIG. 2, one of
the variance futures contract has a value of 625.00 in terms of
variance points 208 and a value of 25.00 in terms of volatility
210. A value of 625.0 is calculated by multiplying a realized
variance calculation of 0.0625 by a scaling factor of 10,000.
Further, a value of 25.00 is calculated by taking the square root
of 625.00 (price in terms of variance points).
[0041] In addition to listing variance futures contracts in terms
of variance points and the square root of variance points, the
prices for variance futures contracts may also be stated in terms
of a decimal, fractions, or any other numerical representation of a
price. Further, scaling factors for the variance derivatives may be
determined on a contract-by-contract basis. Scaling factors are
typically adjusted to control the size, and therefore the price of
a derivative contract.
[0042] Over the course of the variance calculation period, in
addition to listing variance futures contracts in terms of variance
points, the trading facility may also display and disseminate a
cumulative realized variance and an implied realized variance on a
daily basis, or in real-time, to facilitate trading within the
variance futures contract. Cumulative realized variance is an
average rate of the realized variance of a variance futures
contract through a specific date of the variance calculation
period. Thus, using the formula described above, after N.sub.p days
in a variance calculation period, the cumulative realized variance
may be calculated according to the formula:
Cumulative Variance = AF * i = 1 N P R i 2 N P . ##EQU00002##
[0043] Implied realized variance is a weighted average of both the
cumulative realized variance and a most recent closing price of a
variance futures contract during the variance calculation period.
Specifically, implied realized variance is calculated according to
the formula:
Implied Variance = TP - RV * Day Current Day Total Day Left / Day
Total , ##EQU00003##
where TP is the last trading price of the variance futures
contract; RV is the cumulative realized variance; Day.sub.Current
is the total number of trading days that have passed in the
variance calculation period; Day.sub.Total is the total number of
trading days in the variance calculation period; and Day.sub.Left
is the number of trading days left in the variance calculation
period. Referring to FIG. 1, the cumulative realized variance and
implied realized variance values provide investors a tool for
determining when to trade into and out of variance futures
contracts at 116.
[0044] At expiration of the variance calculation period for a
variance futures contract, the trading facility will settle a
variance futures contract at 118 such that the settlement value is
equal to the cumulative realized variance over the specified
variance calculation period. Typically, settlement of variance
futures contracts will result in the delivery of a cash settlement
amount on the business day immediately following the settlement
date. The cash settlement amount on the final settlement date shall
be the final mark to market amount against the final settlement
price of the variance futures contract multiplied by the contract
multiplier.
[0045] FIG. 3 is a block diagram of a system 300 for creating and
trading variance futures contracts. Generally, the system comprises
a variance property module 302, a dissemination module 304 coupled
with the variance property module 302, and a trading module 306
coupled with the dissemination module 304. Typically, each module
302, 304, 306 is also coupled to a communication network 308
coupled to various trading facilities 322 and liquidity providers
324.
[0046] The variance property module 302 comprises a communications
interface 310, a processor 312 coupled with the communications
interface 310, and a memory 314 coupled with the processor 312.
Logic stored in the memory 314 is executed by the processor 312
such that that the variance property module 302 may receive current
values for an underlying asset of a variance futures contract
through the communications interface 310; calculate realized
variance, cumulative realized variance, and implied realized
variance, as described above, for the underlying asset; and pass
the calculated values to the dissemination module 304.
[0047] The dissemination module 304 comprises a communications
interface 316, a processor 318 coupled with the communications
interface 316, and a memory 320 coupled with the processor 318.
Logic stored in the memory 320 is executed by the processor 318
such that the dissemination module 304 may receive the calculated
values from the variance property module 302 through the
communications interface 316, and disseminate the calculated values
over the communications network 308 to various market participants
322, as described above.
[0048] The trading module 306 comprises a communications interface
326, a processor 328 coupled with the communications interface 326,
and a memory 330 coupled with the processor 328. Logic stored in
the memory 330 is executed by the processor 328 such that the
trading module 306 may receive buy or sell orders over the
communications network 308, as described above, and pass the
results of the buy or sell order to the dissemination module 304 to
be disseminated over the communications network 308 to the market
participants 322.
[0049] FIGS. 4a and 4b are a table showing values for a variance
futures contract over a variance calculation period. The first
column 402 represents the number of days that have passed in the
variance calculation period; column 404 shows the daily closing
price of the underlying asset; column 406 shows the natural log of
the current closing price of the underlying asset over the previous
closing price of the underlying asset; column 408 shows the square
of the value of column 406; column 410 shows the summation of the
values in column 408; column 412 shows the cumulative realized
variance on each day; column 414 shows the closing price of the
variance futures contract for each day; and column 416 shows the
calculated implied realized variance for each day.
[0050] As shown in column 402, a variance futures contract with a
90-day variance calculation period typically includes 64 trading
days. In the example, on the first trading day 418, the underlying
asset closes at a value of 1122.20 (420). To calculate the realized
variance for day 1, the natural log is taken of the closing value
420 of the underlying asset on day 1 (1122.20) over the closing
value 422 of the underlying asset on the previous trading day
(1127.02), resulting in a value of -0.0042859 (424). The value of
the natural log is squared, resulting in the value of
1.83693*10.sup.-5 (426). The value of the square of the natural log
of the current day's closing price over the previous day's closing
price is then summed with any previous values in column 408. Due to
the fact there are no previous values on the first day, the
summation is equal to 1.83693*10.sup.-5 (428). The value of the
summation is then divided by the number of trading days in the
variance calculation period that has passed (1) to obtain an
average variance over the variance calculation period, multiplied
by an annualization factor to represent the number of trading days
in a year (252) and multiplied by a scaling factor (10,000),
resulting in a value of 46.29 (430).
[0051] The realized variance of the variance futures contract after
one day can be used with the closing value of the variance futures
contract on the first day 432 (284.00) to calculate the implied
variance 434 according to the implied realized variance formula
described above. Specifically, the implied realized variance is
calculated to be:
Implied Variance = 284.00 - 46.29 * 1 64 63 64 = 287.77 .
##EQU00004##
[0052] This above-described process for the first trading day is
repeated for each trading day in the variance calculation period.
For example on the 20.sup.th day of the variance calculation period
436, the underlying asset closes at 1108.20 (438). The natural log
is taken of the closing value of the current day 438 (1108.20) over
the closing value of the previous closing day 440 (1103.29). The
result of the natural log 441 (0.00444045) is squared 442
(1.97176*10.sup.-5), and summed with the previous values 444
(0.000958131) to obtain a value 446 (0.000977849). The resulting
value is divided by the current number of trading days that have
passed (20) to obtain an average; multiplied by an annualization
factor representing the number of trading days in a year (252); and
multiplied by a scaling factor (10,000) to obtain the cumulative
realized variance 448 of 123.21 on day 20.
[0053] The implied variance of the 20.sup.th day 452 of the
variance calculation period can then be calculated using the
closing value of the variance futures contract 450 on the 20.sup.th
day (203.5) according to the formula described above:
Implied Variance = 203.5 - 123.21 * 20 64 44 64 = 240.00 .
##EQU00005##
[0054] In addition to variance futures contracts, variance
derivatives also encompass variance option contracts. A variance
option contract is a type of option product that has a strike price
set at a cumulative realized variance level for an underlying
asset. The strike price to be listed may be any variance level
chosen by the trading facility.
[0055] As with traditional option contracts, a variance option
contract may include both call variance options and put variance
options. Typically, the holder of a variance call option receives
the right to purchase a cash amount equal to the difference between
the current value of the statistical property reflecting the
variance of the underlying asset and the strike price multiplied by
the multiplier. Similarly, the holder of a variance put option
receives the right to sell a cash amount equal to the difference
between the current value of the statistical property reflecting
the variance of the underlying asset and the strike price
multiplied by the multiplier.
[0056] Due to the fact the variance option contract is based on a
statistical property, in kind settlement is not desired and cash
settlement is employed. Typically, the cash settlement will be
equal to the value of the statistical property reflecting variance
of the underlying asset multiplied by a predefined multiplier. Any
predefined multiplier may be chosen by the trading facility.
[0057] As shown in FIG. 5, to create and trade a variance option
contract an underlying asset is first chosen 502. As with the
variance futures contract, the underlying asset may be selected
based on trading volume of a prospective underlying asset, a
general interest in a prospective underlying asset among market
participants, or for any other reason desired by a trading
facility. The underlying asset for the variance option contract may
be equity indexes or securities; equity fixed income indexes or
securities; foreign currency exchange rates; interest rates;
commodity indexes; commodity or structured products traded on a
trading facility or in the over-the-counter ("OTC") market; or any
other type of underlying asset known in the art.
[0058] Once the underlying asset or assets have been selected at
502, a formula is developed at 504 for generating a value of a
statistical property reflecting the realized variance of the
underlying asset or assets over the defined variance calculation
period. Typically, the formula to generate a value of a statistical
property reflecting realized variance for a variance option
contract is the same formula used to generate a value of a
statistical property reflecting realized variance for the variance
futures contract. Specifically, variance for a variance option
contract is typically calculated according to the formula:
Realized Variance = AF * i = 1 N a - 1 R i 2 N e - 1 , wherein:
##EQU00006## R i = ln P i + 1 P i , ##EQU00006.2##
P.sub.i is an initial value of the underlying asset used to
calculate a daily return, P.sub.i+1 is a final value of the
underlying asset used to calculate the daily return, N.sub.e is a
number of expected underlying asset values needed to calculate
daily returns during the variance calculation period, N.sub.a is an
actual number of underlying asset values used to calculate daily
returns during the variance calculation period, and AF is the
annualization factor.
[0059] As with the variance futures contracts, specific values are
defined at 506 for the variables within the formula for calculating
realized variance during the variance calculation period. The
variance option contract is then assigned a unique symbol at 508
and listed on a trading platform at 510. Generally, the variance
option contract may be assigned any unique symbol that serves as a
standard identifier for the type of standardized variance options
contract.
[0060] Generally, a variance option contract may be listed on an
electronic platform, an open outcry platform, a hybrid environment
that combines the electronic platform and open outcry platform, or
any other type of platform known in the art. Additionally, a
trading facility may disseminate quotes for variance option
contracts over dissemination networks 514 such as the OPRA, the
CBOE Network, an interne website or email alerts via email
communication networks to market participants.
[0061] As seen in FIG. 6, in one embodiment, similar to variance
futures contracts, variance option contracts are listed 600 on a
trading platform for purchase with a strike price in terms of
variance points 604 or a square root of variance points 606. A
variance point is an expected realized variance over a variance
calculation period multiplied by a scaling factor such as
10,000.
[0062] Referring again to FIG. 5, after a variance option contract
is listed on a trading facility, an investor may trade into or out
of the option contract at 516 as is well known in the art, until
the option contract expires at 518.
[0063] FIG. 7 is a block diagram of a system 700 for creating and
trading variance option contracts. Generally, the system comprises
a variance property module 702, a dissemination module 704 coupled
with the variance property module 702, and a trading module 706
coupled with the dissemination module 704. Typically, each module
702, 706, 708 is also coupled to a communication network 708
coupled to various market participants 722.
[0064] The variance property module 702 comprises a communications
interface 710, a processor 712 coupled with the communications
interface 710, and a memory 714 coupled with the processor 712.
Logic stored in the memory 714 is executed by the processor 712
such that that the variance property module 702 may receive current
values for an underlying asset of a variance option contract
through the communications interface 710; calculate realized
variance, as described above, for the underlying asset; and pass
the calculated realized variance the dissemination module 704.
[0065] The dissemination module 704 comprises a communications
interface 716, a processor 718 coupled with the communications
interface 716, and a memory 720 coupled with the processor 718.
Logic stored in the memory 720 is executed by the processor 718
such that the dissemination module 704 may receive the calculated
realized variance from the variance property module 702 through the
communications interface 716, and disseminate the calculated
realized variance over the communications network 708 to various
market participants 722, as described above.
[0066] The trading module 706 comprises a communications interface
726, a processor 728 coupled with the communications interface 726,
and a memory 730 coupled with the processor 728. Logic stored in
the memory 730 is executed by the processor 728 such that the
trading module 706 may receive buy or sell orders over the
communications network 708, as described above, and pass the
results of the buy or sell order to the dissemination module 704 to
be disseminated over the communications network 708 to the market
participants 722.
[0067] FIGS. 8a and 8b are a table showing values for a variance
option contract over a variance calculation period. In one example,
a variance call option contract may have a strike price of 135.00
and be exercised at any time during the 90-day calculation period.
Therefore, a holder of the variance call option contract could only
exercise their option to make a profit during the 90-day variance
calculation period when the cumulative realized variance is
calculated to be above 135.00 such as on days 3-5 (804, 806, 808),
10 (810), 11 (812), 14 (814), 16 (816), 28 (818), 19 (820), 34-37
(822, 824, 826, 828), and 40 (830). On all other trading days of
the variance calculation period, if the holder of the variance call
option exercised their option it would result in a loss.
[0068] Similarly, in another example, a variance call option
contract may have a strike price of 115.00 and only be exercised at
the end of the 90-day calculation period. Therefore, due to the
fact the cumulative realized variance is calculated to be above
115.00 at the end of the 90-day calculation period 831, the holder
of the variance call option may exercise their option for a profit.
However, if the cumulative realized variance was calculated to be
at or below 115.00 at the end of the 90-day calculation period 831,
the holder of the variance option may not exercise their option for
a profit.
[0069] In yet another example, a variance put option contract may
have a strike price of 117.00 and be exercised at any time during
the 90-day calculation period. Therefore, a holder of the variance
put option contract could only exercise their option to make a
profit during the 90-day variance calculation period when the
realized variance is calculated to be below 117.00 such as on days
1 (832), 2 (834), 8 (836), 9 (838), 24 (840), and 26 (842). On all
other trading days of the variance calculation period, if the
holder of the variance put option exercised their option it would
result in a loss.
[0070] Similarly, in another example, a variance put option
contract may have a strike price of 125.00 and only be exercised at
the end of the 90-day calculation period 831. Therefore, due to the
fact the cumulative realized variance is calculated to be below
125.00 at the end of the 90-day calculation period 844, the holder
of the variance option contract may exercise their option for a
profit. However, if the cumulative realized variance was
calculation to be at or above 125.00 at the end of the cumulative
calculation period 831, the holder of the variance option may not
exercise their option for a profit.
[0071] According to another aspect of the present invention,
chooser options may be created based on variance options. A chooser
option is an option wherein the purchaser of the option buys a call
or a put option at some time in the future. The call and the put
option will typically share the same expiration date and the same
strike price (value), although, split chooser options may be
crafted wherein the call and the put options have different
expirations and/or different strikes.
[0072] Chooser options are advantageous in situations in which
investors believe that the price of the underlying asset is for a
significant move, but the redirection of the move is in doubt. For
example, some event, such as the approval (disapproval) of a new
product, a new earnings report, or the like, may be anticipated
such that positive news is likely cause the share price to rise,
and negative news will cause the share price to fall. The ability
to choose whether an option will be a put or a call having
knowledge of the outcome of such an event is a distinct advantage
to an investor.
[0073] The purchase of a chooser option is akin to purchasing both
a put and a call option on the same underlying asset. Typically the
chooser option is priced accordingly. In the present case,
purchasing a variance chooser option amounts to buying both a put
and a call option based on the variance of an underlying asset.
Chooser options may be traded on an exchange just like other
variance derivative. The only accommodations necessary for adapting
an exchange for trading chooser options is that a final date for
making the choice between a call option and a put option must be
established and maintained. Also, post trade processing on the
exchange's systems must be updated to implement and track the
choice of the call or a put once the choice has been made. One
option for processing the chosen leg of a chooser option is to
convert the chooser option into a standard option contract
according to the standard series for the same underlying asset and
having the same strike price as the chosen leg of the chooser
option.
[0074] It is intended that, except for terms explicitly defined in
the specification, the foregoing detailed description should be
regarded as illustrative rather than limiting, and that it should
be understood that it is the following claims, including all
equivalents, that are intended to define the spirit and scope of
this invention.
* * * * *