U.S. patent application number 12/831414 was filed with the patent office on 2010-11-04 for method for executing a single tranche synthetic abs derivative transaction.
This patent application is currently assigned to BARCLAYS CAPITAL INC.. Invention is credited to Jonathan LAI, Jeong Gu LEE.
Application Number | 20100280970 12/831414 |
Document ID | / |
Family ID | 39544297 |
Filed Date | 2010-11-04 |
United States Patent
Application |
20100280970 |
Kind Code |
A1 |
LAI; Jonathan ; et
al. |
November 4, 2010 |
METHOD FOR EXECUTING A SINGLE TRANCHE SYNTHETIC ABS DERIVATIVE
TRANSACTION
Abstract
A Single Tranche Synthetic ABS product is designed to replicate
economics returns of structured finance collateralized debt
obligations (SF CDO) securities and allow parties to express a
leveraged and/or correlation view on a custom ABS portfolio by
transferring a credit risk of a particular transacted tranche of a
portfolio in swap format. The inventions described herein account
for an available funds cap risk of the ABS securities within the
underlying portfolio in a manner equivalent to a cash analog based
on the same underlying portfolio with sequential pay structure.
Inventors: |
LAI; Jonathan; (New York,
NY) ; LEE; Jeong Gu; (Guttenberg, NJ) |
Correspondence
Address: |
MORGAN, LEWIS & BOCKIUS LLP
1701 MARKET STREET
PHILADELPHIA
PA
19103-2921
US
|
Assignee: |
BARCLAYS CAPITAL INC.
New York
NY
|
Family ID: |
39544297 |
Appl. No.: |
12/831414 |
Filed: |
July 7, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11851297 |
Sep 6, 2007 |
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12831414 |
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60842796 |
Sep 6, 2006 |
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Current U.S.
Class: |
705/36R |
Current CPC
Class: |
G06Q 40/06 20130101 |
Class at
Publication: |
705/36.R |
International
Class: |
G06Q 40/00 20060101
G06Q040/00 |
Claims
1-27. (canceled)
28. A computer implemented method comprising: providing a single
tranche derivative transaction, wherein the derivative transaction
relates to a reference portfolio, and wherein the single tranche
derivative transaction relates to a single transacted tranche
within a capital structure including a plurality of reference
tranches, including at least a transacted tranche, a mezzanine
tranche, a senior tranche, and an equity tranche; allocating a
portfolio premium for the reference portfolio in a manner
equivalent to distributing periodic income in a hypothetical
sequential-pay cashflow securitization structure; applying a
sequential allocation of the premium payment in the capital
structure; and determining, by a processor, premium payments for
the transacted tranche and each reference tranche within the
capital structure.
29. The method of claim 17 further comprising calculating, by a
processor, a premium of the transacted tranche n for a time period
t, when the transacted tranche comprises either the mezzanine
tranche or the senior tranche, using the formula: min [ ( OTNA n ,
t * FR n * ACT 360 ) , max ( AAP - n + 1 m RFA t , 0 ) ] ,
##EQU00010## wherein: OTNA.sub.n,t is an outstanding tranche
notional amount for a transacted tranche n at time t, FR.sub.n is a
fixed rate for the transacted tranche n, ACT/360 is a day count
fraction, AAP is an aggregate asset premium, summation index values
n+1, . . . , m correspond to transacted tranches senior to
transacted tranche n, and RFA.sub.t in the n+1, . . . , m summation
is a transacted tranche fixed amount for time period t for a
transacted tranche corresponding to an index value.
30. The method of claim 17 further comprising calculating, by a
processor, a premium of the transacted tranche n for a time period
t, when the transacted tranche comprises an equity tranche, using
the formula: max ( AAP - n + 1 m FA t , 0 ) , ##EQU00011## wherein:
AAP is an aggregate asset premium summation index values n+1, . . .
m correspond to transacted tranches senior to transacted tranche n,
and FA.sub.t in the n+1, . . . , m summation is a fixed amount for
time period t for a transacted tranche corresponding to an index
value.
31. The method of claim 19 wherein the premium is paid in an
impaired equity tranche despite full or partial impairment.
32. The method of claim 18 further comprising calculating, by a
processor, the premium of the transacted tranche, when the
transacted tranche comprises either the mezzanine tranche or the
senior tranche, using the formula: min [ ( S i * OTW i * IPS * ACT
360 ) , max ( AAP t - i + 1 m RFA t , 0 ) ] , ##EQU00012## wherein:
S.sub.i is a reference tranche spread for reference tranche i,
OTW.sub.i is an outstanding tranche width for reference tranche i,
IPS is an initial portfolio size, and AAP.sub.t is an aggregate
asset premium for time period t.
33. The method of claim 21 further comprising calculating, by a
processor, the outstanding width of the transacted tranche using
the formula: max[min(OPP, X,.sub.i+1)-max(X.sub.i, ALP),0],
wherein: OPP is an outstanding portfolio percentage, X.sub.i+1 is a
reference tranche detachment for reference tranche i, X.sub.i is a
reference tranche attachment for reference tranche i, and ALP is an
aggregate loss percentage.
34. The method of claim 21 further comprising calculating, by a
processor, an aggregate portfolio premium using the formula: PRS *
OPS t * ACT 360 , ##EQU00013## wherein: PRS is a portfolio
reference spread, and OPS.sub.t is a sum of outstanding portfolio
size on each day in time period t, divided by number of days in
time period t.
Description
PRIORITY APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Patent Application No. 60/842,796, filed Sep. 6, 2006, titled
Single Tranche Synthetic ABS Transaction. The entire contents of
that application are incorporated herein by reference.
INTRODUCTION
[0002] Methods and specifications are described herein for
executing single tranche synthetic asset backed securities (ABS)
derivative transactions. The synthetic ABS market has experienced
exponential growth following (i) the publication of standard ISDA
documentation for single name ABS CDS transactions, and (ii) the
launch of the ABX credit index and execution of derivative
transactions thereon. Single tranche products are one of the next
stages in the evolution of the synthetic ABS space.
[0003] A Single Tranche Synthetic ABS product is generally a
derivative instrument that is designed to replicate certain
economics returns of structured finance collateralized debt
obligations (SF CDO) securities. Single tranche synthetic ABS
products can allow parties to express a leveraged and/or
correlation view on a custom ABS portfolio by transferring a credit
risk of a particular transacted tranche of a portfolio in swap
format--in essence, providing a synthetic securitization of
securitized assets. Since the transaction is provided in swap
format, a security need not be issued in connection with the
transaction. Several advantages single tranche products have over
conventional SF CDO securities include, for example, (i) superior
leverage--there is no cost of funds hurdle, (ii)
flexibility--portfolios can be customized and removing the need to
place an entire capital structure, (iii) efficiency--minimal
execution time and no fixed costs such as SPVs fees and trustee
expenses, and (iv) other advantages. Single tranche products may be
used in many applications, including as a substitute for SF CDO
securities, or as a hedge to related cash position. Although the
inventions described herein refer specifically to single tranche
synthetic ABS products, it will be understood to one of skill in
the art that the same calculations, formulae and other overarching
concepts can be applied to other transactions and instruments.
[0004] Improvements to single tranche products in the market are
described herein which, among other advantages, minimize basis risk
when hedged with a standard untranched portfolio ABS CDS trade.
[0005] In one embodiment of the invention, a method is provided
that comprises providing a single tranche derivative transaction,
wherein the derivative transaction relates to a reference
portfolio, and wherein the single tranche derivative transaction
relates to a single transacted tranche within a capital structure
including a plurality of reference tranches; allocating an
available funds cap risk in the reference portfolio in reverse
sequence, the reverse sequence beginning with a most subordinate
reference tranche; determining an incurred interest shortfall
amount for each of the reference tranches; allocating one or more
interest shortfall reimbursements sequentially beginning with a
most senior reference tranche that has incurred an interest
shortfall and ending with a subordinate tranche; and determining an
incurred interest shortfall reimbursement amount for each of the
reference tranches. Other features of the invention include that an
available funds cap risk in the single tranche derivative
transaction on an ABS portfolio is equivalent to a hypothetical
sequential-pay cashflow securitization structure based on the same
ABS portfolio.
[0006] In another embodiment, a method is provided that comprises
providing a single tranche derivative transaction, wherein the
derivative transaction relates to a reference portfolio, and
wherein the single tranche derivative transaction relates to a
single transacted tranche within a capital structure including a
plurality of reference tranches, including at least a transacted
tranche, a mezzanine tranche, a senior tranche, and an equity
tranche; allocating a portfolio premium for the reference portfolio
in a manner equivalent to distributing periodic income in a
hypothetical sequential-pay cashflow securitization structure; and
applying a sequential allocation of the premium payment in the
capital structure and determining premium payments for the
transacted tranche and each reference tranche within the capital
structure. Other features of the invention include that a premium
is paid in an impaired equity tranche despite full or partial
impairment.
[0007] In another embodiment of the invention, a method is provided
that comprises: providing a single tranche derivative transaction,
wherein the derivative transaction relates to a reference
portfolio, and wherein the single tranche derivative transaction
relates to a single transacted tranche within a capital structure
containing a plurality of reference tranches; determining a level
of impairment of each of the plurality of reference tranches
following an occurrence of a principal loss in the reference
portfolio; allocating said principal loss in a reverse sequence
among the plurality of reference tranches beginning with a most
subordinate tranche; determining an amount of notional principal to
restore each of the plurality of reference tranches following an
occurrence of a principal shortfall reimbursement or a writedown
reimbursement in the reference portfolio; allocating said principal
shortfall reimbursement or writedown reimbursement in sequence
among the plurality of reference tranches beginning with a most
senior tranche that has been impaired and ending with a most
subordinate tranche; determining an amount of a principal reduction
for each of the plurality of reference tranches following a
principal payment in the reference portfolio; allocating the
principal payment in sequence among the plurality of reference
tranches beginning with the most senior tranche and ending with the
most subordinate tranche, and determining an outstanding tranche
notional amount of the transacted tranche and each of the plurality
of reference tranches based on the allocation of principal losses,
principal shortfall reimbursements, writedown reimbursements, and
principal payments.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 depicts a diagram of a sample synthetic capital
structure for a single tranche transaction according to an
embodiment of the invention;
[0009] FIG. 2 depicts a sample matrix of a synthetic capital
structure for a single tranche transaction according to an
embodiment of the invention;
[0010] FIG. 3 depicts a chart of a comparison of a sample capital
structure and spread distribution according to an embodiment of the
invention;
[0011] FIG. 4 depicts a table of calculations for principal
shortfalls according to an embodiment of the invention;
[0012] FIG. 5 depicts a table of calculations of interest
shortfalls according to an embodiment of the invention; and
[0013] FIG. 6 depicts a table of calculations of interest shortfall
reimbursements according to an embodiment of the invention.
DETAILED DESCRIPTION
[0014] Single tranche derivative transactions represent an
intersection of derivative and securitization technologies. In
general, a single tranche derivative transaction is a synthetic
securitization of credit default swaps (CDS). The underlying CDS
for this particular single tranche derivative transaction has
`pay-as-you-go` (PAUG) settlement. The use of PAUG settlement is
generally limited to asset classes such as ABS, Commercial Mortgage
Backed Securities (CMBS), CDO securities, and other securitized
products. In CDS with PAUG settlement, conventional credit events
such as bankruptcy, restructuring and failure to pay are replaced
with credit events that are usually directly linked to differences
between actual and expected cashflows of a reference obligation.
Such credit events include principal shortfalls, writedowns, and
interest shortfalls. In general, a reference portfolio is agreed to
by the counterparties in the credit derivative transaction and
comprised of fixed income securities including but not limited to
corporate bonds/loans, ABS, CMBS, and CDO securities.
[0015] Conventional credit derivative transactions referencing
corporate issuers generally have (i) a fixed tenor (a tenor is the
term or life of a contract) and a notional (which is a nominal
amount underlying a derivatives contract), and (ii) cash or
physical settlement with respect to the entire transaction
following a single credit event. In contrast, credit derivative
transactions with PAUG settlement have (i) a tenor and notional
linked to the respective maturity and outstanding principal of a
specific obligation, and (ii) PAUG settlement payments are directly
linked to losses on a specific obligation and recoveries,
reimbursements or other payments on such losses are passed through.
Given the complexity of the underlying derivative, applying
securitization technology on this class of credit derivative
represents a challenging structuring endeavor.
[0016] The securitization framework applied to a single tranche
synthetic ABS product described herein is that of a sequential pay
structure. Sequential pay entails that interest and principal
collections are distributed from the top of a capital structure to
the bottom; as a result, losses on the portfolio thereby sustained
from bottom to the top.
[0017] One example of a capital structure is provided in FIG. 1. As
shown, a capital structure can have a plurality of tranches, such
as five tranches 15, which can have specified characteristics 90,
such as a notional, attachment point, detachment point, fixed rate,
loss threshold, loss cap, or other characteristics. Among the five
tranches, there is an equity tranche (25), one or more
mezzanine/senior tranches (50), and a super senior tranche 75.
[0018] A translation of sequential pay structure to the single
tranche derivative context would entail the following:
[0019] (i) A portfolio premium is typically allocated sequentially
through the capital structure (e.g., from a senior tranche to a
subordinate tranche). Although there may be a stated accrual rate
for each reference tranche in the capital structure, a tranche swap
premium is typically capped at a remaining portfolio swap premium
after subtracting the swap premium paid to each senior reference
tranche. In general, a credit protection buyer pays the credit
protection seller such tranche swap premium periodically.
[0020] (ii) Principal payments are generally allocated in sequence
(e.g., from a senior most tranche to the subordinate tranches), and
net principal losses are allocated in reverse sequence (e.g., from
a subordinate tranche to the senior tranches). Net principal
reimbursement are allocated in sequence beginning with the most
senior tranche to have been previously impaired, then to a
subordinate tranche. (An impaired tranche is one that has incurred
a principal loss in the form of a principal shortfall or
writedown.) If the net change causes a reference tranche to be
impaired (or further impaired), the credit protection seller makes
a payment to the credit protection buyer. If the net change causes
the reference tranche notional to be reinstated (in part or in
full), the credit protection buyer makes a payment to the credit
protection seller.
[0021] (iii) A net interest shortfall is typically allocated in
reverse sequence (e.g., beginning with a subordinate tranche to the
senior tranches). Net interest shortfall reimbursements are
allocated in sequence beginning with the most senior reference
tranche to have suffered an incurred interest shortfall then to a
subordinate tranche. The allocations of interest shortfalls are
usually based on a distribution of interest income/swap premium
within the capital structure rather than the principal
attachment/detachment points. As illustrated in FIG. 3, which
compares capital structure and corresponding spread distribution,
there are typically disparities between distribution of the risk of
principal loss and available funds cap risk across the capital
structure.
[0022] In general, a credit protection seller may not be required
to make an interest/principal shortfall payment on a particular
tranche unless the net periodic interest shortfall exceeds the sum
of the swap premium of each subordinate reference tranche; and the
amount paid is usually capped at the amount of the swap premium of
such tranche. The credit protection buyer is typically not required
to make a reimbursement payment unless a net periodic interest
shortfall reimbursement exceeds the sum of the cumulative interest
shortfall amount paid under each senior reference tranche (which
may be increased by compound interest); the amount paid may be
capped at the cumulative interest shortfall amounts paid in respect
of such tranche (as increased by compound interest).
[0023] One of the significant improvements with respect to single
tranche products described herein over other single tranche
products in the market is the transaction accounts for the
available funds cap risk (AFC risk) of the ABS securities within
the underlying portfolio and does so in a manner equivalent to a
cash analog based on the same underlying portfolio with sequential
pay structure. Note that AFC risk is expressed in the form of
interest shortfall amounts in the related CDS with PAUG settlement.
Due to the complexities involved in engineering/structuring a
derivative transaction with these features as detailed above,
single tranche products in the market typically do not address AFC
risk or address it in a very limited manner.
[0024] The development of such a single tranche product provides
substantial benefits to both derivative dealers and customers. For
dealers, among other advantages, it minimizes basis risk between
the single tranche transaction and related single name ABS CDS
hedges (which do typically account for AFC risk). For customers,
the single tranche product becomes a perfect substitute for certain
SF CDO securities with all the aforementioned advantages of
derivatives over cash bonds.
[0025] This technology and inventions described herein may be
applied to other asset classes (e.g. CMBS, SF CDOs.) in respect of
which the related derivatives trade with `spay-as you go`
settlement or other settlement methods.
[0026] Swap Premium
[0027] A swap premium may be allocated sequentially through a
capital structure in order beginning with a senior-most tranche to
the subordinate tranches. Although there may be a stated accrual
rate for each reference tranche in the capital structure, the swap
premium for a particular tranche is capped at the remaining
portfolio swap premium after subtracting the swap premium paid to a
senior reference tranche.
[0028] A swap premium of a mezzanine and senior tranche may be
calculated as the lesser of (i) a product of a fixed rate of such
tranche and an outstanding tranche notional, and (ii) the aggregate
portfolio premium net of premium payments allocated to each senior
reference tranche, using the formula:
[ ( OTNA n , t * FR n * ACT 360 ) , max ( AAP - n + 1 m RFA t , 0 )
] . ##EQU00001##
[0029] The swap premium of an equity tranche may be calculated as
the aggregate portfolio premium net of premium payments allocated
to each senior reference tranche, using the formula:
max ( AAP - n + 1 m FA t , 0 ) . ##EQU00002##
[0030] Using such formulas to calculate a swap premium allows,
among other things, a fully (or partially) impaired equity tranche
to receive periodic premium payments despite full (or substantially
full) principal loss.
[0031] Principal
[0032] Principal payments are typically allocated in sequence
beginning with the senior-most tranche to the subordinate tranches.
The outstanding tranche notional amount of a tranche is calculated
based on an original notional, incurred principal losses, incurred
principal reimbursements, the excess of aggregate principal
payments on the reference portfolio over the initial portfolio size
less the loss cap, using the formula:
max[(OTN.sub.n*ITF.sub.n)-.SIGMA.IPL.sub.n+.SIGMA.IPR.sub.n-max(.SIGMA.P-
P-IPS+LC.sub.n,0),0].
[0033] Principal losses are typically allocated in the capital
structure in a reverse sequence beginning with the most subordinate
tranche to the senior tranches. Incurred principal losses with
respect to a tranche may be calculated as an amount equal to the
lesser of: (i) aggregate periodic principal losses minus aggregate
periodic principal reimbursements (subject to a minimum of zero);
and (ii) the aggregate principal loss amount minus the principal
loss threshold of such tranche, (subject to a minimum of zero); and
(iii) the outstanding tranche notional amount of such tranche from
the previous accrual period, using the formula:
min(max(PPL.sub.l-PPR.sub.l,0), max(APL.sub.l-LT.sub.n),
OTNA.sub.l-1).
[0034] Principal reimbursements are typically allocated in a
sequence beginning with the most senior tranche to have been
previously impaired prior to a payment date. Generally, an incurred
principal reimbursement amount with respect to a tranche is
calculated based on the lesser of: (i), aggregate periodic
principal reimbursement amounts, minus aggregate periodic principal
loss amounts, minus, the excess of aggregate principal losses over
the loss cap; and, (ii) the difference of sum of all incurred
principal losses as of the current accrual period and the sum of
all incurred principal reimbursements as of the prior accrual
period, using the formula:
min(max(PPR.sub.t-PPL.sub.t-max(APL.sub.t-1-LC.sub.i,0),0),
max(.SIGMA.IPL.sub.t-.SIGMA.IPR.sub.t-1,0))
[0035] If a net change in principal, or other measurement of a
reference tranche causes the transacted or reference tranche to be
impaired (or further impaired), a credit protection seller may make
a payment to a credit protection buyer that equals the incurred
principal loss (using, for example, the above formula). If the net
change causes the reference tranche notional to be reinstated or
restored (in part or in full), the credit protection buyer may make
a payment to the credit protection seller equal to an incurred
principal reimbursement (using, for example, the above formula).
Examples of calculations of principal shortfall calculations for a
particular tranche of the capital structure are shown in FIG.
4.
[0036] Interest Shortfalls
[0037] Typically, interest shortfalls are allocated in a reverse
sequence beginning with the most subordinate reference tranche. To
the extent that a shortfall exists, under a single tranche
transaction, a credit protection seller would not be required to
make an interest shortfall payment unless a net interest shortfall
for a particular period exceeds a certain interest shortfall
threshold and such interest shortfall payment may also be subject
to an interest shortfall cap, such amount, an incurred interest
shortfall amount.
[0038] The incurred interest shortfall amount for the transacted
tranche may be calculated as a lesser of (i) a net periodic
interest shortfall less the interest shortfall threshold, and (ii)
the interest shortfall cap, using the formula:
min(max(PIS.sub.t-PISR.sub.t-IST.sub.n,t, 0), ISC.sub.n,t)
[0039] The incurred interest shortfall amount for each reference
tranche may be calculated as a lesser of (i) a net periodic
interest shortfall less an aggregate periodic premium payment of
each subordinate reference tranche, and (ii) the periodic premium
payment of such reference tranche, using the formula:
min ( max ( PIS t - PISR t - 0 i - 1 RFA t , 0 ) , RFA i , t ) .
##EQU00003##
[0040] The inputs required to determine the incurred interest
shortfalls include the following which may be calculated using the
representative formulas:
Interest Shortfall Threshold = 0 n - 1 RFA t . ##EQU00004##
[0041] Reference Tranche Fixed Amounts:
min [ ( S i * OTW i * IPS * ACT 360 ) , max ( AAP t - t + 1 m RFA t
, 0 ) ] . ##EQU00005##
[0042] The inputs required to determine the reference tranche fixed
amounts include the following which may be calculated using the
representative formulas:
outstanding tranche width=max[min(OPP,
X,.sub.i+1)-max(X.sub.i,ALP),0]
aggregate asset premium = PRS * OPS t * ACT 360 ##EQU00006##
[0043] Interest Shortfall Reimbursements
[0044] Interest shortfall reimbursements may be allocated in
sequence beginning with a most senior reference tranche to have
suffered an incurred interest shortfall prior to such payment date.
A credit protection buyer may not be required to make a
reimbursement payment unless or until a net interest shortfall
reimbursement for a particular period is greater than the incurred
interest shortfall amount. Payments in respect of interest
reimbursement typically do not exceed a cumulative incurred
interest shortfall of a reference/transacted tranche. To simulate
the effect of deferred or defaulted interest within hypothetical
securitization structure, cumulative incurred interest shortfalls
for each tranche are increased by compounded interest each accrual
period they remain unreimbursed
[0045] Incurred interest shortfall reimbursement amount for the
transacted tranche calculated as a lesser of (i) the net periodic
interest shortfall reimbursement less a cumulative excess interest
shortfall amount, and (ii) a product of the cumulative incurred
interest shortfall from the previous period and a compounding
factor of the transacted tranche, using the formula:
min(max(PISR.sub.t-PIS.sub.t-CEIS.sub.n,t,0),
CIIS.sub.n,t-1*ISCF.sub.n,t).
[0046] Incurred interest shortfall reimbursement amount for a
reference tranche is calculated as a lesser of (i) a net periodic
interest shortfall reimbursement less a cumulative excess interest
shortfall amount of each reference tranche, and (ii) a product of a
cumulative incurred interest shortfall of each reference tranche
from a prior period and a compounding factor of such reference
tranche, using the formula:
min ( max ( PISR t - PIS t - i + 1 m ( RCIIS t - 1 * RISCF t ) , 0
) , RCIIS i , t - 1 * RISCF i , t ) . ##EQU00007##
[0047] The inputs required to determine the incurred interest
shortfalls include the following which may be calculated using the
representative formulas:
Cumulative Excess Interest Shortfall Amount = n + 1 m RCIIS t .
##EQU00008##
Cumulative Incurred Interest Shortfall Amount for the transacted
tranche=IIS.sub.n,t-IISR.sub.n,t+(CIIS.sub.n,t-1*ISCF.sub.n,t)
Cumulative Incurred Interest Shortfall Amount for a reference
tranche=RIIS.sub.i,l-RIISR.sub.i,l+(RCIIS.sub.i,l-1*RISCF.sub.i,l)
Compounding Factor = 100 % + ( FR n + LIBOR t ) * ACT 360
##EQU00009## Reference Tranche Compounding Factor = 100 % + ( S i +
LIBOR t ) * ACT 360 ##EQU00009.2##
[0048] An exemplary embodiment of the transaction is described in
termsheet attached as Appendix A according to the following terms
and conditions tor a single tranche synthetic ABS transaction. A
swap confirmation template utilized by derivative counterparties in
connection with the execution of this single tranche synthetic ABS
transaction is attached as Appendix B.
[0049] It will be appreciated that the present invention has been
described by way of example only, and that improvements and
modifications may be made to the invention without departing from
the scope or spirit thereof. v,1-34/2
* * * * *