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.

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: 
         [0000]    
       
         
           
             
               [ 
               
                 
                   ( 
                   
                     
                       OTNA 
                       
                         n 
                         , 
                         t 
                       
                     
                     * 
                     
                       FR 
                       n 
                     
                     * 
                     
                       ACT 
                       360 
                     
                   
                   ) 
                 
                 , 
                 
                   max 
                   ( 
                   
                     
                       AAP 
                       - 
                       
                         
                           ∑ 
                           
                             n 
                             + 
                             1 
                           
                           m 
                         
                          
                         
                             
                         
                          
                         
                           RFA 
                           t 
                         
                       
                     
                     , 
                     0 
                   
                   ) 
                 
               
               ] 
             
             . 
           
         
       
     
         [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: 
         [0000]    
       
         
           
             
               max 
               ( 
               
                 
                   AAP 
                   - 
                   
                     
                       ∑ 
                       
                         n 
                         + 
                         1 
                       
                       m 
                     
                      
                     
                         
                     
                      
                     
                       FA 
                       t 
                     
                   
                 
                 , 
                 0 
               
               ) 
             
             . 
           
         
       
     
         [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: 
         [0000]      max[(OTN n *ITF n )−ΣIPL n +ΣIPR n −max(ΣPP−IPS+LC 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: 
         [0000]      min(max(PPL l −PPR l ,0), max(APL l −LT n ), OTNA 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: 
         [0000]      min(max(PPR t −PPL t −max(APL t-1 −LC i ,0),0), max(ΣIPL t −ΣIPR 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 t -PISR t -IST n,t , 0), ISC 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: 
         [0000]    
       
         
           
             
               min 
                
               
                 ( 
                 
                   
                     max 
                      
                     
                       ( 
                       
                         
                           
                             PIS 
                             t 
                           
                           - 
                           
                             PISR 
                             t 
                           
                           - 
                           
                             
                               ∑ 
                               0 
                               
                                 i 
                                 - 
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             
                               RFA 
                               t 
                             
                           
                         
                         , 
                         0 
                       
                       ) 
                     
                   
                   , 
                   
                     RFA 
                     
                       i 
                       , 
                       t 
                     
                   
                 
                 ) 
               
             
             . 
           
         
       
     
         [0040]    The inputs required to determine the incurred interest shortfalls include the following which may be calculated using the representative formulas: 
         [0000]    
       
         
           
             
               Interest 
                
               
                   
               
                
               Shortfall 
                
               
                   
               
                
               Threshold 
             
             = 
             
               
                 ∑ 
                 0 
                 
                   n 
                   - 
                   1 
                 
               
                
               
                   
               
                
               
                 
                   RFA 
                   t 
                 
                 . 
               
             
           
         
       
     
         [0041]    Reference Tranche Fixed Amounts: 
         [0000]    
       
         
           
             
               min 
               [ 
               
                 
                   ( 
                   
                     
                       S 
                       i 
                     
                     * 
                     
                       OTW 
                       i 
                     
                     * 
                     IPS 
                     * 
                     
                       ACT 
                       360 
                     
                   
                   ) 
                 
                 , 
                 
                   max 
                   ( 
                   
                     
                       
                         AAP 
                         t 
                       
                       - 
                       
                         
                           ∑ 
                           
                             t 
                             + 
                             1 
                           
                           m 
                         
                          
                         
                             
                         
                          
                         
                           RFA 
                           t 
                         
                       
                     
                     , 
                     0 
                   
                   ) 
                 
               
               ] 
             
             . 
           
         
       
     
         [0042]    The inputs required to determine the reference tranche fixed amounts include the following which may be calculated using the representative formulas: 
         [0000]      outstanding tranche width=max[min(OPP, X, i+1 )−max( X   i ,ALP),0] 
         [0000]    
       
         
           
             
               aggregate 
                
               
                   
               
                
               asset 
                
               
                   
               
                
               premium 
             
             = 
             
               PRS 
               * 
               
                 OPS 
                 t 
               
               * 
               
                 ACT 
                 360 
               
             
           
         
       
     
         [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: 
         [0000]      min(max(PISR t −PIS t −CEIS n,t ,0), CIIS n,t-1   *ISCF   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: 
         [0000]    
       
         
           
             
               min 
                
               
                 ( 
                 
                   
                     max 
                      
                     
                       ( 
                       
                         
                           
                             
                               
                                 PISR 
                                 t 
                               
                               - 
                               
                                 PIS 
                                 t 
                               
                               - 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     + 
                                     1 
                                   
                                   m 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       RCIIS 
                                       
                                         t 
                                         - 
                                         1 
                                       
                                     
                                     * 
                                     
                                       RISCF 
                                       t 
                                     
                                   
                                   ) 
                                 
                               
                               , 
                               0 
                             
                           
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       RCIIS 
                       
                         i 
                         , 
                         
                           t 
                           - 
                           1 
                         
                       
                     
                     * 
                     
                       RISCF 
                       
                         i 
                         , 
                         t 
                       
                     
                   
                 
                 ) 
               
             
             . 
           
         
       
     
         [0047]    The inputs required to determine the incurred interest shortfalls include the following which may be calculated using the representative formulas: 
         [0000]    
       
         
           
             
               Cumulative 
                
               
                   
               
                
               Excess 
                
               
                   
               
                
               Interest 
                
               
                   
               
                
               Shortfall 
                
               
                   
               
                
               Amount 
             
             = 
             
               
                 ∑ 
                 
                   n 
                   + 
                   1 
                 
                 m 
               
                
               
                 
                   RCIIS 
                   t 
                 
                 . 
               
             
           
         
       
     
         [0000]      Cumulative Incurred Interest Shortfall Amount for the transacted tranche=IIS n,t −IISR n,t +(CIIS n,t−1 *ISCF n,t ) 
         [0000]      Cumulative Incurred Interest Shortfall Amount for a reference tranche=RIIS i,l −RIISR i,l +(RCIIS i,l−1 *RISCF i,l ) 
         [0000]    
       
         
           
             
                 
             
              
             
               
                 Compounding 
                  
                 
                     
                 
                  
                 Factor 
               
               = 
               
                 
                   100 
                    
                   % 
                 
                 + 
                 
                   
                     ( 
                     
                       
                         FR 
                         n 
                       
                       + 
                       
                         LIBOR 
                         t 
                       
                     
                     ) 
                   
                   * 
                   
                     ACT 
                     360 
                   
                 
               
             
           
         
       
       
         
           
             
               Reference 
                
               
                   
               
                
               Tranche 
                
               
                   
               
                
               Compounding 
                
               
                   
               
                
               Factor 
             
             = 
             
               
                 100 
                  
                 % 
               
               + 
               
                 
                   ( 
                   
                     
                       S 
                       i 
                     
                     + 
                     
                       LIBOR 
                       t 
                     
                   
                   ) 
                 
                 * 
                 
                   ACT 
                   360 
                 
               
             
           
         
       
     
         [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