System and Method for Determining the Market Risk Margin Requirements Associated with a Credit Default Swap

Abstract

A system and computer-implemented method for determining a margin requirement associated with a plurality of financial instruments within a portfolio is disclosed. The system and method implement steps and procedures for analyzing the portfolio including the plurality of financial instruments where analyzing further includes determining a first time-series of returns for the plurality of financial instruments, determining a second time-series of returns for the plurality of financial instruments where the second time-series occurs after the first time-series, and calculating the correlation between the first time-series of returns and the second time-series of returns. The system and method implement further steps and procedures for calculating residuals and volatilities for the plurality of financial instruments within the portfolio.

What is claimed is: 
     
         1 . A computer-implemented method for determining a multi-factor risk margin requirement associated with a portfolio comprising one or more positions with respect to a plurality of financial instruments, the method comprising:
 receiving a plurality of data associated with the plurality of financial instruments within the portfolio;   determining, by a processor, a first risk value based on at least a first portion of the received plurality of data, comprising:
 determining a first time-series of returns for the first portion of the plurality of financial instruments, 
 determining a second time-series of returns for the first portion of the plurality of financial instruments, wherein the second time-series occurs after the first time-series, 
 calculating the correlation between the first time-series of returns and the second time-series of returns, 
 calculating residuals and volatilities for the first portion of the plurality of financial instruments within the portfolio as a function of the first time-series of returns, 
 calculating a correlation matrix and degrees-of-freedom utilized to simulate standardized residuals for each of the first portion of the plurality of financial instruments within the portfolio, 
 generating simulated returns as a function of the simulated standardized residuals and the returns, 
 generating a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns, and 
 calculating the first risk value based on a risk percentile associated with the spread distribution; 
   determining, by the processor, a second risk value based on at least a second portion of the received plurality of data, the second risk margin characterizing the risk within a specific segment of a market; and   calculating a multi-factor risk margin requirement based on at least the first risk value and the second risk value.   
     
     
         2 . The computer-implemented method of  claim 1 , wherein at least one of the plurality of financial product comprises a credit derivative. 
     
     
         3 . The computer-implemented method of  claim 2 , wherein each of the plurality of credit derivatives comprises a credit default swap. 
     
     
         4 . The computer-implemented method of  claim 1 , wherein calculating residuals and volatilities further comprises:
 applying an autocorrelation function to the time-series of returns for the plurality of financial instruments within the portfolio.   
     
     
         5 . The computer-implemented method of  claim 1 , wherein calculating residuals and volatilities further comprises:
 applying an autoregression model to the first time-series of returns and second time-series of returns; and   applying a Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model to the first time-series of returns.   
     
     
         6 . The computer-implemented method of  claim 5 , wherein the GJR-GARCH model is represented as:
   σ t   2   =K+δσ   t-1   2 +αε t-1   2 +φε t-1   2   I   t-1  
   where σ t  is the time-dependent standard deviation,   ε t  is the return residual which ε t  is the return residual equals the time-dependent standard deviation σ t  multiplied by a random number selected from a Gaussian distribution;   K is a constant;   δ is the GARCH parameter;   α is the ARCH parameter;      is the leverage parameter; and   I is the indicator parameter.   
     
     
         7 . The computer-implemented method of  claim 1 , wherein the plurality of standardized residuals are determined as a function of the standard deviation associated with each financial instrument within the portfolio. 
     
     
         8 . A computer-implemented method for determining a margin requirement associated with a portfolio comprising a plurality of credit default swap instruments, the method comprising:
 receiving a plurality of data associated with a plurality of financial instruments within the portfolio;   determining, using a processor, a systematic risk margin based on at least a portion of the received plurality of data, comprising:
 determining a correlated time-series of returns based on a pair of time-series of returns, each captured at a different time, for the plurality of credit default swap instruments, 
 analyzing the correlated time-series of returns based on a time-series of expected returns for each of the credit default swap instruments in the portfolio generated from an autoregression model, 
 calculating one or more residuals and volatilities associated with the time-series of expected returns for each of the credit default swap instruments in the portfolio based on a Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (“GJR-GARCH”) model to simulate noise associated with each of the one or more residuals, 
 standardizing the one or more residuals and volatilities, 
 applying an autocorrelation function to the standardized residuals and a square of the standardized residuals, 
 calibrating a student-t copula to the correlated standardized residuals determined by the autocorrelation function to generate a correlation matrix and degrees-of-freedom in order to simulate standardized residuals for each of the plurality of financial instruments within the portfolio, 
 generating simulated returns as a function of the simulated standardized residuals and the simulated noise, 
 generating a spread distribution for the portfolio, wherein the portfolio is iteratively repriced as a function of the simulated returns, and 
 calculating the systemic risk margin based on a risk percentile associated with the spread distribution, wherein the systemic margin requirement is determined based on the margin risk; 
 determining, using the processor, a curve risk margin based on at least a second portion of the received plurality of data; 
 determining, using the processor, a convergence and divergence risk margin based on at least a third portion of the received plurality of data; 
 determining, using the processor, a sector risk margin based on at least a fourth portion of the received plurality of data; 
 determining, using the processor, an idiosyncratic risk margin based on at least a fifth portion of the received plurality of data; 
 determining, using the processor, a liquidity risk margin based on at least a sixth portion of the received plurality of data; 
 determining, using the processor, a basis risk margin based on at least a seventh portion of the received plurality of data; and 
 calculating, using the processor, a multi-factor risk margin based on one more of the determined risk margins. 
   
     
     
         9 . The computer-implemented method of  claim 9 , wherein the autoregression model is represented as: 
       
         
           
             
               
                 X 
                 t 
               
               = 
               
                 c 
                 + 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     p 
                   
                    
                   
                       
                   
                    
                   
                     
                       a 
                       i 
                     
                      
                     
                       X 
                       
                         t 
                         - 
                         i 
                       
                     
                   
                 
                 + 
                 
                   ɛ 
                   t 
                 
               
             
           
         
         where X t  is the time-series of returns; 
         c is a constant; 
         ε t  represents the noise; and 
         a i  to a p  are autoregression parameters. 
       
     
     
         10 . The computer-implemented method of  claim 9 , wherein the Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) model is represented as:
   σ t   2   =K+δσ   t-1   2 +αε t-1   2 +φε t-1   2   I   t-1  
   where σ t  is the time-dependent standard deviation;   ε t  is the return residual that equals the time-dependent standard deviation σ t  multiplied by a random number selected from a Gaussian distribution;   K is a constant;   δ is the GARCH parameter;   α is the ARCH parameter;      is the leverage parameter; and   I is the indicator parameter.   
     
     
         11 . The computer-implemented method of  claim 9 , wherein generating simulated returns includes replicating joint movements between each of the plurality of credit default swap instruments within the portfolio. 
     
     
         12 . The computer-implemented method of  claim 9 , wherein the simulated standardized residuals are generated utilizing a Cholesky decomposition and the correlation matrix and degrees-of-freedom. 
     
     
         13 . The computer-implemented method of  claim 9 , wherein the pair of time-series of returns includes a first time-series of returns determined at a first time and a second time series of returns determined at a second time, and wherein the first time is a time period that occurs before the second time. 
     
     
         14 . The computer-implemented method of  claim 14 , wherein the first time is defined as one day before the second time period. 
     
     
         15 . A system for determining a margin requirement associated with a plurality of credit derivatives within a portfolio, the system comprising:
 a processor;   a memory in communication with the processor, wherein the memory is configured to stored processor-executable instructions to:
 receive a plurality of data associated with the plurality of financial instruments within the portfolio; 
 determine a systematic risk margin based on at least a first portion of the received plurality of data, comprising:
 calculating a degree of similarity between a first time-series of returns for the plurality of credit derivatives and a second, subsequent time-series of returns for the plurality of credit derivatives, 
 determining a correlated time-series of returns based on the first time-series of returns and the calculated degree of similarity, 
 calculate residuals and volatilities for the correlated time-series of returns, 
 standardizing the correlated time-series of returns to determine a correlation matrix and degrees-of-freedom, 
 simulating standardized residuals for each of the plurality of financial instruments within the portfolio as a function of the correlation matrix and degrees-of-freedom, 
 generating simulated returns as a function of the simulated standardized residuals and the returns, 
 generating a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns, and 
 calculating the systemic risk margin based on a risk percentile associated with the spread distribution; 
 
 determine a sector risk margin based on at least a second portion of the received plurality of data; 
 calculate a multi-factor risk margin based on one more of the determined risk factors; and 
 send data indicative of the multi-factor risk margin to an output device. 
   
     
     
         16 . The system of  claim 15 , wherein each of the plurality of credit derivatives comprises a credit default swap. 
     
     
         17 . The system of  claim 15 , wherein instructions are further executable to:
 determine a convergence and divergence risk margin based on at least a third portion of the received plurality of data.   
     
     
         18 . The computer-implemented method of  claim 15 , wherein the degree of similarity is calculated as a function of an autocorrelation function utilizing the first and second time-series of returns. 
     
     
         19 . The computer-implemented method of  claim 15 , wherein the residuals and volatilities are further calculated as a function of an autoregression model and a Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model applied to the time-series of returns. 
     
     
         20 . The computer-implemented method of  claim 15 , wherein the plurality of standardized residuals are determined as a function of the standard deviation associated with each financial instrument within the portfolio.