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, the determining 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 a 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, and 
 calculating the first risk value based on the correlation, the residuals, and the volatilities; and 
   calculating, by the processor, a multi-factor risk margin requirement based on at least the first risk value.   
     
     
         2 . The computer-implemented method of  claim 1 , wherein the calculating the first risk value comprises:
 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
 wherein the calculating the first risk value is based on a risk percentile associated with the spread distribution. 
   
     
     
         3 . The computer-implemented method of  claim 2 , wherein the plurality of standardized residuals are determined as a function of the standard deviation associated with each financial instrument within the portfolio. 
     
     
         4 . The computer-implemented method of  claim 1 , further comprising:
 determining 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 wherein the calculating a multi-factor risk margin requirement further comprises calculating the multi-factor risk margin requirement based on at least the first risk value and the second risk value.   
     
     
         5 . 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.   
     
     
         6 . 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.   
     
     
         7 . 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;   φ is the leverage parameter; and   I is the indicator parameter.   
     
     
         8 . A computer readable memory including instructions 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, that when executed on a computer are operable to cause the computer to:
 receive a plurality of data associated with the plurality of financial instruments within the portfolio;   determine a first time-series of returns for the first portion of the plurality of financial instruments;   determine 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;   calculate a correlation between the first time-series of returns and the second time-series of returns;   calculate 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;   calculate a first risk value based on the correlation, the residuals, and the volatilities; and   calculate a multi-factor risk margin requirement based on at least the first risk value.   
     
     
         9 . The computer readable memory of  claim 8 , wherein the instructions are further configured to:
 calculate 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,   generate simulated returns as a function of the simulated standardized residuals and the returns,   generate a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns, and   wherein the first risk value calculation is based on a risk percentile associated with the spread distribution.   
     
     
         10 . The computer readable memory of  claim 9 , wherein the plurality of standardized residuals are determined as a function of the standard deviation associated with each financial instrument within the portfolio. 
     
     
         11 . The computer readable memory of  claim 8 , wherein the instructions are further configured to:
 determine 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 wherein the multi-factor risk margin requirement is calculated based on at least the first risk value and the second risk value.   
     
     
         12 . The computer readable memory of  claim 8 , wherein the residuals and the volatilities further are calculated through the application of an autocorrelation function to the time-series of returns for the plurality of financial instruments within the portfolio. 
     
     
         13 . The computer readable memory of  claim 8 , wherein the residuals and volatilities are calculated through the application of an autoregression model to the first time-series of returns and second time-series of returns, and a Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model to the first time-series of returns. 
     
     
         14 . The computer readable memory of  claim 13 , 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;   φ is the leverage parameter; and   I is the indicator parameter.   
     
     
         15 . A system for determining a margin requirement associated with a plurality of credit derivatives within a portfolio, the system comprising:
 a memory operable to store a plurality of data associated with the plurality of financial instruments within the portfolio;   a processor, in communication with the memory, and configured to:
 determine a first time-series of returns for the first portion of the plurality of financial instruments; 
 determine 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; 
 calculate a correlation between the first time-series of returns and the second time-series of returns; 
 calculate 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; 
 calculate a first risk value based on the correlation, the residuals, and the volatilities; and 
 calculate a multi-factor risk margin requirement based on at least the first risk value. 
   
     
     
         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 the first time is defined as one day before the second time period. 
     
     
         18 . The system 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. 
     
     
         19 . The system of  claim 15 , wherein the processor is further configured to:
 calculate 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,   generate simulated returns as a function of the simulated standardized residuals and the returns,   generate a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns, and   wherein the first risk value calculation is based on a risk percentile associated with the spread distribution.   
     
     
         20 . The system of  claim 19 , wherein the plurality of standardized residuals are determined as a function of a standard deviation associated with each financial instrument within the portfolio.