System and method for determining the market risk margin requirements associated with a credit default swap
First Claim
1. A computer-implemented method for determining a margin requirement associated with a plurality of financial instruments within a portfolio, the method comprising:
- determining a time-series of returns for the plurality of financial instruments within the portfolio;
calculating residuals and volatilities for the plurality of financial instruments within the portfolio as a function of the determined the time-series of returns;
applying a student-t copula to a standardized version of the calculated residuals to determine a correlation matrix and degrees-of-freedom utilized 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 returns;
generating a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns; and
calculating a margin risk based on a risk percentile associated with the spread distribution.
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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 determining a time-series of returns for the plurality of financial instruments within the portfolio, calculating residuals and volatilities for the plurality of financial instruments within the portfolio as a function of the determined the time-series of returns, applying a student-t copula to a standardized version of the calculated residuals to determine 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 returns, generating a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns, and calculating a margin risk based on a risk percentile associated with the spread distribution.
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Citations
18 Claims
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1. A computer-implemented method for determining a margin requirement associated with a plurality of financial instruments within a portfolio, the method comprising:
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determining a time-series of returns for the plurality of financial instruments within the portfolio; calculating residuals and volatilities for the plurality of financial instruments within the portfolio as a function of the determined the time-series of returns; applying a student-t copula to a standardized version of the calculated residuals to determine a correlation matrix and degrees-of-freedom utilized 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 returns; generating a spread distribution for the portfolio, wherein the portfolio is repriced as a function of the simulated returns; and calculating a margin risk based on a risk percentile associated with the spread distribution. - View Dependent Claims (2, 3, 4, 5, 6)
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7. A computer-implemented method for determining a margin requirement associated with a plurality of credit default swap instruments within a portfolio, the method comprising:
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determining a time-series of returns for the plurality of instruments within the portfolio; applying an autocorrelation function to the determined time-series of returns; implementing an autoregression model as a function of the time-series of returns, wherein the autoregression model produces a correlated time-series of expected returns for each of the credit default swap instruments in the portfolio; implementing a Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) model utilizing the correlated time-series of expected returns, wherein the model describes volatility associated with the credit default swap instruments within the portfolio; standardizing the residual and volatility data determined from the GJR-GARCH model to simulate noise associated with each residual; applying the autocorrelation function to the standardized residuals and a square of the standardized residuals; calibrating a student-t copula to the correlated standardized residual data 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 repriced as a function of the simulated returns; and calculating a margin risk based on a risk percentile associated with the spread distribution. - View Dependent Claims (8, 9, 10, 11, 12)
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13. A system for determining a margin requirement associated with a plurality of financial instruments within a portfolio, the system comprising:
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a processor; a memory in communication with the processor, wherein the memory is configured to stored processor-executable instructions to; determine a time-series of returns for the plurality of financial instruments within the portfolio; calculate residuals and volatilities for the time-series of returns for the plurality of financial instruments within the portfolio; apply a student-t copula to a standardized version of the calculated residuals to determine a correlation matrix and degrees-of-freedom; simulate standardized residuals for each of the plurality of financial instruments within the portfolio as a function of the correlation matrix and degrees-of-freedom; 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 calculate a margin risk based on a risk percentile associated with the spread distribution. - View Dependent Claims (14, 15, 16, 17, 18)
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Specification