System and method for determining the market risk margin requirements associated with a credit default swap

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.

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 the credit derivative 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 4 , wherein calculating residuals and volatilities further comprises:

applying an autoregression model to each of the time-series of returns; and

applying a Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model to the time-series of returns.

6. The computer-implemented method of claim 1 , wherein the standardized version of the residuals is determined as a function of the standard deviation associated with each financial instrument within the portfolio.

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:

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.

8. The computer-implemented method of claim 7 , wherein the auto-regression 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.

9. The computer-implemented method of claim 7 , wherein 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 I t-1

where σ t is the time-dependent standard deviation, ε t is the return residual, ε t is the return residual equals the time-dependent standard deviation σ t multiplied by a random number selected from a Gaussian distribution, the variable K is a constant, δ is the GARCH parameter, α is the ARCH parameter, is the leverage parameter, and I is the indicator parameter.

10. The computer-implemented method of claim 7 , wherein generating simulated returns includes replicating joint movements between each of the plurality of credit default swap instruments within the portfolio.

11. The computer-implemented method of claim 7 , wherein generating a spread distribution for the portfolio includes iteratively repricing each of the plurality of credit default swap instruments within the portfolio.

12. The computer-implemented method of claim 7 , wherein the simulated standardized residuals are generated utilizing a Cholesky decomposition and the correlation matrix and degrees-of-freedom.

13. A system for determining a margin requirement associated with a plurality of financial instruments 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:

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.

14. The system of claim 13 , wherein at least one of the plurality of financial products comprises a credit derivative.

15. The system of claim 14 , wherein, wherein the credit derivative comprises a credit default swap.

16. The computer-implemented method of claim 13 , wherein the residuals and volatilities are calculated as a function of an autocorrelation function utilizing the time-series of returns.

17. The computer-implemented method of claim 16 , 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.

18. The computer-implemented method of claim 13 , wherein the standardized version of the residuals is determined as a function of the standard deviation associated with each financial instrument within the portfolio.