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:

analyzing the portfolio including the plurality of financial instruments, wherein analyzing further comprises:

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, wherein 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;

calculating residuals and volatilities for 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 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 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 1 , wherein 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 standardized version of the residuals is 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 plurality of credit default swap instruments within a portfolio, the method comprising:

determining a correlated time-series of returns based on a pair of time-series of returns for the plurality of credit default swap, wherein the time-series of returns are captured at different times;

analyzing the correlated time-series of returns based on an autoregression model, wherein the autoregression model produces a time-series of expected returns for each of the credit default swap instruments in the portfolio;

calculating residual and volatility data associated with the time-series of expected returns for each of the credit default swap instruments in the portfolio

standardizing the residual and volatility data determined from a GJR-GARCH model to simulate noise associated with each residual;

applying an 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.

9. The computer-implemented method of claim 8 , 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 8 , 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 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 8 , 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 8 , wherein generating a spread distribution for the portfolio includes iteratively repricing each of the plurality of credit default swap instruments within the portfolio.

13. The computer-implemented method of claim 8 , wherein the simulated standardized residuals are generated utilizing a Cholesky decomposition and the correlation matrix and degrees-of-freedom.

14. The computer-implemented method of claim 8 , 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.

15. The computer-implemented method of claim 14 , wherein the first time is defined as one day before the second time period.

16. 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:

calculate 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;

determine 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;

standardize the correlated time-series of returns 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.

17. The system of claim 16 , wherein, wherein the credit derivative comprises a credit default swap.

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

20. The computer-implemented method of claim 16 , wherein the standardized version of the residuals is determined as a function of the standard deviation associated with each financial instrument within the portfolio.