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

• US 8,131,634 B1
• Filed: 10/27/2011
• Issued: 03/06/2012
• Est. Priority Date: 09/15/2009
• Status: Active Grant

• Current Assignee: Chicago Mercantile Exchange, Inc. (CME Group Incorporated)
• Original Assignee: Chicago Mercantile Exchange, Inc. (CME Group Incorporated)
• Inventors: Shah, Pavan
• Primary Examiner(s): Havan, Thu Thao
• Application Number:
  US13/283,204
• Publication Number:
  US 20120041898A1
• Time in Patent Office: 131 Days
• Field of Search: 705 35- 37
• US Class Current: 705/37
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

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.

Claims

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:

9. The computer-implemented method of claim 7, wherein Glosten-Jagannathan-Runkle generalized autoregressive conditional heteroskedasticity (GJR-GARCH) model is represented as:

σ

_t²=K+δ

σ

_t-1²+α

ε

_t-1²+φ

ε

_t-1I_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.