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

• US 8,321,333 B2
• Filed: 01/24/2012
• Issued: 11/27/2012
• 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:
  US13/357,261
• Publication Number:
  US 20120130923A1
• Time in Patent Office: 308 Days
• Field of Search: 705 35- 40
• US Class Current: 705/37
• CPC Class Codes: G06Q 40/00 Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• CPC Class Codes: G06Q 40/04 Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

Determination of a margin requirement associated with a plurality of financial instruments within a portfolio is disclosed for analyzing the portfolio including determining a first and second time-series of returns for the financial instruments, where the second time-series occurs after the first, and calculating the correlation between the first and second time-series of returns. The system and method further implement calculating residuals and volatilities for the 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 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:

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

_t²=K+δ

σ

_t-1²+α

ε

_t-1²+φ

ε

_t-1²I_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:

10. The computer-implemented method of claim 8, 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-1²I_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.