Dynamic credit spread model

1. A system for valuing a credit hybrid, the system comprising:

at least one processor; and

at least one computer readable memory unit in communication with the at least one processor, wherein the at least one memory unit comprises computer instructions which, when executed by the at least one processor, cause the at least one processor to calculate a value for the credit hybrid based on a forward hazard rate model that models the forward hazard rate based on a stochastic differential equation that includes a jump term for the hazard rate, wherein the jump term is based on a non-negative function of the hazard rate and a discontinuous process and wherein the stochastic differential equation additionally includes a drift term for the hazard rate and a Brownian motion term for the forward hazard rate, and wherein the stochastic differential equation is:

dh tT =μ tT h dt+σ tT h dB t h +G ( h tT ) dN t

where T is the maturity of a corresponding hazard rate, μ tT h is a drift term, σ tT h is a hazard rate volatility, B t h is a continuous-time Brownian motion function, G(h tT ) is a non-negative function of the hazard rate h tT , and N t is a discontinuous process with frequency λ, and G(h tT )dN t is the jump term.

2. The system of claim 1 , wherein the at least one memory unit further comprises computer instructions which, when executed by the at least one processor, cause the at least one processor to calibrate the forward hazard rate model.

3. The system of claim 2 , further comprising a database in communication with the at least one processor for storing calibration data used to calibrate the forward hazard rate model.

4. The system of claim 1 , wherein the discontinuous process is a Poisson process.

5. A system for valuing a credit hybrid, the system comprising:

at least one processor;

a database in communication with the at least one processor, wherein the database comprises calibration data, and

at least one computer readable memory unit in communication with the at least one processor and the database, wherein the at least one memory unit comprises computer instructions which, when executed by the at least one processor, cause the at least one processor to:

calibrate, using the calibration data stored in the database, a forward hazard rate model that models the forward hazard rate based on a stochastic differential equation that includes a jump term for the hazard rate, wherein the jump term is based on a non-negative function of the hazard rate and a discontinuous process, wherein the stochastic differential equation additionally includes a drift term for the hazard rate and a Brownian motion term for the forward hazard rate, wherein the stochastic differential equation is:

dh tT =μ tT h dt+σ tT h dB t h +G ( h tT ) dN t

where T is the maturity of a corresponding hazard rate, μ tT h is a drift term, σ tT h is a hazard rate volatility, B t h is a continuous-time Brownian motion function, G(h tT ) is a non-negative function of the hazard rate h tT , and N t is a discontinuous process with frequency λ, and G(h tT )dN t is the jump term; and

calculate a value for the credit hybrid based on the calibrated forward hazard rate model.

6. The system of claim 5 , wherein the at least one processor is programmed to calculate the value of the credit hybrid based on Monte Carlo simulations.

7. The system of claim 6 , wherein the at least one processor is programmed to calibrate the forward hazard rate model based on Monte Carlo simulations.

8. The system of claim 5 , wherein the discontinuous process is a Poisson process.

9. An article comprising a computer readable medium having stored thereon instructions, which when executed by a processor cause the processor to calculate a value of a credit hybrid by:

calibrating a forward hazard rate model that models the forward hazard rate based on a stochastic differential equation that includes a jump term for the hazard rate, wherein the stochastic differential equation is:

dh tT =μ tT h dt+σ tT h dB t h +G ( h tT ) dN t

where T is the maturity of a corresponding hazard rate, μ tT h is a drift term, σ tT h is a hazard rate volatility, B t h is a continuous-time Brownian motion function, G(h tT ) is a non-negative function of the hazard rate h tT , and N t is a discontinuous process with frequency λ, and G(h tT )dN t is the jump term; and

calculating the value for the credit hybrid based on the calibrated forward hazard rate model.

10. The article of claim 9 , wherein the discontinuous process is a Poisson process.

11. A method of calculating a value of a credit hybrid comprising:

calibrating, with a processor, a forward hazard rate model that models the forward hazard rate based on a stochastic differential equation that includes a jump term for the hazard rate, wherein the jump term is based on a non-negative function of the hazard rate and a discontinuous process and wherein the stochastic differential equation additionally includes a drift term for the hazard rate and a Brownian motion term for the forward hazard rate, and wherein the stochastic differential equation is:

dh tT =μ tT h dt+σ tT h dB t h +G ( h tT ) dN t

where T is the maturity of a corresponding hazard rate, μ tT h is a drift term, σ tT h is a hazard rate volatility, B t h is a continuous-time Brownian motion function, G(h tT ) is a non-negative function of the hazard rate h tT , and N t is a discontinuous process with frequency λ, and G(h tT )dN t is the jump term;

calculating, with the processor, the value for the credit hybrid based on the calibrated forward hazard rate model; and

storing the value of the credit hybrid.

12. The method of claim 11 , wherein calculating the value of the credit hybrid comprises calculating the value of the credit hybrid using Monte Carlo simulations.

13. The method of claim 11 , wherein calibrating the forward hazard rate model comprises calibrating the forward hazard rate model using Monte Carlo simulations.

14. The method of claim 11 , further comprising, after calculating the value of the credit hybrid, making a trade to hedge the credit hybrid.

15. The method of claim 11 , wherein the discontinuous process is a Poisson process.