Cox-Ingersoll-Ross Model
Posted: Wed Feb 20, 2013 11:24 am
Hello,
in quantitative finance, there are two groups of models for stochastic interest rates and the term-structure. The basis of the first group is Vasicek, "An Equilibrium Characterisation of the Term Structure", in: Journal of Financial Economics 5 (1977), pp. 177–188. Vasicek assumes that interest rates follow an Ornstein-Uhlenbeck mean reverting process. The second group is based on Cox, Ingersoll and Ross, "A Theory of the Term Structure of Interest Rates", in Econometrica 53 (1985), pp. 363-384. CIR apply a mean-reverting square root process. Both models could be estimated by state space models and there are some working papers and articles available estimating the models empirically by Kalman filters. As the Vasicek model assumes that the error terms are normally distributed, it is not a problem to estimate this model with the dlm instruction in RATS.
However, the problem is the CIR model. Chen and Scott, "Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model", in: The Journal of Real Estate Finance and Economics 27 (2003), pp.143-172, point out that the residuals of the mean-reverting square root process follow a non-central chi-squared distribution and estimate the model by an extended Kalman filter.
My question is, how could I estimate a CIR model with an extended Kalman filter in RATS. Has anybody already replicated a CIR model presented in the literature?
Best regards
Peter
in quantitative finance, there are two groups of models for stochastic interest rates and the term-structure. The basis of the first group is Vasicek, "An Equilibrium Characterisation of the Term Structure", in: Journal of Financial Economics 5 (1977), pp. 177–188. Vasicek assumes that interest rates follow an Ornstein-Uhlenbeck mean reverting process. The second group is based on Cox, Ingersoll and Ross, "A Theory of the Term Structure of Interest Rates", in Econometrica 53 (1985), pp. 363-384. CIR apply a mean-reverting square root process. Both models could be estimated by state space models and there are some working papers and articles available estimating the models empirically by Kalman filters. As the Vasicek model assumes that the error terms are normally distributed, it is not a problem to estimate this model with the dlm instruction in RATS.
However, the problem is the CIR model. Chen and Scott, "Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model", in: The Journal of Real Estate Finance and Economics 27 (2003), pp.143-172, point out that the residuals of the mean-reverting square root process follow a non-central chi-squared distribution and estimate the model by an extended Kalman filter.
My question is, how could I estimate a CIR model with an extended Kalman filter in RATS. Has anybody already replicated a CIR model presented in the literature?
Best regards
Peter