Pranab K. Mandal, Dmitri Danilov
We consider continuous time short rate model. While a number of methods exist for the estimation of the parameters of such models, the estimation of the possible latent factors (e.g., stochastic volatility) in the model has received relatively little attention.
When the underlying setup is nonlinear and non-Gaussian the most frequently used extended Kalman filter (EKF) leads to inconsistent estimate of the parameters, though without high bias (de Jong (2000)). We use the Kitagawa type stochastic filtering algorithm, which provides a method to obtain the likelihood function deterministically, to estimate the model and the unobserved components.
Comparison on simulated data shows that the Kitagawa method provides better results than EKF for the parameter values atypical in financial applications. In cross-sectional estimation use of the Kitagawa method solves the inconsistency problem of EKF without needing to apply numerically more demanding methods such as efficient method of moments or indirect inference method.