Application of Filtering Methods in Asset Pricing

Filtering methods such as the Kalman Filter (KF) and its extended algorithms have been widely used in estimating asset pricing models in many topics such as rational stock bubble, interest rate term structure and derivative pricing. The basic idea of filtering is to cast the discrete or continuous time series model of asset prices into a discrete state-space model where the state variables are the latent factors driving the system and the observable variables are usually asset prices. Based on a state-space model, we can choose a specific filtering method to compute its likelihood and estimate unknown parameters using maximum likelihood method. The classical KF can be used to estimate the linear state-space model with Gaussian measurement error. If the model becomes nonlinear, we can rely on Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) or Particle Filter (PF), for estimation. For a piecewise linear state-space model with regime switching, the Mixture Kalman Filter (MKF), which inherits merits of both KF and PF, can be employed. However, if the measurement error is non-Gaussian, only PF is the applicable method. For each filtering method, we review its algorithm, application scope, computational efficiency and asset pricing applications. This chapter provides a brief summary of applications of filtering methods in estimating asset pricing models.