This chapter surveys filtering methods, where the state of an unobserved dynamic model is inferred based on noisy observations. In linear and gaussian models, the Kalman Filter is applicable. We provide a brief description of the method and an example with a gaussian factor model of yields. More general models can be tackled using sequential monte carlo (SMC) techniques (also called particle filters). Here, the filtering distribution of the unobserved states is approximated by a swarm of particles and recursively update these particles using importance sampling and resampling. We give brief review of the methodology, illustrated throughout by the example of inferring asset values from noisy equity prices in a structural credit risk model. The MATLAB code implementing the examples is available.
FULOP, A. (2012). Filtering Methods. In: Handbook of Computational Finance. 1st ed. Springer, pp. 439-467.