Financial Filtering and Model Calibration

Abstract

<p>The main topic of the thesis is the hidden Markov chain filtering for diffusions with jumps. The finite-dimensional filters are obtained for various statistics including the state of the hidden Markov chain. EM (Expectation Maximum) algorithm is then applied to the estimation of parameters of the hidden Markov chain. Based on some financial phenomena, we propose a model, called regime switching mean reverting with jump model, for an asset price or interest rate. We apply the filtering methodology to this model and obtain the estimator for the mean reverting level. Monte Carlo simulation is performed in estimating the parameters of hidden Markov chain. The numerical methods for stochastic differential equations which are used in diffusion with jump model are discussed. Some fundamental results on stochastic calculus and some basic methods on generating random variables and sample paths are provided.</p>