Fitting Stochastic Volatility Models in the Presence of Irregular Sampling via Particle Methods and the EM Algorithm

Stochastic volatility (SV) models have become increasingly popular for explaining the behaviour of financial variables such as stock prices and exchange rates, and their popularity has resulted in several different proposed approaches to estimating the parameters of the model. An important feature of financial data, which is commonly ignored, is the occurrence of irregular sampling because of holidays or unexpected events. We present a method that can handle the estimation problem of SV models when the sampling is somewhat irregular. The basic idea of our approach is to combine the expectation-maximization (EM) algorithm with particle filters and smoothers in order to estimate parameters of the model. In addition, we expand the scope of application of SV models by adopting a normal mixture, with unknown parameters, for the observational error term rather than assuming a log-chi-squared distribution. We address the problems by using state-space models and imputation. Finally, we present simulation studies and real data analyses to establish the viability of the proposed method. Copyright 2008 The Authors. Journal compilation 2008 Blackwell Publishing Ltd