PARAMETER ESTIMATION IN STOCHASTIC VOLATILITY MODELS WITH MISSING DATA USING PARTICLE METHODS AND THE EM ALGORITHM

The main concern of financial time series analysis is how to forecast future values of financialvariables, based on all available information. One of the special features of financial variables,such as stock prices and exchange rates, is that they show changes in volatility, or variance,over time. Several statistical models have been suggested to explain volatility in data, andamong them Stochastic Volatility models or SV models have been commonly and successfullyused. Another feature of financial variables I want to consider is the existence of severalmissing data. For example, there is no stock price data available for regular holidays, suchas Christmas, Thanksgiving, and so on. Furthermore, even though the chance is small,stretches of data may not available for many reasons. I believe that if this feature is broughtinto the model, it will produce more precise results.The goal of my research is to develop a new technique for estimating parameters of SVmodels when some parts of data are missing. By estimating parameters, the dynamics ofthe process can be fully specified, and future values can be estimated from them. SV modelshave become increasingly popular in recent years, and their popularity has resulted in severaldifferent approaches proposed regarding the problem of estimating the parameters of the SVmodels. However, as of yet there is no consensus on this problem. In addition there hasbeen no serious consideration of the missing data problem. A new statistical approach basedon the EM algorithm and particle filters is presented. Moreover, I expand the scope ofapplication of SV models by introducing a slight modification of the models.