Discrete Time Stochastic Volatility Model

Abstract

In this dissertation we propose a new model which captures observed features of asset prices. The model reproduces the skewness and fat tails of asset returns by introducing a discretized variance gamma process as the driving innovation process, in addition to a double gamma process to reflect the stochastic nature of volatility coefficients. The leverage effect between returns and volatilities is built in by a polynomial function describing the relationship between these two variables. One application of this model is to price volatility contracts whose payoffs depend on realized variance or volatility. Because of the scarcity of market quotes and consequent unavailability of risk neutral calibration, we propose a new scheme of pricing based on the model estimated from historical data. The estimation of the model parameters is carried out by maximizing likelihood function, which is calculated through a combination of Expectation-Maximization and Particle Filter algorithm. The resulting distribution is transformed by concave distortions, the extent of which reflects the risk aversion level of market.