Parameter Estimation for Geometric Lѐvy Processes with Stochastic Volatility

In finance, various stochastic models are used to model the price movements of financial instruments. After Robert Merton’s (1976) seminal work, several jump-diffusion models for option pricing and risk management have been proposed. In this work, we add alpha-stable Lѐvy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use sample characteristic functions approach and study parameter estimation for discretely observed stochastic differential equations driven by Lѐvy noises. We also discuss the consistency and asymptotic behavior of the proposed estimators. Simulation results and applications to real data sets will be presented. We will also introduce a model where the volatility is not constant.