European option pricing for GARCH dynamic infinite activity Levy processes based on parameter learning

In this paper, we consider a three-dimension state space model for establishing a discrete-time dynamic Levy process, including time-varying drift, conditional volatility and stochastic jump activity. Then we obtain the equivalent non-arbitrage pricing model through local risk-neutral valuation relationship (RNVR). Taking non-Gaussian ARMA-NGARCH model as our benchmark, we construct a discrete time dynamic Levy process with GARCH effect for modeling S&P500 index. Furthermore we jointly estimate the parameters of the model and study the option pricing performance based on Bayesian learning approach. Research results show that our dynamic Levy process can depict the time-varying drift rate, conditional volatility and infinite activity styles. Meanwhile, Bayesian approach improves the option valuation ability of our model. Infinite jump models are significant superior and increase the pricing accuracy of implied volatility. We also find that unscented particle filtering (UPF) has the best estimation performance, non-Gaussian models in the yield prediction are of no significant difference, but the rapidly decreasing tempered stable processes (RDTS) have minimum errors for option pricing. ©, 2014, Systems Engineering Society of China. All right reserved.