Bayesian Option Pricing Using Stochastic Volatility Models with Fat-tailed Errors

This paper mainly explore price option based on the stochastic volatility with fat-tails errors and "level effect" by correlation factor, which is defined between underlying asset and stochastic volatility. Firstly, we develop Morkov Chain Monte Carlo (MCMC) method to calibrate uncertain parameters in this model under Martingale measure. There is a strong evidence in favor of fait-tailed feature under Martingale measure for daily data. Furthermore, we will detail statements as to how to compute predictive densities under Martingale measure with uncertain parameters. When pricing options on S&P 500 index, substantial improvements are found compared to a stochastic volatility.