Option Pricing And Empirical Research With Monte Carlo Method Based On Lévy Process

Options are important tool for investors to avoid risks effectively and realize hedging.Classic Black-Scholes model is based on the assumption that assets' price process subject to geometric Brown motion,then option pricing can be given by formula,but empirical studies found that the assumption does not accord with the actual financial market,data shows that asset's volatility has gathered effect and leverage effect,and assets' yield has peak and thick tail phenomenon.Therefore,the researchers use conditional heteroscedasticity model and Lévy process to correct Black-Scholes model.This paper studies option pricing models which is based on Lévy process and conditional heteroscedasticity model,and application of Monte Carlo method in option pricing,then Shanghai 50 ETF options are studies empirically.First of all,Monte Carlo simulation steps for Black-Scholes model are givend,model's parameters are estimated by the Shanghai 50 ETF yield data and model price is simulate,then differences between model price and market price are analyzed.Secondly,pricing models which's volatility subject to GARCH,EGARCH and TGARCH are studied,model's parameters are estimated under real probability measures,and option price is simulated by Monte Carlo method under risk neutral measures.At last,pricing models which's volatility subject to conditional heteroscedastic model and its' s yield subject to Lévy process of option is studied,according to the pricing precision of conditional heteroscedastic model,the bset conditional heteroscedastic model is chosed to describe assets' volatility,and the Lévy process such as VG,NIG and CGMY are chosed to describe assets' yield,model price is simulated by Monte Carlo method under those assumptions and differences between model price and market price are analyzed.Empirical research selected Shanghai 50 ETF call option and put option each 3 copies which expires on March 28,2018.Empirical research show that call options' model price is more closed to market price than put options;Secondly,on the view of different models,GARCH,EGARCH and TGARCH model are all better than Black-Scholes model,and TGARCH model is the best of conditional heteroscedastic m-odels;Thirdly,Lévy-TGARCH models is better than TGARCH model,and the NIGTGARCH model is the best in Lévy-TGARCH models.