Comparison Of Alternative Stochastic Volatility Models

With the rapid development of global economic integration and financial market, financial derivatives become more and more important, option is a kind of widely used financial instruments, Options can be divided into European and American options by using the strike time, American option holders can advance execution options, European option can only be exercised at the expiration date. An option gives the right, but not the obligation.For European options,BS is a classic options pricing model in the market, it is a basic assumption of BS model options of the underlying stock price follows geometric Brownian motion. Under the assumption,the stock volatility is constant.As a matter of fact,by the option price on the market of implied volatility is not constant,but varies with the striking price of an option and the option of remaining life changing,which is observed by people" volatility smile"phenomenon.In order to explain "very few volatility",the researchers in the BS model is proposed on the basis of a large number of new midels,including stochastic volatility option pricing models mainly,it produce effective deeply for the research of theoretical and development.This article investigate the improvement in the pricing of S&P500index op tions when stochastic volatility option pricing models:(1)the ad hoc Black and Sch oles procedure that fits the implied volatiliy surface,(2)GARCH type model,(3)cont inuous-time stochastic volatility model.,(4)variance gamma model.We find that Hest on’s model outperforms the other models in terms of effectiveness for in-sample p ricing,out-of-sample pricing.Looking at valution errors by moneyness,pricing an d hedging errors are highest for out-of-the money options, and decrease as we mo ve to in-the-money options in all models.the stochastic volatility models cannot mi tigate the "volatility smiles"effects found in cross-sectional options data, but can r educe the effects better than the Black Scholes model.Heston and Nandi’s model s hows the worst performance,but the performance of the Black and Scholes model is not far behind the stochastic volatility option pricing model...