Based On Bayesian Method Of GARCH Type Of Quanto Options Pricing

The classical Black-Scholes models assume that volatility is a constant,which is inconsistent with the actual market data.When the real stock price process exists heteroscedasticity,the classical Black-Scholes model can not describe the heteroscedastic feature correctly.Therefore,how to correctly on the option pricing problem is an important theoretical proposition and finance practice.This paper use t-GARCH model and asymmetric t-GARCH model with their error terms follow student t distributed to describe the volatility of the sequence of the underlying asset returns.Under the bayesian framework,by setting reasonable prior density,we combine it with the likelihood function to get the posterior density functions for all parameters in volatility model.Then we estimate volatility model parameters with the help of MCMC method.On the other hand,the predictive density function is derived so as to predict quanto options prices.This article has carried on empirical researchs based on the Nasdaq 100 index.The empirical results show that t-GARCH model and asymmetric t-GARCH model have less difference in estimating model parameters under different MCMC method.In the asymmetric t-GARCH(1,1)model,the negative disturbance has a stronger effect than the positive disturbance,showing that asset returns sequences have "Leverage effect”.Also,the mean of predicitive volatility in asymmetric t-GARCH(1,1)model is higher than the corrresponding t-GARCH model,So the asymmetric t-GARCH model captures the market situation better.Finally,we predict quanto options prices under fixed exchange rate.Note that the exchange rate between RMB and Dollar fluctuates obviously,indicating that to establish quanto options is of great significance to international investors.By matlab software simulation,based on t-GARCH model and asymmetric t-GARCH model,we obtain the BS price and predicitive price for quanto options written on the nasdaq 100 stock index with 15-day maturity date.