Pricing Of Quanto Option And Empirical Illustration Based On Bayesian Method

Before the paper investigates the pricing of qoanto option under fixed exchange rate,stochastic volatility model with leverage effect(SVL)of the log-return of the underlying asset is studied.Given that the volatility is implicit in the SVL model,the Bayesian method is utilized to estimate the unknown parameters.Any of the unknown parameter is random variables in bayesian statistics,which can be inferred by posterior probability density function combined prior information and sample information.When the posterior probability density function is not classical,the unknown parameter can be estimated by using the sampling algorithm and the Markov chain Monte Carlo method.Therefore,compared with the traditional approache,the Bayesian method is flexible and effective to handle complicated model.The main contributions of this paper are listed as follows:1.The paper studies the SVL models which the distribution of the random error terms of the log-return and the log-volatility are student T distribution and variance gamma distribution.Firstly,the Bayesian inference is carried out in the SVL model which the distribution of the random error terms of the log-return and the log-volatility are variance gamma distribution(Referred to as SVL—VG-VG model).And then the other three SVL models are statistically analyzed,which include the SVL model with the random error terms of the log-return and the log-volatility are student T distribution(Referred to as SVL—T-T model),the SVL model with the random error term of the log-return is variance gamma distribution and the random error term of log-volatility is student T distribution(Referred to as SVL—VG-T model),and the SVL model with the random error term of the log-return is student T distribution as well as the random error term of log-volatility is variance gamma distribution(Referred to as SVL—T-VG model).Finally,Bayesian model averaing scheme is applied for the four different individual SVL model in the paper,and two different individual SVL model,three different individual SVL model and four different individual SVL model are considered respectively by using Bayesian model averaing scheme.2.The bayesian method is used to do empirical research based on sample data of Micron Technology,inc's Daily Closing price in the nasdaq stock market from July 1,2014 to July 1,2017.Then,all models of this paper are applied for the pricing of quanto option under fixed exchange rate.The results show that: when the option is in-the-money and at-the-money,the pricing effect of quanto option using SVL—T-VG model is superior to use the other three different individual SVL models,which are SVL— VG-VG model,SVL— T-T model and SVL— VG-T model.Then we consider the pricing of quanto option of the different individual SVL model in bayesian model averaing scheme.The results show that: the pricing effect of quanto option of bayesian model averaing scheme which consider SVL—VG-VG model and SVL—T-VG model is better than the pricing effect of quanto option of bayesian model averaing scheme which consider by three different individual SVL models and the four different individual SVL models.It is also interesting to find that the pricing effect of quanto option of the bayesian model averaging which consider the model SVL—VG-VG and model SVL—T-VG is better than the pricing effect of quanto option used by individual SVL model when the option is in-the-money and at-the-money.