Bayesian Inference And Empirical Study On European Option Pricing

In the field of finance,option occupies an inseparable part and plays a positive role in the stable development of the financial market.Reasonable and correct pricing of options is especially important.The assumption that the volatility of stock price is constant in the classical Black-Scholes option pricing model is not consistent with the reality.Because the Bayesian method regards the unknown parameters of the model as random variables,it's better to solve the problem that some parameters in the model are not random.Moreover,the inference of unknown parameters in the model is more reasonable than that of classical statistical method because of the Bayesian method combines the prior information and the sample information.So this paper makes a statistical inference on the option pricing problem based on the Bayesian method.The main work of this paper is as follows:1.In this paper,the posterior density of European call option price is derived using the Black-Scholes(BS)option pricing model with two noninformation priors which are reference prior and Jeffreys prior.The Monte Carlo method is used for numerical simulation,and the error of the simulated volatility and the option price is given,and the error comparison is carried out.Numerical results show that the option pricing effect under reference prior is better than the option pricing effect under the Jeffreys prior.2.The Bayesian method is introduced into the AHBS model in this paper,and the posterior density function of the parameters of the volatility function is obtained,and the empirical numerical simulation is carried out.The empirical results show that the error between the simulated price and the real value of option price is small.Finally,the numerical simulation of Bayesian inference results based on the BS models with reference prior and Jeffreys prior are compared with the AHBS model with conjugate prior,and the experimental results are analyzed.The results show that the pricing results of the AHBS model are more accurate.3.Bayesian model averaging method is used to inference the option price of AHBS model in this paper.An empirical analysis of the option price model after the Bayesian model averaging is carried out,and the results are compared with the above AHBS model under conjugate prior.The results show that the Bayesian model averaging model is more accurate for the option pricing.