Black-scholes Option Pricing Based On Bayesian Statistical Inference

Under the Black-Scholes option pricing model,it is generally assumed that the risk-free interest rate is constant,and volatility is obtained by different method,to study option pricing.In this paper,the risk-free interest rate and volatility are taken as unknown parameters and comprehensively studies by Bayesian methon.The main work in this paper is as follows:1.Under the Black-Scholes option pricing model,this paper studies the expected return rate based on Bayesian method,and looks for more valuable stocks from the stock price indexes of different industries.Both expected return and volatility are regarded as unknown parameters,the joint posterior kernel of unknown parameters is obtained by conjudge prior method,and the Metropolis-within-Gibbs algorithm is designed to sample the unknown parameters.The numerical simulation shows that the industry index with higher expected rate of return has higher actual rate of return.In addition,there are significantly more stocks with positive real returns in industry sectors with higher expected returns.The positive or negative actual return rate of a stock can be predicted according to the expected return rate of stock.Therefore,it can provide an investment strategy for stock investment.2.Under the Black-Scholes option pricing model,this paper studies the price European call options based on Bayesian method.Different from previous pricing methods,we regard risk-free interest rate and volatility as unknown parameters in our model.And the joint posterior kernel of unknown parameters is obtained through the method of no-information prior and conjugate prior.The Metropolis-within-Gibbs algorithm is designed to sample the unknown parameters,and the predicted value of option price is obtained by MC method.In the numerical simulation,it is found that the proposed method has more accurate pricing results compared with traditional pricing method,and the pricing result of conjugate prior method is better than that of no-information prior method.It is found that the market risk-free rate is significantly different from the estimated result.