Monte Carlo Option Pricing Based On Bayesian Model Averaging(BMA) Method

In recent years,the development of the financial derivatives market has truned into a key factor affecting the global economic growth.Financial derivatives have hedging,investment arbitrage and other functions.On the one hand,it brought innovation to the financial market and accelerated the development of the financial market.On the other hand,because of its leveraging,it may cause huge losses when the investment is unsuitable.The financial derivatives market initially developed stock index futures,and then the derivatives of interest rates and exchange rates.Options are the most flexible and lowest cost products of financial derivatives,and they also have great potential for development.On February 9,2015,the Shanghai Stock Exchange listed and traded the Shanghai 50ETF options contract,and the domestic capital market entered a new era of options.Domestic scholars' study is increased gradually on the option pricing.The classical model for option pricing is B-S model.However,with the further research,we find that the real market situation may not be consistent with the theoretical hypothesis.In theory,logarithmic yield is normally distributed,but in the real market,it is characterized by“leptokurtosis and fat-tail”.In addition,the implied volatility is not constant,and there is a jump.In view of these conditions,we need to modify the traditional model.Monte Carlo pricing method is to simulate the underlying asset price path and predict the average return of option so as to get the estimated price of option.The advantage of this pricing method is that we do not have a deep understanding of the option pricing model,and we can directly use the Monte Carlo method to simulate,and the error convergence rate is not dependent on the dimension of the problem,so it has a great advantage in the pricing of high dimensional options.In addition,the Monte Carlo method does not limit the distribution hypothesis,it can be normal,log normal distribution,t distribution,and the spread distribution of band jump.The core of option pricing lies in the estimation of volatility.The volatility model has experienced a continuous development in recent years.From the GARCH model to the HAR model,the accuracy of the volatility is constantly improved.In this paper,we use the 5 minute high frequency data of Shanghai 50ETF index from March 1,2016 to March 2,2018 as the research sample to model and predict the volatility.The volatility prediction models are used in this paper include 5 GARCH family models,6 HAR family realized volatility models and Bias model average(BMA)method.Then the 30-day volatility of the forecast is carried out the option pricing with Monte Carlo simulation.The article chooses 15 options as samples,including 6 in-the-money(ITM)options,4 at-the-money(ATM)options and 5 out-of-the money(OTM)options.Finally,the pricing results are compared with the real value of the Shanghai 50ETF option to evaluate its pricing effect.Through empirical analysis,we prove that the logarithmic yield of 50ETF in Shanghai stock market has obvious characteristics such as peak,thick tail,jump and so on,and the stock market is affected by different fluctuating components in the past.Different volatility components are caused by investor behavior of different holding periods(short,medium and long term).The realized volatility is more affected by short-term fluctuation and less affected by medium and long term fluctuation in the process of option pricing.The estimated value of the option price is smaller than the real value in the vast majority of the whole prediction time.It also shows that there is an undervaluation in the market,which causes the price of the option to deviate from its intrinsic value.Through the GARCH model,the realized volatility model and the BMA method,the option pricing is carried out respectively.The results show that the BMA method has the best pricing effect,the realized volatility model is the next,and the GARCH family model is the worst.From the perspective of options,ITM option pricing is much more accurate than ATM and OTM options.