Establishment,Comparison And Application Analysis Of European Option Pricing Model In Fractional Brown Market

February 9,2015,China's first option,the Shanghai 50ETF options listed on the Shanghai Stock Exchange,its listing means that the options market in China formally established.Options as a financial derivatives,has always been a hot topic in the field of financial research.From the birth of the standard BS model to the pricing model considering the market friction,the stochastic interest rate and so on;the establishment of the model from the standard Brownian motion to the fractional Brownian motion;deriving from the model of the financial asset price to the continuous change Model Establishment in the Case of Random Jump.Etc.These are all that the theory and model of option pricing are being enriched and developed,and it is becoming more complicated.On the basis of many theoretical and 50ETF options listed in the background,this article carried out three aspects of the study.On the one hand,this paper establishes the option pricing model with both the transaction cost and the stochastic interest rate under the fractional Brownian motion.In the choice of stochastic interest rate model,this paper chooses the Vasicek interest rate model under the fractional Brownian motion.After the model is established,the model is put into the 50ETF option market,and it is compared with the standard B-S model to verify the validity of the model.In the empirical analysis,because there is no data of zero coupon in the market,this paper chooses to replace the actual market price with the theoretical price.Although it will produce the deviation,it is also a way to make the model feasible.On the other hand,this paper uses the Monte Carlo method to simulate the option price and compare it with the standard B-S model.In this part,we first describe the Monte Carlo simulation step of the fractional Brownian motion subscript,and then find the best simulation times.Finally,we compare the Monte Carlo simulation price and the standard B-S model price.On the last hand,the 50ETF option in China is used as the object of study,and the effectiveness of the option pricing model under the fractional Brownian motion considering the transaction cost is compared and analyzed.In the comparison of efficacy,four kinds of error measurement are selected.In the model selection,taking into account the transaction costs have a significant impact on the option price,fractional Brown sports can reflect the long-term memory of the financial market,so chose Sun Lin(2009),Wang Xiaotian(2010),Xiao Wei Lin(2014)established three Pricing model as a theoretical basis.It is clear which pricing model is more suitable for China's options market and whether the option price in the market is overestimated or underestimated,which is of great significance to the stability of China's options market.More types of options to provide guidance.In the above empirical analysis,this paper uses EViews software to carry out the normality test to verify the fractal characteristics of China's financial market.Based on the R/S analysis method,the Hurst index H is estimated by using the matlab software.The maximum likelihood estimation method is used to estimate the interest rate recovery rate and the long-term rate of interest rate in the Vasicek stochastic interest rate model.In contrast to the effectiveness of the model,this paper uses the mean square error,mean absolute error,maximum absolute error and minimum absolute error.By comparing the four kinds of errors,it is concluded that the option pricing model considering the transaction cost and the stochastic interest rate and the option pricing model under the fractional Brownian motion with the transaction cost are better than the standard B-S model.However,the theoretical price of these models and the actual price gap,especially in the early fitting is better,to the late deviation is relatively large,so the model needs to be further improved.The innovation of this paper can be divided into two aspects.The first aspect is to establish the option pricing model under the Brownian motion of the stochastic interest rate and the transaction cost,and the empirical analysis is carried out.In general,in the current sub-fractional Brownian exercise to the option pricing is still very little,so this article selected the sub-fractional Brownian movement direction.The second aspect is to use the 50ETF option data to analyze the three options pricing models under the fractional Brownian motion with transaction costs.In the empirical analysis,four kinds of error measurement criteria were selected to evaluate the fitting effect of each model,and the error results of the three models were compared with the standard B-S model.