Option Pricing Under A Class Of Stochastic Volatility Models

In the rapid development of financial history,financial derivatives have been widely promoted and applied.The option is a very important type of financial derivatives,we have important significance to the reasonable pricing of options on the trading strategy.The classical black option pricing model without transaction costs in continuous time is the price of the assets of follows geometric Brownian motion and the assumption of the the without transaction costs,but this does not accord with the actual situation.In 1985,Leland first put forward the option pricing model with proportional transaction costs.The model modifies the assumption that there is no transaction costs,and obtains the corresponding European option pricing formula under the discrete time and proportional transaction costs,but the model is still based on the geometric Brownian motion of the stock price.In this paper,we study the option pricing with a kind of stochastic volatility model.Assuming stock price St satisfied dS_t = ?S_td_t+?aS_td(W_t?)Where ?,?>0 are constant,(Wt)r>0.is the standard Brownian motion,? is independent of(Wt)t?0,the probability density function of ? is . When a>O,a>0,x>0,we give the following close solution,which is the minimal mean square error sense under incomplete information situation.In particular.(?);whereTo the above formula,we use MATLAB from the following aspects of empirical to do the numerical research and analysis.First,we compared the influence of the new model pricing formula and Leland option pricing formula on the option pricing under different parameters and different transaction frequency,which the model characteristics are deeply analyzed.Secondly,we selected the options of China's current listing transaction-SSE stock options to analyze the error of the pricing results under two models,including the bullish call option contract expired in April,the contract code is respectively.10000857,10000858,10000859,10000860,10000861;Date is a call options contract expiring in may 2005,the contract code is 10000869,10000870,10000871,10000872,10000873;Date is a call options contract expiring in June 2005,the contract code is 10000797,10000798,10000799,10000800,10000801;Date is a call options contract expiring in September 2005,the contract code is 10000843,10000844,10000845,10000846,10000847;According to our data,the option price of the Leland model is far higher than the real option price,And the pricing error rate of Leland model is higher than the pricing error of the new model.Finally,through the options simulation trading competition held in oriental wealth,we selected the Shanghai 50 ETF call option as an investment.The contract code is 10000797,date is 2016.11.29,the maturity is 2017.6.22,and the strike price is 2.3,and arbitrage is realized by the pricing formula of the model.