An Empirical Study Of 50ETF Option Pricing Under The Stochastic Volatility Model

Option is an important financial derivative in the financial market and plays an important role in asset management and risk hedging.Chinese financial market has entered the era of options since the Shanghai stock exchange formally launched the ShangZheng 50 ETF option trade in February 2015.Although the trading of 50 ETF options is not as active as the mature financial market in foreign countries,but the introduction of the 50 ETF option has made a great significance to the improvement of China's financial derivative market system.Since the birth of the option,the research on options has been focused on options pricing and the strategy of options.In 1973,Black and Scholes proposed the BS option pricing model,which formally opened the door of research on option pricing.BS model theorys' starting point is the change of stock price process which is subject to the geometric wiener process.Based on a series of constraint conditions,using the risk neutral pricing rule and self-financing strategy,we can get a partial differential equation.Then solve the partial differential of analytical solution,in this way,we can get the pricing formula of European call option.The pricing formula of European put option is obtained through the option parity formula.However,because a series of assumptions of the BS model are too idealistic and deviate from the real situation of the market,the pricing results of the BS model often deviate from the real price of real price of the market.In order to improve BS model and solving the defects existing in BS model,subsequent scholars began to study the option pricing problem under the assumption of relaxed BS model.One of the important assumptions of BS model is that underlying asset volatility is always constant.But in practice,there are usually financial asset price volatility heteroscedasticity and volatility is random,showing the return on assets distribution presents the characteristics of "rush thick tail".Subsequent scholars for researches on the option pricing problem under stochastic volatility,by volatility are assumed to be a stochastic process,it is concluded that a series of stochastic volatility model,such as the CEV model,jump diffusion model,Heston model,SABR model,etc.But,most of stochastic volatility models do not have analytical solution,the vast majority of the model in the pricing process can only be obtained by monte carlo numerical calculation methods,such as,speed slow,inefficient when to provide investment decision,easy to miss trading opportunities.The Heston model and SABR model have analytical solutions,which have an incomparable advantage over other stochastic volatility models when calculating the option price.Although Heston model and SABR model has absolute advantage in pricing efficiency,but the model forms are extremely complex,be estimated parameters is more,there are a large number of local extreme value point,this gives model parameter estimates that caused great difficulties.The traditional nonlinear least squares estimator can not estimate such model,while the optimization algorithms such as differential evolution and simulated annealing are easy to get into local minima in the optimization process.This article USES the parallel global search ability of genetic algorithm to estimate the stochastic volatility model,genetic algorithm because of its features can be a good jump out of local minimum value,and then search to the optimal solution,has the very good robustness.Based on empirical research for the Shanghai 50 etf,found that stochastic volatility model calculation of option prices significantly than the BS model calculation more accurate,more close to the real market price,illustrates the random fluctuations in the performance of the option pricing model is superior to classical BS model.At the same time,the genetic algorithm is higher than the traditional parameter estimation method and the operation time is shorter.