Comparative Study Of Several Computational Methods For Volatility Of Options Pricing

Option pricing is one of the greatest achievements of modern finance.Option is a basic financial derivative instrument,which is widely used in risk management.Options have nonlinear characteristics.The most obvious difference between options and linear products such as futures and stocks is that options increase the volatility dimension compared with linear products.Options expand the trading dimension from the two-dimensional price direction to the three-dimensional volatility dimension,increasing the freedom and selectivity of trading,but also increasing the complexity of pricing.Therefore,how to accurately price options and estimate volatility are worthy of further study.In this paper,we use the Shanghai Stock Exchange 50ETF option data to calculate the deviation between the theoretical price and the actual price based on the Black Scholes pricing model and Merton jump diffusion pricing model.By comparing and analyzing the pricing situation of the two models under different volatility calculation methods and predicting the option price,we can provide effective reference information for the option market and investors’ trading strategies.The main research work of this paper is divided into the following three aspects:In the first part,we first consider the descriptive statistical analysis of the closing price and yield series of the underlying assets of Shanghai 50ETF options in the sample range.The results show that the return series is stable and does not obey the normal distribution.Therefore,the Black-Scholes model and Merton jump diffusion model can be used for pricing prediction of Shanghai 50ETF options.In the second part,the volatility of option pricing under the two models is calculated by using the return series and Shanghai 50ETF option data,which is mainly divided into historical volatility and implied volatility.For the historical volatility of Black-Scholes model,the standard deviation of yield series is used as the estimation value of volatility,and the implied volatility is calculated by Newton-Raphson iteration,Steffensen iteration,dichotomy,trial and error method and chord section method.For Merton jump diffusion model,the method of parameter estimation based on outlier test is used.The implied volatility is calculated by trial and error method and chord section method based on the implied volatility of Black-Scholes model.In the third part,We substitute the option parameters and volatility parameters into Black Scholes model and Merton jump diffusion model under the different calculation methods of volatility,then we compared the option model price with the actual price.The empirical results show that the implied volatility based option price prediction is better than the historical volatility based option price prediction,and among all the methods to calculate the implied volatility,the chord cut method is more accurate,and the prediction effect of substituting into the pricing model is better.