Study On Implied Volatility And Option Pricing Based On Neural Network

In the modern financial market,option is an important financial derivative.Pricing and risk management are the two core issues of option.The option pricing method based on model is limited by specific assumptions,which often brings model risk.This paper adopts data-driven option pricing method and risk management method.This kind of method is to establish neural network to fit the nonlinear function relationship between input and output.This paper establishes the implied volatility model and option pricing model based on deep neural network.According to the difference of option value degree(in the money,at the money and out of the money)and term(short-term,medium-term and long-term),nine network models are established for the above two problems respectively.In the implied volatility model,the degree of value,the ratio of option price to strike price,risk-free interest rate and residual term are used as the input of the model,and the implied volatility is used as the output to establish the model.The empirical analysis is carried out with the white sugar futures options listed in Zhengzhou commodity exchange.The empirical results show that: first,the nine network structures are different,and the different degree of value and term have different hidden layers and hidden units;Second,when the value of the option changes from out of the money to in the money,the volatility presents the phenomenon of "volatility smile";Third,the prediction error of at the money option is less than that of out of the money option,and the prediction error of out of the money option is less than that of in the money option.In the option pricing model,the underlying asset price,strike price,volatility,risk-free interest rate and term are taken as input variables,and the option price is taken as output variables.The empirical results show that: first,the nine network structures are different,and different value degrees and terms have different hidden layers and hidden units;Second,according to the degree of value of options,the error of in the money options is the smallest,while the error of out of the money options is the largest;Third,according to the remaining maturity of options,the error of long-term options is the smallest,and the error of short-term options is the largest.Based on the option pricing model based on deep neural network,this paper establishes the accurate calculation method and numerical calculation method of Greek value,which provides theoretical support for investors’ risk management of options.The research methods and results of this paper can provide theoretical guidance for researchers engaged in option work and the industry.