The Expansion Of Heston Model And Its Application In Option Pricing

With the accelerated pace of financial reform and financial opening,options and other derivatives have become necessary financial products in mature financial markets.How to reasonably price options has become a hot topic in academia.The thesis focuses on the option pricing method based on the continuous stochastic volatility model and achieves the following main results:(1)The Heston model is extended by replacing the CIR process with the CEV process,that is,the fixed variance elastic coefficient is replaced with a variable variance elastic coefficient.According to Ito’s lemma and(35)-hedging principle,the partial differential equations for European options are established,and the closed solution of European option prices is obtained by using the characteristic function method.The existence of closed solutions reduces the difficulty of model parameter estimation and improves the option pricing effectiveness.The differential evolution algorithm is used to estimate the parameters of the extended Heston model,which can converge to the global optimal solution.Empirical analysis is carried out using historical data of the Shanghai Stock Exchange 50 ETF European Call Options from 2015 to 2018.The results show that the elastic coefficient of variance obtained by the parameter estimation is not Heston In the model,the extended Heston model fits the implied volatility better than the Heston model.(2)Based on the Heston model,a binomial tree pricing method for calculating American option prices that is independent of the path is proposed.The asset price change process and the volatility variance change process are modeled as two independent trigeminal tree models,and then the two The threetree model is meshed into a tree.From the expiration date of the known return,the binomial tree model of American put option pricing is obtained by backward calculation.Empirical analysis was conducted using the historical data of soybean meal futures American put options in 2019.The analysis results show that the fitting effect of the binomial tree pricing method based on the Heston model on the American option price is better than the binary tree pricing method based on the BS model.