Study On European Option Pricing With Transaction Fees Under The Mixed Hedging Strategy

In recent years,people's investment ideals have gradually become stronger,and financial derivatives have also been frequently used in risk management.As a key issue in options trading,the issue of option pricing has attracted the attention and in-depth study of many scholars.Under the ideal Black-Scholes option pricing model,the implied volatility of options should be a horizontal line with respect to different execution prices.However,empirical analysis shows that the implied volatility varies with the execution price,and the curve drawn presents a skewed or smiling shape.This shows that the Black-Scholes option pricing model has certain flaws.In the real world,there are transaction fees in financial markets,and transactions are conducted at discrete times.On the other hand,investor trading behavior also has a certain impact on the formation of option prices,which makes the pricing of options have certain pricing errorsIn response to the above problems,we consider the impact of investor behavior on option pricing and propose the following mixed hedging strategy pricing options:where ?(?t,T,X)obtained by fitting the past implied volatility data is the function about the expiration time T and the execution price X.Under the condition of discrete time and payment of proportional transaction fee,this paper studies the option pricing problem based on the above mixed avoidance strategy.First,we give a detailed derivation of the European option pricing formula and the Asian option pricing formula under this condition.Secondly,it proves that the evasion error of the European call option pricing formula with transaction fee under the mixed hedging strategy tends to zero in the sense of probability convergence.Finally,we use our new model and B-S model,Leland model,modified Leland model for numerical comparison and empirical analysis.The following conclusions are drawn:(1)Numerical analysis shows that compared with the Leland model and the modified Leland model,the price of the option calculated by our model is closer to the cost of hedging,and the cost of hedging is smaller;(2)The Monte Carlo simulation shows that the new model we get,the Leland model and the modified Leland model have the same convergence results.Among them,under the virtual value option,the new model we obtained is better than the Leland model and the modified Leland model;(3)The empirical analysis shows that when the expiration date is not lower than 9/252(9 trading days),the price calculated by our model is closer to the real market price than B-S model and Leland model,and the approximation is extremely high;(4)Empirical analysis shows that there is a strong correlation between the trading behavior of the investors and the implied volatility smiles.