Research On Pricing Of Behavioral Derivatives Based On Deep Learnin

Option is one of the most common financial derivatives.However,the assumption of "rational economic man" in the traditional option pricing model does not accord with the reality.In order to better explain the financial market anomalies,the Behavioral Option Pricing Model(BOPM)is based on the framework that investors are bounded rationality.The numerical solutions of BOPM’s European basket options have been given by some scholars,but the pricing problems of BOPM’s American basket options and American exotic options have not been solved.Therefore,this paper uses unsupervised Deep Learning(DL)method to find the optimal stop-time strategy,so as to solve the pricing problems of BOPM’s American basket options,three types of American exotic options(American arithmetic mean call Asian option,American knock-out barrier option and American lookback option).Firstly,in order to solve the problem of slow convergence of DL algorithm,this paper proposes an improved DL-PAF algorithm considering the integration of three strategies,namely income function,variance reduction technique and parameter sharing between neural networks.Then,for different types of options,DL-PAF algorithm is used to price American basket options and three types of American exotic options,and compared with other algorithms and existing research results.Finally,the influence of four investor behavior parameters on American exotic option pricing is studied.The findings are as follows:(1)Compared with DL algorithm,DL-PAF algorithm has higher computational efficiency,less fluctuation of pricing results and higher accuracy.(2)In the pricing of American basket options,when the number of underlying assets is particularly large,the pricing efficiency of DL-PAF algorithm is higher than that of traditional American option pricing method.(3)Taking the pricing results of other algorithms as the standard,the numerical experiment proves the accuracy of DLPAF algorithm in the pricing of three types of American exotic options.Moreover,among the four investor behavior parameters,the degree of irrationality has the greatest influence on the American exotic option price,followed by the proportion of the stability of imperfect rational investors,and the speed of investors’ stabilization and the degree of herding effect have the least influence.