Numerical Solution Of FBSDE Based On Monte-Carlo Regression

As early as the 18 th century,foreign scholars have begun to carry out theoretical research on options.Through continuous development,the research on options in foreign financial field has become mature.In contrast,China’s research in this field started late,but with the continuous updating and improvement of the financial market system,the research on options in China has gradually become active.Nowadays,the types of options are increasingly complex,and more and more financial investors participate in the expiration right.The option pricing problem has become a major focus in the financial market.In recent years,the continuous development of backward stochastic differential equation has made it appear in the field of option pricing.Because of its good mathematical properties,it can exactly meet the needs of derivatives pricing in the financial market.Therefore,it is of great significance to study forward and backward stochastic differential equations for the development of financial markets.However,how to solve forward and backward stochastic differential equations is a difficulty in this field.Generally speaking,it is difficult to find the analytical solution of a group of forward-backward stochastic differential equations,and the numerical solution can only be found through numerical research.This paper starts with this problem to carry out relevant research.In this paper,first of all,the development history of option pricing and the current development status are introduced,and then the theoretical background for solving the numerical solution of forward and backward stochastic differential equations is explained one by one,which provides a strong theoretical support for this paper.When solving the numerical solution of forward and backward stochastic differential equation,the key step is to calculate the conditional mathematical expectation of the discrete equation.In this paper,we use Fourier-cos transform to solve the approximate value of the mathematical expectation of these two conditions,and analyze its error,and prove that the error is convergent.Then the least squares Monte Carlo regression method is used to find its coefficients.Finally,the effectiveness of this method is verified by numerical experiments,which provides a new idea for the issues related to option pricing.