Research On The Application Of Fourier-cos Method In Financial Option Pricing

Option pricing has always been favored by many investors.As an important derivative tool in venture investment transaction,risk hedging and risk aversion,its pricing has become a hot topic in the field of financial mathematics.In recent years,backward stochastic differential equations have been widely studied and applied.In general,it is difficult to obtain the analytical solution to backward stochastic differential equations.So it is important to give the numerical solutions.Some methods of numerical solutions to backward stochastic differential equations have been proposed gradually.Among these methods,Fourier-cos transformation is considered to be effective.The main difficulty of discretization of backward stochastic differential equations is to deal with conditional mathematical expectations.From the definitions,properties and basic conclusions of forward backward stochastic differential equations,this paper sorts out the basic methods of discretization,and obtains the discretization results of one-dimensional and two-dimensional forward backward stochastic differential equations by using Feynmam-Kac theorem.Based on the successful application of Fourier-cos transformation to deal with option pricing,this paper gives approximate expressions of conditional expectations by means of conditional characteristic functions,as well as error analysis.Combined with Monte Carlo method,a regression-based method for solving forward backward stochastic differential equations is proposed.Numerical experimental results show that the algorithm is stable and effective.The focus of this paper is to use Fourier-cos transformation to price a class of Bermuda redeemable bonds.Combining with pricing principle and conditional characteristic functions,the pricing process is optimized.This paper focuses on the discretization of two-dimensional forward backward stochastic differential equations.The approximate expression of mathematical expectation of two-dimensional conditions is obtained by using Fourier COS-COS method,and the validity of this scheme is verified by taking a basket of European option pricing as the research object,which indeed expands the option pricing model.