Research On Characteristic Finite Element Method Of Black-Scholes Equation For Option Pricing

As a new type of derivative product in today's financial markets,options play a more and more important role in the financial market.The issue of pricing has also attracted the attention of financial scholars.After some studies by financial experts and mathematician-s,at present,there are many numerical methods for option pricing problems.Because the Black-Scholes equations satisfied by the option pricing problem contain convection terms,the numerical oscillations are prone to occur by ordinary numerical methods.For this reason,this paper discretizes the first-order derivative of the time and space of the Black-Scholes equation along the direction of the characteristic line,and gives a stable numerical method-characteristic finite element method-for solving the option pricing problem.This paper mainly considers the problem of two-asset European and American option pricing.Firstly,construct the characteristic finite element method for the Black-Scholes equation of the pricing problem of the two-asset European option.At the same time,give the error estimates in L2-order and H1-order,the numerical examples verify the theoretical results.Error analysis and numerical results show that this method has good convergence and stability,and overcomes the numerical oscillating phenomenon.Then,the characteristic finite element method is applied to the pricing problem of the two-asset American option,and the numerical examples verify the effectiveness of this method.