The Finite Difference Method For Pricing American Lookback Options Under CEV Model

The outbreak of the pandemic in 2019 has greatly hindered the development of the financial sector in various countries around the world.In order to protect the interests of risk averse investors,countries have continuously improved the types and functions of financial derivatives.A variety of exotic options are deeply loved by investors,making research on medium-term option pricing in the financial field even more important.This article chooses the CEV Model(Constant Variance Elasticity Model),It can better describe the changes in the actual financial market.The pricing problem of American lookback options is studied through the CEV model,which to some extent enriches the theoretical research of financial derivatives and provides reference for pricing methods of insurance and securities companies.This paper studies the finite difference method for the pricing of American lookback options under the CEV model.First,the mathematical model of American lookback options under the CEV model is established.For the numerical solution of the pricing of American lookback options,take American lookback put option as an example,and then use the finite difference method to solve it,And analyzed the compatibility of the difference scheme and the stability and convergence of the difference decomposition.Then,we studied the pricing problem of American lookback options in the time fractional order CEV model.We first weighted the high-precision explicit difference scheme and the high-precision implicit difference scheme to obtain a high-precision difference method,Then the mathematical induction method and Fourier method are used to analyze the stability and convergence of the high-precision difference scheme.Finally,the numerical simulation shows that the high-precision difference scheme is feasible to solve the American lookback option under the fractional CEV model.