The Option Pricing Research Based On WENO Method

The classical Black-Scholes model occupies an important position in the financial markets. But the hypothesis of underlying asset prices are continuous changes and assets transaction don’t pay the cost of trading is not consistent with actual situation. In this paper, on the basis of the basic hypothesis we expand the model to one with transaction costs, and focus on the numerical solution of option pricing which based on WENO schemes. The main contents are as follows.(1) Numerical scheme for option pricing based on CRWENO scheme,MWENO scheme and TVD-RK3 method is constructed. The scheme efficiently removes the spurious solutions close to discontinuities and keep the high-order oaccuracy around non-smooth pionts as well as smooth pionts. In addition, a predictor-corrector scheme based on CRWENO scheme and BDF techniques is proposed for American put options.(2) Option pricing model with transaction costs is studied. A high accurate and efficient numerical scheme based on CRWENO scheme and NRK method is proposed for the non-linear Black-Scholes model. The NRK method is modified with non-traditional time-varying boundary. Set the volatility model RAPM, Leland’s and Barles & Soner’s for example to analysis the scheme, both in theoretical and numerical facts. The scheme relaxes the requirement of time step, keeps the high order and efficiently for dealing the problem of oscillations occur around the nonsmooth points.(3) Studied the application of finite volume scheme based on WENO method in option pricing. Firstly, introduce the finite volume scheme, and then improve it to a high order and compact scheme, at the same time apply it into the pricing of European option, Butterfly option and American option pricing, and the numerical analysis is given.