New Numerical Methods Research For Several Option Pricing Modeling

For three option pricing modeling having important significance:Black-Scholes modeling(equation), continuous payment of dividends under the Black-Scholes modeling, with transaction costs of the Black-Scholes modeling; this paper constructs the predictor-corrector scheme and the asymmetry scheme of the Black-Scholes modeling, constructs the universal scheme (θscheme) of the other two modeling; analyzes computational stability and convergence, obtains stability and convergence evidence, gives error estimate. The numerical experiment using American put option results show that:when the universal difference scheme is equivalent to predictor-corrector scheme, the predictor-corrector scheme is better than the asymmetry scheme in the computational stability. Numerical experimental results are consistent with theoretical analysis, indicating predictor-corrector scheme for solving American option is practical and feasible; the universal difference scheme (θscheme) of the other two modeling is also effective.