A Second-order Finite Difference Scheme for a Type of Black-Scholes Equation
نویسندگان
چکیده
In this paper we consider a backward parabolic partial differential equation, called the Black-Scholes equation, governing American and European option pricing. We present a numerical method combining the Crank-Nicolson method in the time discretization with a hybrid finite difference scheme on a piecewise uniform mesh in the spatial discretization. The difference scheme is stable for the arbitrary volatility and arbitrary asset price. It is shown that the scheme is second-order convergent with respect to both time and spatial variables. Numerical results support the theoretical results.
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