Abstract
In this paper, we briefly review the finite difference method (FDM) for the Black–Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.
Highlights
The well-known Black–Scholes (BS) partial differential equation (PDE) [1,2] is an accurate and efficient mathematical model for option pricing
The main contribution of this paper is to present the detailed finite difference method (FDM) for the BS equations for pricing derivative securities and provide the MATLAB codes for the one, two, and three-dimensional numerical implementation so that the beginners can use the provided codes for their research projects without wasting time for debugging the implementation [21]
We briefly reviewed the FDM for the numerical solution of the BS equations and provided the MATLAB codes for numerical implementation
Summary
The well-known Black–Scholes (BS) partial differential equation (PDE) [1,2] is an accurate and efficient mathematical model for option pricing. Hout and Valkov [7] obtained the European two-asset options by the FDM based numerical method considering non-uniform grids. In [12], Zhao and Tian investigated FDMs for solving the fractional BS equation, and studied the stability and convergence of the proposed first- and second-order implicit numerical schemes. In [18], Rao proposed an FDM for a generalized BS equation (non-constant interest rate and volatility) and proved that the scheme is second-order accurate spatially and temporally. The main contribution of this paper is to present the detailed FDM for the BS equations for pricing derivative securities and provide the MATLAB codes for the one-, two-, and three-dimensional numerical implementation so that the beginners can use the provided codes for their research projects without wasting time for debugging the implementation [21]. In the Appendix A, we provide the MATLAB codes for the numerical implementation for one-, two-, and three-dimensions
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