High Order Approximation of Derivatives With Applications To Pricing of Financial Derivatives
Journal of Computational and Applied Mathematics
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In this paper, we first compare three different methods for approximating the first and second derivatives from function values given at scattered points. Then we propose to use the most accurate derivative approximation method in a forward Euler scheme to solve the general Black–Scholes equation. We prove the scheme's stability and error estimate. Many numerical examples applying to pricing of financial derivatives are presented to demonstrate the efficiency and accuracy of our scheme.
Black–Scholes equation; High-order compact finite difference method; Option pricing models; Radial basis function
High Order Approximation of Derivatives With Applications To Pricing of Financial Derivatives.
Journal of Computational and Applied Mathematics, 398