A high order method for pricing of financial derivatives using Radial Basis Function generated Finite Differences

Slobodan Milovanović and Lina von Sydow

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 174, issue C, 205-217

Abstract: In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher accuracy. Still, the discretization matrix is fairly sparse. As a model problem, we consider the pricing of European options in 2D. Since such options have a discontinuity in the first derivative of the payoff function which prohibits high order convergence, we smooth this function using an established technique for Cartesian grids. Numerical experiments show that we acquire a fourth order scheme in space, both for the uniform and the nonuniform node layouts that we use. The high order method with the nonuniform node layout achieves very high accuracy with relatively few nodes. This renders the potential for solving pricing problems in higher spatial dimensions since the computational memory and time demand become much smaller with this method compared to standard techniques.

Keywords: Pricing of financial derivatives; Radial Basis Function generated Finite Differences; High order methods; Smoothing of initial data (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:174:y:2020:i:c:p:205-217

DOI: 10.1016/j.matcom.2020.02.005

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