Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme

Abstract

This paper will demonstrate how European and American option prices can be computed under the jump-diffusion model using the radial basis function (RBF)interpolation scheme. The RBF interpolation scheme is demonstrated by solving an option pricing formula, a onedimensional partial integro-differential equation (PIDE). We select the cubic spline radial basis function and propose a simple numerical algorithm to establish a finite computational range for the improper integral of the PIDE. This algorithm can improve the approximation accuracy of the integral with the application of any quadrature. Moreover, we offer a numerical technique termed cubic spline factorisation to solve the inversion of an ill-conditioned RBF interpolant, which is a well-known research problem in the RBF field. Finally, we numerically prove that in the European case, our RBF-interpolation solution is second-order accurate for spatial variables, while in the American case, it is second-order accurate for spatial variables and first-order accurate for time variables.

A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

“…Fausshauer et al, 2004a;Hon and Mao, 1999;Larsson et al, 2008;Pettersson et al, 2008). (Chan, 2010) and (Chan, 2011) extended these studies to jump-diffusion models, which are finite activity. The present paper contributes to this growing literature by showing that the RBF scheme can deal with singular Lévy measures, without needing to make major modifications to the scheme, and by testing it on an important class of examples, the Lévy-models of the CGMY-KoBol class.…”

Forecasting the Acquisition of University Spin-Outs: An RBF Neural Network Approach

“…An increasingly popular and promising approach to solve option pricing models is the use of numerical methods based on RBF [24]. Chan and Hubbert (2014) [25] demonstrated how European and American option prices can be computed under the jump-diffusion model using the RBF interpolation scheme. An implementation of RBF method for solving Black-Scholes-type partial differential equations (PDEs) is proposed to price the swaptions in the absence of credit risk [26].…”

Calculating the single-domain heat conduction with heat source problem by virtual boundary meshfree Galerkin method

“…The radial basis function interpolation (RBFI) [18][19][20] is an important way to interpolate the unknown physical field on the boundary or in the domain. Here, the boundary-type radial basis function interpolation is simply introduced as follow.…”