A comparison of numerical methods to solve fractional partial differential equations

Abstract

A comparison of two numerical methods - ¯nite di®erence and Adomian decomposition method (ADM) - to solve a variety of fractional partial dif- ferential equations that occur in ¯nance are investigated. These fractional partial di®erential equations fall into the class of L¶evy models. They are known as the Finite Moment Log Stable (FMLS), CGMY and the extended Koponen (KoBol) models. Convergence criteria for these models under the numerical methods are studied. ADM fails to accurately price a claim writ- ten on these models. However, the ¯nite di®erence scheme works well for the FMLS and KoBol models.