A comparison of numerical methods to solve fractional partial differential equations
Date
2010-03-15T11:44:26Z
Authors
Marom, Ofir
Journal Title
Journal ISSN
Volume Title
Publisher
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.