Fractional Diffusion Models of Option Prices in Markets With Jumps

Physica A, 374, pages 749–763, 2007

29 Pages Posted: 4 Oct 2006 Last revised: 11 Mar 2013

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: August 1, 2006

Abstract

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.

Keywords: Fractional-Black-Scholes, Lévy-Stable processes, FMLS, KoBoL

JEL Classification: G12, G13

Suggested Citation

Cartea, Álvaro, Fractional Diffusion Models of Option Prices in Markets With Jumps (August 1, 2006). Physica A, 374, pages 749–763, 2007, Available at SSRN: https://ssrn.com/abstract=934809 or http://dx.doi.org/10.2139/ssrn.934809

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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