Fractional diffusion models of option prices in markets with jumps

Álvaro Cartea () and Diego del-Castillo-Negrete

Physica A: Statistical Mechanics and its Applications, 2007, vol. 374, issue 2, 749-763

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; CGMY; Fractional calculus; Riemann–Liouville fractional derivative; Barrier options; Down-and-out; Up-and-out; Double knock-out (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (46)

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Related works:
Working Paper: Fractional Diffusion Models of Option Prices in Markets with Jumps (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:374:y:2007:i:2:p:749-763

DOI: 10.1016/j.physa.2006.08.071

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