Fractional Diffusion Models of Option Prices in Markets with Jumps

Álvaro Cartea () and Diego del-Castillo-Negrete

No 604, Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics

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 Levy 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 Levy 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; Levy-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: 2006-04
New Economics Papers: this item is included in nep-fmk
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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https://eprints.bbk.ac.uk/id/eprint/26938 First version, 2006 (application/pdf)

Related works:
Journal Article: Fractional diffusion models of option prices in markets with jumps (2007)
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