Publication: Fractional diffusion models of option prices in markets with jumps
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Publication date
2006-08-11
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Birkbeck, University of London, School of Economics, Mathematics and 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 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
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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