Publication: Fractional diffusion models of option prices in markets with jumps
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Publication date
2007-02
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Tutors
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Publisher
Elsevier
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
Description
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
Bibliographic citation
Physica A, 2007, v. 374, n. 2, pp. 749–763