Fractional diffusion models of option prices in markets with jumps
AbstractMost 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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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 374 (2007)
Issue (Month): 2 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
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;
Other versions of this item:
- Cartea, Álvaro & Castillo Negrete, Diego del, 2007. "Fractional diffusion models of option prices in markets with jumps," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12179, Universidad Carlos III de Madrid.
- Alvaro Cartea & Diego del-Castillo-Negrete, 2006. "Fractional Diffusion Models of Option Prices in Markets with Jumps," Birkbeck Working Papers in Economics and Finance 0604, Birkbeck, Department of Economics, Mathematics & Statistics.
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