Cartea, ÁlvaroCastillo Negrete, Diego del2011-09-232011-09-232007-02Physica A, 2007, v. 374, n. 2, pp. 749–7630378-4371http://hdl.handle.net/10016/12179Most 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 derivedapplication/pdfeng©ElsevierFractional-Black–ScholesLévy-stable processesFMLSKoBoLCGMYFractional calculusRiemann–Liouville fractional derivativeBarrier optionsDown-and-outUp-and-outDouble knock-outresearch articleEmpresa10.1016/j.physa.2006.08.071open access7492763Physica A374