文章基本信息

标题：Fractional Diffusion Models of Option Prices in Markets with Jumps
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作者：Álvaro Cartea ; Diego del-Castillo-Negrete
期刊名称：Birkbeck Working Papers in Economics and Finance / School of Economics, Mathematics and Statistics, Birkbeck College
印刷版ISSN：1745-8587
出版年度：2006
卷号：2006
出版社：London University
摘要：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 L´evy 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 L´evy 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.