<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.</p></abstract>

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.

A fuzzy approach to option pricing in a Levy process setting

Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland

The John Paul II Catholic University of Lublin, ul. Konstantynów 1H, 20-708 Lublin, Poland

International Journal of Applied Mathematics and Computer Science

{"article-title":"A fuzzy approach to option pricing in a Levy process setting"}

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy...

A fuzzy approach to option pricing in a Levy process setting

Published Online: Sep 30, 2013

Page range: 613 - 622

DOI: https://doi.org/10.2478/amcs-2013-0046

This content is open access.