Option pricing with fuzzy parameters via monte carlo simulation

Abstract

Very nice applications of the stochastic simulation approach, both via MC and QMC, can be found in all areas that rely on modeling via stochastic processes, such as finance. However, since estimation of financial quantities is often very challenging, many scholars suggest to specify some parts of financial models by means of fuzzy sets theory. In this contribution the recent knowledge of fuzzy numbers and their approximation is utilized in order to suggest fuzzy-MC simulation approach to option price modeling in terms of fuzzy-random variables. In particular, we suggest to replace a crisp volatility parameter in the standard market model by a fuzzy random variable, which can be easily evaluated by Monte Carlo simulation. Application possibilities are shown on illustrative examples. © 2011 Springer-Verlag Berlin Heidelberg.