Alternative processes for option pricing in uncertain environment

During last decades the stochastic simulation approach, both via MC and QMC has been vastly applied and subsequently analyzed in almost all branches of science. Very nice applications can be found in areas that rely on modeling via stochastic processes, such as finance. However, since financial quantities -- opposed to natural processes -- depend on human activity, their modeling is often very challenging. Many scholarstherefor suggest to specify some parts of financial models by means of fuzzy set theory. Since many financial problems are too complex to be solved analytically even in a crisp case, it can be efficient to apply (Quasi) Monte Carlo simulation. In this contribution the recent knowledge of fuzzy numbers and their approximation is utilized in order to suggest fuzzy-MC simulation to option price modeling in terms of fuzzy-random variables. In particular, we suggest three distinct fuzzy-random processes as an alternative to a standard crisp model. Application possibilities are shown on illustrative examples.

Keywords:

fuzzy random variable , fuzzy stochastic process , option pricing