Imprecise input data and option valuation problem

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, as for any other approach, the most crucial step is feeding the assumed model with data and estimation of model parameters. It is a matter of fact that financial processes are instable in time and often switch their regimes. Several scholars therefor suggest to specify some parts of financial models by means of fuzzy set theory. 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 and show application possibilities of one of them on illustrative example.