Calibration of financial models using quasi-Monte Carlo

Abstract

In the area of financial mathematics Monte Carlo simulation is often successfully used to estimate the prices of certain products. However in many cases calibrating Monte Carlo based models to market prices turns out to be difficult due to stochastic noise arising in the objective functionals.

This noise can be reduced by the use of fixed point-sets of random numbers which are reused for every new set of parameters (i.e. in every new step of the optimization algorithm used for calibration).

In this paper we argue that the above technique can be enhanced by using fixed low discrepancy point-sets (quasi-Monte Carlo method) instead of ones originating from Pseudo-Random-Number generators. The method is applied to two different financial models and the results are compared with the classical one.