Monte‐Carlo Pricing Issues

Monte-Carlo techniques may be fairly considered as the easiest way to deal with multi-asset or path-dependent payoffs. This chapter develops a method for sampling a set of correlated assets under the multivariate Gaussian model. It also investigates some techniques to reduce the variability of simulation outputs, whatever the payoff. The chapter deals only with multivariate Gaussian distributions: it means that mutual dependencies among assets are measured, two at a time, by the coefficient of linear correlation or, more simply, the correlation ρ. One major drawback of Monte-Carlo techniques is that their accuracy depends heavily on the efficiency of random number generators (RNG). The variability of the simulation results points to some potential error in the pricing. Variance reduction techniques are specifically designed to reduce the empirically observed standard deviation, without changing the RNG. This chapter reviews three of them: Antithetic variates, Importance sampling and Control variates.