On pricing discrete barrier options using conditional expectation and importance sampling Monte Carlo

G. Okten, E. Salta and A. Goncu

Mathematical and Computer Modelling,, Vol. 47, pp. 484-494, 2008

Abstract

Estimators for the price of a discrete barrier option based on conditional expectation and importance sampling variance reduction techniques are given. There are erroneous formulas for the conditional expectation estimator published in the literature: we derive the correct expression for the estimator. We use a simulated annealing algorithm to estimate the optimal parameters of exponential twisting in importance sampling, and compare it with a heuristic used in the literature. Randomized quasi-Monte Carlo methods are used to further increase the accuracy of the estimators.