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

Authors:
Giray ÖKten;Emmanuel Salta;Ahmet GöNcü
Affiliations:
Department of Mathematics, Florida State University, Tallahassee FL 32306-4510, United States;Department of Mathematics, Florida State University, Tallahassee FL 32306-4510, United States;Department of Mathematics, Florida State University, Tallahassee FL 32306-4510, United States
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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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.