Unbiased Monte Carlo valuation of lookback, swing and barrier options with continuous monitoring under variance gamma models

Abstract

We introduce fast and unbiased methods for Monte Carlo valuation of lookback, swing, and barrier options under variance gamma models. For the valuation of lookback and swing options, a procedure to draw samples of the final value, infimum, and supremum of variance gamma processes with an additional drift term up to arbitrary precision is developed; for barrier options, a separate method is designed to improve the performance by exploiting the particular payout structure. All algorithms substantially rely on adaptive difference-of-gammas bridge sampling, a newly introduced enhancement of the truncated difference-of-gammas bridge sampling method originally presented by Avramidis et al (2003) and successfully applied to lookback and barrier option valuation by Avramidis (2004) and Avramidis and L'Ecuyer (2006). By applying our algorithms to examples treated by Avramidis (2004) and Avramidis and L'Ecuyer (2006) we observe considerable reductions in computational effort and memory requirements. Furthermore, our algorithms feature a priori bounds on the bias, whereas Avramidis and L'Ecuyer (2006) are restricted to a posteriori bounds.