Efficient pricing of barrier options with the variance-gamma model

Authors:
Athanassios N. Avramidis
Affiliations:
Université de Montréal, Montréal, Canada
Venue:
WSC '04 Proceedings of the 36th conference on Winter simulation
Year:
2004

Citing 1
Cited 2

New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes

Proceedings of the 35th conference on Winter simulation: driving innovation

Efficient Monte Carlo and Quasi--Monte Carlo Option Pricing Under the Variance Gamma Model

Management Science
Efficient Monte Carlo and Quasi--Monte Carlo Option Pricing Under the Variance Gamma Model

Management Science

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Abstract

We develop an efficient Monte Carlo algorithm for pricing barrier options with the variance gamma model (Madan, Carr, and Chang 1998). After generalizing the double-gamma bridge sampling algorithm of Avramidis, L'Ecuyer, and Tremblay (2003), we develop conditional bounds on the process paths and exploit these bounds to price barrier options. The algorithm's efficiency stems from sampling the process paths up to a random resolution that is usually much coarser than the original path resolution. We obtain unbiased estimators, including the case of continuous-time monitoring of the barrier crossing. Our numerical examples show large efficiency gain relative to full-dimensional path sampling.