Efficient pricing of barrier options with the variance-gamma model

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 an...

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Bibliographic Details
Main Author: Avramidis, A.N.
Format: Conference Proceeding
Language:English
Subjects:
Bridges
Closed-form solution
Contracts
Extrapolation
Monitoring
Monte Carlo methods
Pricing
Sampling methods
Upper bound
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Summary: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.
DOI:10.1109/WSC.2004.1371500