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 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.