Efficient pricing of barrier options with the variance-gamma model

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Description/Abstract

We develop an efficient Monte Carlo algorithm for pricing
barrier options with the variance gamma model \cite{fMAD98a}.
After generalizing the double-gamma bridge sampling algorithm
of \citeN{fAVR03a}, 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.