Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Elementary Numerical Analysis: An Algorithmic Approach
Elementary Numerical Analysis: An Algorithmic Approach
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient pricing of barrier options with the variance-gamma model
WSC '04 Proceedings of the 36th conference on Winter simulation
Quasi-Monte Carlo methods in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
Inverting the symmetrical beta distribution
ACM Transactions on Mathematical Software (TOMS)
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
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We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoffs, we obtain a pair of estimators (named low and high) with expectations that (1) are monotone along any such bridge sampler, and (2) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive (infinitely expensive in some situations) to compute. By using these bounds with extrapolation techniques, we obtain significant efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi--Monte Carlo to reduce the variance and thus further improve the efficiency. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options.