Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes
Proceedings of the 35th conference on Winter simulation: driving innovation
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
Inverting the symmetrical beta distribution
ACM Transactions on Mathematical Software (TOMS)
Non-Gaussian asset allocation in the federal thrift savings plan
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Simulation of a Lévy process by PCA sampling to reduce the effective dimension
Proceedings of the 40th Conference on Winter Simulation
Revisit of stochastic mesh method for pricing American options
Proceedings of the 40th Conference on Winter Simulation
A practical view of randomized quasi-Monte Carlo: invited presentation, extended abstract
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Journal of Engineering and Technology Management
Fast orthogonal transforms and generation of Brownian paths
Journal of Complexity
Revisit of stochastic mesh method for pricing American options
Operations Research Letters
Simulating Lévy Processes from Their Characteristic Functions and Financial Applications
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Inverse transform method for simulating Levy processes and discrete Asian options pricing
Proceedings of the Winter Simulation Conference
| Hi-index | 0.01 |
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.