New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes

Authors:
Athanassios N. Avramidis;Pierre L'Ecuyer;Pierre-Alexandre Tremblay
Affiliations:
Université de Montréal, Montréal, Canada;Université de Montréal, Montréal, Canada;Université de Montréal, Montréal, Canada
Venue:
Proceedings of the 35th conference on Winter simulation: driving innovation
Year:
2003

Citing 10
Cited 6

Algorithm 654: FORTRAN subroutines for computing the incomplete gamma function ratios and their inverse

ACM Transactions on Mathematical Software (TOMS)
Algorithm 659: Implementing Sobol's quasirandom sequence generator

ACM Transactions on Mathematical Software (TOMS)
Latin supercube sampling for very high-dimensional simulations

ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A generalized discrepancy and quadrature error bound

Mathematics of Computation
Variance with alternative scramblings of digital nets

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Variance Reduction via Lattice Rules

Management Science
Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities

Management Science
SSJ: SSJ: a framework for stochastic simulation in Java

Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Quasi-monte carlo methods in practice: quasi-monte carlo methods for simulation

Proceedings of the 35th conference on Winter simulation: driving innovation
Smoothness and dimension reduction in Quasi-Monte Carlo methods

Mathematical and Computer Modelling: An International Journal

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
Efficient Monte Carlo and Quasi--Monte Carlo Option Pricing Under the Variance Gamma Model

Management Science
Simulation of a Lévy process by PCA sampling to reduce the effective dimension

Proceedings of the 40th Conference on Winter Simulation
Beta approximations for bridge sampling

Proceedings of the 40th Conference on Winter Simulation
Dirichlet Bridge Sampling for the Variance Gamma Process: Pricing Path-Dependent Options

Management Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study algorithms for sampling discrete-time paths of a gamma process and a variance gamma process, defined as a Brownian process with random time change obeying a gamma process. The attractive feature of the algorithms is that increments of the processes over longer time scales are assigned to the first sampling coordinates. The algorithms are based on having in explicit form the process' conditional distributions, are similar in spirit to the Brownian bridge sampling algorithms proposed for financial Monte Carlo, and synergize with quasi-Monte Carlo techniques for efficiency improvement. We compare the variance and efficiency of ordinary Monte Carlo and quasi-Monte Carlo for an example of financial option pricing with the variance-gamma model, taken from Madan, Carr, and Chang (1998).