Simulation of the Multivariate Generalized Hyperbolic Distribution using Adaptive Importance Sampling
Marco Bee, Roberto Benedetti · 45th Scientific Meeting of the Italian Statistical Society · 2010
In this paper we use Adaptive Importance Sampling for simulating the multivariate Generalized Hyperbolic Distribution and computing tail probabilities. Adaptive Importance Sampling is an extension of classical Importance Sampling that updates sequentially the instrumental density at each iteration. Under the only condition that the density is known in closed form, the method can be used for sampling multivariate distributions and estimate quantities of interest. Some simulations experiments and a real-data application show that, for the problem at hand, the method has an excellent performance, which makes this technique an appealing alternative to more traditional sampling algorithms, whose implementation for the simulation of the Generalized Hyperbolic Distribution is not straightforward