The stochastic collocation Monte Carlo sampler
Highly efficient sampling from ‘expensive’ distributions
L.A. Grzelak (TU Delft - Numerical Analysis, Rabobank)
JAS Witteveen (Centrum Wiskunde & Informatica (CWI))
C.W. Oosterlee (Centrum Wiskunde & Informatica (CWI), TU Delft - Numerical Analysis)
M. Suárez-Taboada (University of A Coruna)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
In this article, we propose an efficient approach for inverting computationally expensive cumulative distribution functions. A collocation method, called the Stochastic Collocation Monte Carlo sampler (SCMC sampler), within a polynomial chaos expansion framework, allows us the generation of any number of Monte Carlo samples based on only a few inversions of the original distribution plus independent samples from a standard normal variable. We will show that with this path-independent collocation approach the exact simulation of the Heston stochastic volatility model, as proposed in Broadie and Kaya [Oper. Res., 2006, 54, 217–231], can be performed efficiently and accurately. We also show how to efficiently generate samples from the squared Bessel process and perform the exact simulation of the SABR model.