The Stochastic Collocation Monte Carlo Sampler: Highly Efficient Sampling from 'Expensive' Distributions

Quantitative Finance, 2018, Forthcoming

25 Pages Posted: 24 Nov 2014 Last revised: 13 May 2018

See all articles by Lech A. Grzelak

Lech A. Grzelak

Delft University of Technology

Jeroen Witteveen

Center for Mathematics and Computer Science (CWI)

Maria Suarez-Taboada

University of A Coruña

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: December 1, 2015

Abstract

In this article we propose an efficient approach for inverting computationally expensive cumulative distribution functions. The collocation method, called the Stochastic Collocation Monte Carlo Sampler (SCMC Sampler), within the 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 and independent samples from standard normals. We will show that with this path independent collocation approach the so-called exact simulation of the Heston stochastic volatility model, as proposed in (Broadie and Kaya, 2006), 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.

Keywords: Exact Sampling, Heston, Squared Bessel, SABR, Stochastic Collocation, Lagrange Interpolation, Monte Carlo

JEL Classification: C63, G12, G13

Suggested Citation

Grzelak, Lech Aleksander and Witteveen, Jeroen and Suarez-Taboada, Maria and Oosterlee, Cornelis W., The Stochastic Collocation Monte Carlo Sampler: Highly Efficient Sampling from 'Expensive' Distributions (December 1, 2015). Quantitative Finance, 2018, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2529691 or http://dx.doi.org/10.2139/ssrn.2529691

Lech Aleksander Grzelak (Contact Author)

Delft University of Technology ( email )

Netherlands
00310655731315 (Phone)

Jeroen Witteveen

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

Maria Suarez-Taboada

University of A Coruña ( email )

Campus Elviña s/n
A Coruña, Galicia 15071
Spain

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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