The stochastic collocation Monte Carlo sampler

Highly efficient sampling from ‘expensive’ distributions

Journal article (2018)

Authors

L.A. Grzelak Rabobank, Numerical Analysis - EEMCS
J.A.S. Witteveen Centrum Wiskunde & Informatica (CWI)
C.W. Oosterlee Centrum Wiskunde & Informatica (CWI), Numerical Analysis - EEMCS
María Suárez-Taboada University of A Coruna
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2018 L.A. Grzelak, J.A.S. Witteveen, C.W. Oosterlee, M. Suárez-Taboada
DOI
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https://doi.org/10.1080/14697688.2018.1459807
Monte Carlo Heston SABR Stochastic collocation Exact sampling Lagrange interpolation Squared Bessel
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.