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The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions

L. A. Grzelak, J. A. S. Witteveen, M. Suárez-Taboada and C. W. Oosterlee

Quantitative Finance, 2019, vol. 19, issue 2, 339-356

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.

Date: 2019
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