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

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 numb...

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Bibliographic Details
Published in:Quantitative finance 2019-02, Vol.19 (2), p.339-356
Main Authors: Grzelak, L. A., Witteveen, J. A. S., Suárez-Taboada, M., Oosterlee, C. W.
Format: Article
Language:English
Subjects:
Exact sampling
Heston
Lagrange interpolation
Monte Carlo
SABR
Squared Bessel
Stochastic collocation
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Summary: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.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2018.1459807