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.

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Rabobank Nederland, Utrecht, The Netherlands
Quantitative Finance
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Grzelak, L. A., Witteveen, J., Suárez-Taboada, M., & Oosterlee, K. (2018). The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions. Quantitative Finance, 19(2), 339–356. doi:10.1080/14697688.2018.1459807