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.

Exact sampling, Heston, Lagrange interpolation, Monte Carlo, SABR, Squared Bessel, Stochastic collocation
Rabobank Nederland, Utrecht, The Netherlands
Quantitative Finance
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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