Grzelak, LechWitteveen, Jeroen A. S.Suárez-Taboada, M.Oosterlee, Cornelis2024-07-182024-07-182019Grzelak, 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, 19(2), 339–356. https://doi.org/10.1080/14697688.2018.14598071469-76881469-7696http://hdl.handle.net/2183/38158[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.engAtribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Exact samplingHestonSquared BesselSABRStochastic collocationLagrange interpolationMonte Carlojournal articleopen access10.1080/14697688.2018.1459807