Print Email Facebook Twitter The stochastic collocation Monte Carlo sampler Title The stochastic collocation Monte Carlo sampler: Highly efficient sampling from ‘expensive’ distributions Author Grzelak, L.A. (TU Delft Numerical Analysis; Rabobank) Witteveen, J.A.S. (Centrum Wiskunde & Informatica (CWI)) Oosterlee, C.W. (TU Delft Numerical Analysis; Centrum Wiskunde & Informatica (CWI)) Suárez-Taboada, M. (University of A Coruna) Date 2018 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. Subject Exact samplingHestonLagrange interpolationMonte CarloSABRSquared BesselStochastic collocation To reference this document use: http://resolver.tudelft.nl/uuid:3c3c26ce-93bf-4e2f-ad91-4b92f33660a1 DOI https://doi.org/10.1080/14697688.2018.1459807 ISSN 1469-7688 Source Quantitative Finance, 1-18 Part of collection Institutional Repository Document type journal article Rights © 2018 L.A. Grzelak, J.A.S. Witteveen, C.W. Oosterlee, M. Suárez-Taboada Files PDF The_stochastic_collocatio ... utions.pdf 1.06 MB Close viewer /islandora/object/uuid:3c3c26ce-93bf-4e2f-ad91-4b92f33660a1/datastream/OBJ/view