The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions
| Autor: | Lech A. Grzelak, María Suárez-Taboada, Jeroen A. S. Witteveen, Cornelis W. Oosterlee |
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| Přispěvatelé: | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Rok vydání: | 2018 |
| Předmět: |
050208 finance
Polynomial chaos Collocation Bessel process Stochastic volatility Computer science Cumulative distribution function 05 social sciences Monte Carlo method Lagrange interpolation Exact sampling SABR volatility model Squared Bessel Stochastic collocation Collocation method 0502 economics and business Applied mathematics 050207 economics Monte Carlo General Economics Econometrics and Finance Finance Heston SABR |
| Zdroj: | Quantitative Finance, 19(2), 339-356 Quantitative Finance |
| ISSN: | 1469-7696 1469-7688 |
| DOI: | 10.1080/14697688.2018.1459807 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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