The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions
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http://hdl.handle.net/2183/38158
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The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributionsFecha
2019Cita bibliográfica
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, 19(2), 339–356. https://doi.org/10.1080/14697688.2018.1459807
Resumen
[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.
Palabras clave
Exact sampling
Heston
Squared Bessel
SABR
Stochastic collocation
Lagrange interpolation
Monte Carlo
Heston
Squared Bessel
SABR
Stochastic collocation
Lagrange interpolation
Monte Carlo
Versión del editor
Derechos
Atribución-NoComercial-SinDerivadas 4.0 Internacional
ISSN
1469-7688
1469-7696
1469-7696