TY - JOUR
T1 - The stochastic collocation Monte Carlo sampler
T2 - Highly efficient sampling from ‘expensive’ distributions
AU - Grzelak, L.A.
AU - Witteveen, J.A.S.
AU - Oosterlee, C.W.
AU - Suárez-Taboada, M.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Exact sampling
KW - Heston
KW - Lagrange interpolation
KW - Monte Carlo
KW - SABR
KW - Squared Bessel
KW - Stochastic collocation
UR - http://www.scopus.com/inward/record.url?scp=85048156753&partnerID=8YFLogxK
U2 - 10.1080/14697688.2018.1459807
DO - 10.1080/14697688.2018.1459807
M3 - Article
AN - SCOPUS:85048156753
SN - 1469-7688
SP - 1
EP - 18
JO - Quantitative Finance
JF - Quantitative Finance
ER -