The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions
提出一种随机配置蒙特卡洛采样器，通过多项式混沌展开框架，仅需少量原始分布求逆和标准正态样本即可生成大量蒙特卡洛样本，适用于Heston和SABR等随机波动率模型的精确模拟。
<p>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.</p>