发表机构
Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于算子分裂的蒙特卡洛模拟方案，用于Ornstein-Uhlenbeck驱动随机波动率模型下的期权定价，通过解析子步骤解决数值挑战，在精度-速度权衡上优于现有方案，尤其适用于路径依赖期权。
AI 中文摘要
我们通过算子分裂方法，为Ornstein-Uhlenbeck驱动随机波动率模型下的期权定价开发了一种高效的蒙特卡洛模拟方案。通过对控制随机微分方程进行巧妙的分裂，我们的算子分裂方案在所有子步骤中均允许解析解，因此其实现简化为仅需模拟少量正态随机变量。这解决了其他模拟方案中两个典型的数值挑战，即条件积分方差的采样和特征函数的路径wise逆积分变换。有三个开创性的模拟方案试图克服上述两个数值挑战，包括Zeng等人（2023）的Hilbert插值方案、Choi（2025）的Karhunen-Lo`eve展开方案以及基于Brignone和Sgarra（2026）的Inverse Gaussian分布的矩匹配方案。我们进行了数值测试，以比较使用我们的算子分裂方案与这三个开创性方案在期权定价中的精度-速度性能。我们发现，在所有方案中，我们的方案在精度-速度权衡方面表现良好，特别是在为具有大量监测时刻的路径依赖期权定价时。我们的方案性能可以通过保鞅控制变量和基于条件的方差缩减得到很好的增强。
英文摘要
We develop an efficient Monte Carlo simulation scheme for pricing options under the Ornstein-Uhlenbeck driven stochastic volatility model via the operator splitting approach. With an ingenious splitting of the governing stochastic differential equations, our operator splitting scheme admits analytic solutions in all sub-steps, so its implementation is simplified to require simulation of a few normal variates. This resolves the two typical numerical challenges in other simulation schemes, namely, sampling of conditional integrated variance and pathwise inverse integral transform of characteristic functions. There are three pioneering simulation schemes that attempt to overcome the above two numerical challenges. These include the Hilbert interpolation scheme of Zeng et al. (2023), Karhunen-Lo`eve expansion scheme of Choi (2025) and moment matching scheme based on the Inverse Gaussian distribution of Brignone and Sgarra (2026). We performed numerical tests to compare accuracy-speed performance of pricing options using our operator splitting scheme with these three pioneering schemes. We found that our scheme competes favorably well in terms of accuracy-speed tradeoff among all these schemes, in particular for pricing path dependent options with a large number of monitoring instants. The performance of our scheme can be well enhanced by martingale-preserving control variates and variance reduction via conditioning.
