论文标题
用于计算GPU上衍生物灵敏度的准蒙特卡洛方法
Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU
论文作者
论文摘要
选项的计算希腊人对于风险管理至关重要。传统的路径和有限差异方法在高阶希腊人和具有不连续收益功能的选项方面工作较差。基于准蒙特卡洛的有条件路线方法（QMC-CPW）的选项希腊人可以有效平滑期权的回报功能，从而在计算灵敏度时可以提高效率。文献中还证明，通过将GPU应用于高度可行的金融问题（例如计算希腊人）来获得的计算速度提高。我们使用CUDA平台将QMC-CPW与GPU上的仿真配对。我们估计了三种异国情调的三种选择：算术亚洲，二进制亚洲和回顾，估计了三角洲，维加和伽马·希腊人。 QMC-CPW的好处是通过降低差异因子的$ 1.0 \ times 10^{18} $所显示的，而且由于我们在最准确的方法上实现超过$ 200 $ x的顺序CPU实现，通过使用GPU的使用来提高计算速度。
The calculation of option Greeks is vital for risk management. Traditional pathwise and finite-difference methods work poorly for higher-order Greeks and options with discontinuous payoff functions. The Quasi-Monte Carlo-based conditional pathwise method (QMC-CPW) for options Greeks allows the payoff function of options to be effectively smoothed, allowing for increased efficiency when calculating sensitivities. Also demonstrated in literature is the increased computational speed gained by applying GPUs to highly parallelisable finance problems such as calculating Greeks. We pair QMC-CPW with simulation on the GPU using the CUDA platform. We estimate the delta, vega and gamma Greeks of three exotic options: arithmetic Asian, binary Asian, and lookback. Not only are the benefits of QMC-CPW shown through variance reduction factors of up to $1.0 \times 10^{18}$, but the increased computational speed through usage of the GPU is shown as we achieve speedups over sequential CPU implementations of more than $200$x for our most accurate method.
