计算GPU导数灵敏度的拟蒙特卡罗方法
Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU
摘要：
期权希腊人的计算是风险管理的重要内容。传统的路径法和有限差分法对高阶希腊人和具有不连续支付函数的期权的效果很差。基于拟蒙特卡罗的条件路径方法（QMC-CPW）的选项希腊人允许有效地平滑选项的支付函数，允许在计算灵敏度时提高效率。在文献中还证明了通过将GPU应用于高度并行的金融问题（例如计算希腊人）来提高计算速度。我们使用CUDA平台将QMC-CPW与GPU上的模拟配对。我们估计三角洲，织女星和伽玛希腊三个异国情调的选择：算术亚洲，二进制亚洲，和回望。不仅是QMC-CPW的好处显示通过方差缩减因子高达$1.0 \times 10^{18}$，但增加的计算速度，通过使用GPU的显示，因为我们实现了加速超过$200$ x的顺序CPU实现我们最准确的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
