運用圖形處理器增進計算巴黎選擇權價格的效能

Abstract

隨著電腦運算處理能力地增加，在評價金融衍生性商品時也能達到更有效率且正確的結果；而也因為金融商品之計算價格有時會有時間的急迫性，因此如何用電腦硬體和演算法增進計算速度和正確性就成為重要的課題。 在本篇論文中我們使用巴黎選擇權和圖形處理器來做例子，巴黎選擇權為一種擁有障礙選擇權特性的一種路徑相關選擇權。Li和Zhao提出利用生成函數來計算巴黎選擇權的價格，我們在中央處理器和圖形處理器上實作出該方法。結果表示由於圖形處理器有著強大的平行運算能力，因此在執行時間上比中央處理器少上許多，尤其當期數值越大越明顯，而最後價格和中央處理器運算後的價格幾無差異。也因此我們可以更快速地獲得巴黎選擇權的價格而不失其精確度。

As computing power increases, we can get faster and more correct results in pricing derivatives. How to improve speed and correctness by computer hardware and algorithms is an important issue because pricing financial products is often a time-critical task. In this thesis we use Parisian options and GPUs as an example. Parisian options are path-dependent options with barrier-like features. Binb-Qing Li and Hai-Jian Zhao proposed to price Parisian options by generating functions. We implement this method in both CPUs and GPUs. The results show that the execution time used by GPUs is much smaller than those by CPUs because of their powerful parallel-processing capabilities, especially when number of periods grows bigger. As a result, we can price Parisian options faster and with accuracy.