標題: 利用快速傅立葉轉換增加蒙地卡羅評價衍生性金融商品的效率Efficient Valuation of Financial Derivatives by Monte Carlo Simulations with Fast Fourier Transform 作者: 尤頌文Sung-Wen Yu許元春王克陸Yuan-Chung SheuKeh-Leh Wang應用數學系所 關鍵字: 快速傅立葉轉換;蒙地卡羅;馬丁格爾;變異數;分析;FFT;Delta;Martingale;Monte Carlo Simulations;Analysis 公開日期: 2006 摘要: 在本篇文章中，我們提出了使用快速傅立葉演算法來加速蒙地卡羅評價選擇權的方法。我們以快速傅立葉演算法計算選擇權的Delta值，並且利用這些Delta值去建立馬丁格爾控制變異數項來降低估計值的變異數。我們發現結合快速傅立葉演算法與馬丁格爾控制變異數方法在增加運算效率方面是非常有用的，並且也保留了運算的正確性。同時我們也討論了利用快速傅立葉演算法的誤差分析。In this paper, we proposed the use of Fast Fourier transform (FFT) method to accelerate Monte Carlo simulations in option pricing. The method of FFT is applied to compute the Deltas of the options. These Deltas are essential in construct martingale control for variance reduction. We find that the combination of the FFT method with the martingale control variate method is very useful to reduce the computational time while preserving the accuracy of simulations. The error analysis of using FFT method is also discussed. URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009422512http://hdl.handle.net/11536/81298 Appears in Collections: Thesis

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