亞式選擇權評價：使用快速傅利葉轉換與辛普森法則

Abstract

本文將指出一種有效率性的演算法，可以快速而準確地求算離散式固定履約價型亞式選擇權價格。這個演算法並不依賴Black-Scholes假設，在應用上具有彈性，可以適用於多種對於標的價格分配的假設以符合實證現象，例如：厚尾現象。 本文將延伸Carverhill-Clewlow (1990)和Benhamou (2002)的結果，在快速傅利葉轉換之上加入Simpson法則和三次多項式內插法以提升計算精確度。

In this thesis, we introduce an efficient algorithm for pricing discrete Asian options with fixed strike price. Our algorithm does not rely on the Black-Scholes assumption and is flexible for many kinds of underlying densities. Our algorithm can be applied to capturing many empirical phenomena, such as fat-tail effect. Based on the Fast Fourier Transform (FFT), our algorithm using Simpson’s rule and the 3rd-order polynomial interpolation is an enhanced version of the algorithms of Carverhill and Clewlow (1992) and Benhamou (2002). The contribution of this thesis is an improved convergence rate to the order of 4.