標題: Pricing Asian option by the FFT with higher-order error convergence rate under Levy processes
作者: Chiu, Chun-Yuan
Dai, Tian-Shyr
Lyuu, Yuh-Dauh
資訊管理與財務金融系 註:原資管所+財金所
Department of Information Management and Finance
關鍵字: Pricing;Fast Fourier Transform;Asian option;Newton-Cotes integration formula
公開日期: 1-二月-2015
摘要: Pricing Asian options is a long-standing hard problem; there is no analytical formula for the probability density of its payoff even when the process of the underlying asset follows the simple lognormal diffusion process. It is known that the density function of a discretely-sampled Asian option\'s payoff can be efficiently approximated by the Fast Fourier Transform (FFT). As a result, we can accurately price the option under more general Levy processes. This paper shows that the pricing error of this approach, called the FFT approach, can be decomposed into the truncation error, the integration error, and the interpolation error. We prove that previous algorithms that follow the FFT approach converge quadratically. To improve the error convergence rate, our proposed algorithms reduce the integration error by the higher-order Newton-Cotes formulas and new integration rules derived from the Lagrange interpolating polynomial. The interpolation error is reduced by the higher-order Newton divided-difference interpolation formula. Consequently, our algorithms can be sped up by the FFT to achieve the same time complexity as previous algorithms, but with a faster error convergence rate. Numerical results are given to verify the efficiency and the fast convergence of our algorithms. (c) 2014 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.amc.2014.12.002
http://hdl.handle.net/11536/124355
ISSN: 0096-3003
DOI: 10.1016/j.amc.2014.12.002
期刊: APPLIED MATHEMATICS AND COMPUTATION
Volume: 252
起始頁: 418
結束頁: 437
顯示於類別:期刊論文