英文标题：
《Singular Fourier-Pad\\\'e Series Expansion of European Option Prices》
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作者：
Tat Lung Chan
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最新提交年份：
2017
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英文摘要：
We apply a new numerical method, the singular Fourier-Pad\\\'e (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in L\\\'evy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with non-smooth probability density functions, they cause the Gibbs phenomenon, accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. Moreover, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques.
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中文摘要：
我们采用了一种新的数值方法，即Driscoll和Fornberg（2001年，2011年）发明的奇异Fourier-Pad（SFP）方法，对列维和仿射过程中的欧式期权进行定价。此应用背后的动机是降低当前傅立叶技术用于近似分段连续（非光滑）概率密度函数时的低效性。当快速傅立叶变换和傅立叶级数等技术应用于具有非光滑概率密度函数的价格和对冲期权时，它们会导致吉布斯现象，因此，对于具有跳跃值或导数的密度函数，这些技术会缓慢收敛。这严重影响了这些技术的效率和准确性。在本文中，我们使用SFP方法推导了定价公式及其期权希腊，以解决Gibbs现象并恢复全局谱收敛速度。此外，我们还表明，我们的方法需要少量的条款来产生快速的误差收敛，并且它能够准确地为任何欧洲类型的期权定价，无论是在货币中还是在货币中，还是在期限很长/很短的情况下。此外，我们还对期权定价中的SFP方法进行了误差界分析。与现有方法相比，这种新方法在数值实验中表现良好。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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