英文标题：
《Speed and biases of Fourier-based pricing choices: A numerical analysis》
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作者：
Ricardo Cris\\\'ostomo
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最新提交年份：
2018
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英文摘要：
We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black-Scholes-Merton framework. We rank the speed and accuracy of the competing choices, showing which methods require smaller truncation ranges and which are the most efficient in terms of sampling densities. While all implementations converge well in the Bates jump-diffusion model, Attari\'s formula is the only Fourier-based method that does not blow up for any Variance Gamma parameter values. In terms of speed, the use of strike vector computations significantly improves the computational burden, rendering both fast Fourier transforms (FFT) and plain delta-probability decompositions inefficient. We conclude that the multi-strike version of the COS method is notably faster than any other implementation, whereas the strike-optimized Carr Madan\'s formula is simultaneously faster and more accurate than the FFT, thus questioning its use.
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中文摘要：
我们比较了七种基于傅立叶变换的实现的CPU工作和定价偏差。我们的分析表明，当我们离开Black-Scholes-Merton框架时，截断和离散化误差显著增加。我们对竞争选择的速度和准确性进行排序，显示哪些方法需要较小的截断范围，哪些方法在采样密度方面最有效。虽然所有实现在Bates跳跃扩散模型中都能很好地收敛，但Attari公式是唯一一种基于傅立叶的方法，它不会对任何方差Gamma参数值爆炸。在速度方面，使用打击向量计算显著提高了计算负担，使得快速傅立叶变换（FFT）和纯delta概率分解效率低下。我们得出的结论是，COS方法的多重打击版本明显比任何其他实现都快，而打击优化的Carr-Madan公式同时比FFT更快、更准确，因此对其使用提出了质疑。
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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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