为期权定价实现快速傅立叶变换 [英] Implementing a Fast Fourier Transform for Option Pricing

问题描述

我需要一些有关正在进行的小项目的提示。我的目标是实现可用于期权定价的快速傅立叶变换算法（FFT）。

I'm in need of some tips regarding a small project I'm doing. My goal is an implementation of a Fast Fourier Transform algorithm (FFT) which can be applied to the pricing of options.

首先要考虑的是：哪个FFT？ strong>

First concern: which FFT?

有很多不同的FFT算法，其中最著名的是Cooley-Tukey。我的想法是：我更喜欢最简单的方法，因为这不是论文或大型项目，而只是一门算法课程。但是它必须与期权定价兼容（与大多数定价相反-在我们的一般文献参考中，图像/声音处理的应用很好）。因此，这取决于所提供的输入形式（我需要一些建议）。我熟悉一些改进，例如小数FFT，混合基数FFT等。但是这些改进似乎很复杂且受优化/性能驱动，与我的项目无关。

There are a lot of different FFT algorithms, the most famous one being Cooley-Tukey. My thoughts on this: I prefer the most simple one, since this is no thesis or big project, just a course on Algorithms. But it has to be compatible with option pricing (in contrast with the most - well in our general literature- referenced application of images/sound processing). So it depends on the form of input that is provided (on which I need some advice). I'm familiar with the several improvements, like a Fractional FFT, mixed-radix FFT etc. But these seem pretty complex and optimization/performance driven, which is not relevant for my project.

第二个担忧：哪种定价模式？

我猜布莱克-舒尔斯（BS）有点扁平，我我知道BS之后出现的几种模型。因此，出于与上述目标相同的目的，我最初希望使用Heston模型。

I Guess Black-Scholes (BS) is a bit too 'flat' and I am aware of the several models that emerged after BS. So, with the same objectives as stated above, I'd initially prefer the Heston model.

有很多考虑因素，事实是我可以

There are a lot of considerations, and the truth is that I just can't see the wood for the trees.

一些背景信息：

我的背景是数学（理论）理学学士学位，所以我对傅立叶变换有一定的了解。

My background is a B.Sc in Mathematics (Theoretical), so I have some understanding of Fourier transforms.

目标是用于计算期权定价的有效FFT实现。它不一定是最快的（没有极端的优化）。目标是试图了解所选的FFT并具有实际的工作应用程序。

The goal is a working FFT implementation for calculating option pricing. It does not have to be the fastest (no extreme optimization). The goals are trying to understand the chosen FFT and having a real-world working application.

那么您能否就选择提供一些建议？

So could you give some advice on the choices?

我已经阅读了很多有关FFT的论文+期权定价，说出Google头几页上的所有热门歌曲。但是，这些研究的起因是更高的。

I've read a lot of papers on FFT + Option pricing, say all the decent hits on googles first few pages. But those studies were written with a much 'higher' cause.

推荐答案

我一直在研究这个主题-将FFT应用于期权定价-已有数周的时间。事实证明，在该主题上有大量工作要做，因此亚历山大（Alexandre）暗示它几乎没有用。

I've been researching this topic - FFTs applied to options pricing - for a few weeks now. It turns out there's an extensive body of work on the subject, so it's hardly futile as Alexandre implies.

我发现的最易读的基础论文来自Carr和Madan -www.math.nyu.edu/research/carrp/papers/pdf/jcfpub.pdf-但是，还有许多细节级别各异的Google可以通过期权定价傅里叶搜索找到。

The most readable basic paper I've found is from Carr and Madan - www.math.nyu.edu/research/carrp/papers/pdf/jcfpub.pdf - but there are many others in varying levels of detail, which Google will find via "option pricing Fourier" search.

我可能会在不久的将来在R中对此进行编码；我正在尝试找到合适的期权价格数据源进行测试。

I may be coding this up in R in the near future; I'm trying to locate a decent source of options price data for testing.

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