# Questions tagged [fourier-transform]

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### From Fourier Transforms to Option Values

I am trying to understand how Fourier transforms & Characteristics functions can be used to calculate option values. However, I am having difficulty following the process that is used in several ...
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### From VG and NIG processes to GBM

I would like to find out if it is possible to reduce: the Madan-Seneta Variance Gamma (VG) model; the Barndorff-Nielsen Normal Inverse Gaussian (NIG) model to the standard Black-Scholes through a ...
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### In Carr-Madans option pricing method, why do they use FFT?

In the famous fourier option pricing method by Carr-Madan, (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4044&rep=rep1&type=pdf), the crucial formula is They evaluate this by ...
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### Most accurate Fourier transform method for extreme OTM options

I need to calculate vanilla options prices for extreme moneyness range of e.g. (0%,1000%) under the Heston model for various parameter values that satisfy Feller. Which Fourier method (or other method)...
654 views

### Where does 1/2 in Fourier Transform method of pricing options come from?

I am reading Jianwe Zhu's Applications of Fourier Transform to Smile Modeling. On page 26, the author is describing how to use the Fourier tranform to price vanilla European call options. If $f_j$ is ...
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### How can we compute copula functions by using Fast Fourier transformation?

Q1. If a copula is expressed in terms of its moment generating function then how can this copula can be computed by using Fast Fourier Transformation? Q2. Can we use copula to evaluate spread option ...
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### How do you derive this Carr-Madan-like equation?

How do you derive equation (3) below? The equation is tagged as equation (11) in this paper: http://janroman.dhis.org/finance/IR/Heston%E2%80%93Hull%E2%80%93White%20Model%20Part%20I.pdf There are ...
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3k views

### Fourier transform for stock price forecasting

I am trying to forecast stock prices using Fast Fourier Transform, and plot historical, "future" (i.e. real) and forecast prices on the same chart to visually compare the accuracy of the ...
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### When do Fourier inversion methods run into problems?

So in my courses, we always priced options either with Monte Carlo methods, or some sort of PDE discretization. Then I looked up Fourier inversion methods on my own that rely on the characteristic ...
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### To what extent are Lévy processes used in financial engineering?

I know that (time changed) Lévy processes are actively researched in the academic world, including tools such as minimal entropy martingale pricing measures and fast Fourier transforms. To what extent ...
1k views

### Stock market cycles with Fourier Transform - amplitude vs. phase

There is this Wikipedia article on cycles in stock market data, which describes a 5-step process of finding dominant cycles in price data where step 2 reads: Step 2: Subsequently, a cycles engine ...
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### How Fourier Transform creates the filters?

I would like to know how the fourier transform creates filters to extract the constituent signals? I did learn from a book it extracts the spike information and then analyze and combine those ...
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### How much math is needed to understand Fourier Transform methods for option pricing?

I know of FDM and MC methods for option pricing, but have little to no experience with Fourier Methods. I am intending to dive into the literature on using Fourier methods for option pricing, ...
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### What's some good literature for Fourier transform methods?

I am looking for literature on Fourier methods in Quantitative Finance. I've been googling and found the book "Fourier Transform Methods in Finance" (Wiley), but the book seems poorly reviewed. ...
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### Fourier transform of a European put

In book The concepts and practice of mathematical finance, in the context of illustrating the stochastic volatility model, the Fourier transform $\hat{P}(\xi, V, T)$ of a European put $P(x, V, T)$ is ...
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### Fourier transform Carr-Madan method on an arbitrar initial $S_0$ values

As mentioned in Carr-Madan's paper, here, the European call option is: $$C_T(k)=\frac{e^{\alpha k}}{\pi}\int_0^\infty\mathcal{Re}\left(e^{-iuk}\psi(u)\right)du$$ where  \psi(u)=e^{-rT}\frac{\phi_T(...
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### Heston model with underlying BS dynamics always gives 1/2 of the right value, what am I doing wrong?

Just as an exercise I'm trying to follow this paper: https://arxiv.org/ftp/arxiv/papers/1502/1502.02963.pdf In the section 2.2 it calculates the value of a Call using the characteristic function of ...
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49 views

### COS method for Wishart Heston Model

NOTE: This code is a piece of code I am using for a master's thesis, so I do not expect someone to do the work for me, but I gladly accept suggestions of any kind. However, I am trying to get the ...
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### spectral entropy as stock volatility

There are many way to capture to stock volatility and most common is Beta. But problem with beta this is difficult to select ...
73 views

### Characteristic Function Kou (2002) Model

I'm looking for the correct characteristic function for the Kou (2002) jump diffusion model. Can someone help me? Because if I try to look at it online everyone forgot $r$ and $S_0$. This is what I ...
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178 views

### Cyclic analysis for trading signal generation

I would like to build trading signals using cyclic analysis in order to obtain a forecast afterwards. I had a look in literature and Hurst analysis, Fourier, etc, are used However, I am struggling to ...
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