# Questions tagged [fourier-transform]

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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 ...
115 views

### 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)...
118 views

### Why do we need approximation in option pricing?

We know that we can get a closed form for European option price. And we can calculate directly the normal distribution accumulation. But I saw that people use many approximation methods such as ...
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### Change of the stock price dynamics while pricing using the Fourier transform techniques

Right now I am trying to understand how we can use the Fourier theorem in obtaining the formula for option pricing (from Zhu J., "Modular pricing of options"). While modeling the interest ...
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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 ...
201 views

### To what extent are Lévy processes used in financial engineering?

I know that (time changed) LĆ©vy processes are actively researched in the academic world, including tools such as minimal entropy martingale pricing measures and fast Fourier transforms. To what extent ...
563 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 ...
237 views

### 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, ...
223 views

### 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 ...
114 views

### 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 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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### Pricing options by IFT under the Heston and Nandi (2000) model: odd behavior

I am working on option pricing using GARCH models and, currently, I am coding the pricing of options under the Heston and Nandi (2000) model. This model admits a quasi analytical formula for pricing ...