# Questions tagged [fourier-transform]

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### 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 ...
1 vote
272 views

### Option pricing using characteristic function

I'm currently on a mission trying to calculate option prices using the rough Heston model. I've found that this is usually done using the characteristic function of the model, but I must admit that I ...
• 109
1 vote
416 views

### 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 ...
• 356
631 views

### 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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### 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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1k 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 ...
• 131
68 views

### 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 ...
• 135
1 vote
443 views

### Option pricing using discrete fourier transform (python)

I am trying to implement the pricing formula for a European (call) option given in Ales Cerny's paper "Introduction to Fast Fourier Transform in Finance" (paper can be found here), as ...
70 views

### 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 ...
242 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)...
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1 vote
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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 ...
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1 vote
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