Questions tagged [fourier-transform]

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Dynamic PSD threshold for FFT

I am using signal denoising as explained by Steve Brunton, who explains that FFT is data data-driven SVD. I can select important components by selecting singular values that capture 90% of the ...
Bharat Sharma's user avatar
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69 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 ...
SimoPape's user avatar
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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 ...
user69406's user avatar
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229 views

StatArb : Fourier transform to find the perfect factor?

We have a basic mean reverting strategy. Given a bench of assets, we are looking for the best linear combination of them such as the resulting normalized time series would be noisy at high frequencies ...
Jerem Lachkar's user avatar
5 votes
1 answer
659 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 ...
user60799's user avatar
1 vote
2 answers
854 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 ...
Trettman's user avatar
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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 ...
Giogre's user avatar
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3 votes
2 answers
1k 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 ...
user54908's user avatar
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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 ...
Luigi87's user avatar
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3 votes
1 answer
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 ...
lazarea's user avatar
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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 ...
Hiperfly's user avatar
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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 ...
ThisIsGonnaBeCool's user avatar
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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 ...
Elizabeth's user avatar
5 votes
2 answers
412 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)...
user avatar
1 vote
1 answer
523 views

How to find characteristic function in Fourier Cosine method (COS method) by Fang and Oosterlee

Fang and Oosterlee (2009) introduced Fourier-Cosine method (COS method) in their paper. The formula to price an option is approximately $$e^{-r\Delta t} \sum_{k=0}^{N-1}' Re\left\{ \phi\left( \frac{k\...
Idonknow's user avatar
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11 votes
1 answer
440 views

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 ...
Lisa Ann's user avatar
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1 vote
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Fourier transform of price function

If the expiry value is given by $f(x,T) = e^{-c x}$ for $x \ge a$ and 0 otherwise and c is a +ve constant, prove that in the Fourier domain: $$ (c + j \omega) F(\omega, 0) = e^{-rT} e^{-a(c+j\omega)}...
s5s's user avatar
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150 views

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 ...
Stéphane's user avatar
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1 vote
0 answers
119 views

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(...
Pandaaaaaaa's user avatar
3 votes
1 answer
151 views

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 ...
fewf's user avatar
  • 31
5 votes
1 answer
591 views

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 ...
ewofeo's user avatar
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1 vote
2 answers
1k views

Beginner FFT (Fourier) transforms on closing prices for Apple

I don't know math very well, but I have been programming for many years. I would like to use FFT as a parameter to a ML model. The FFT is diving down sharply. I tried many stocks and its the same. ...
Michael Joyner's user avatar
2 votes
1 answer
565 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, ...
tryOut's user avatar
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2 votes
2 answers
183 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. ...
Thanksu's user avatar
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1 vote
1 answer
555 views

Python Numpy FFT array size limit?

I am trying to find the price of an Option based on the fft technique within the binomial model and it works fine until N>40000 where I start getting negative values and weird convergene and I am not ...
FatFeynman's user avatar
1 vote
1 answer
104 views

Transform of payoff function $w_c=(\sqrt{y}-K)^+$ [closed]

I am working on a project where I price EU call options written on the VIX index. The payoff function of interest looks like $w_c=(\sqrt{y}-K)^+$ where K is the strike price and y is the value of $...
Michael's user avatar
  • 21
4 votes
0 answers
185 views

Zero-rebate barrier option pricing under the Heston model

I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model: $$dS_t=\mu S_tdt+\sqrt{v_t}S_tdW^S_t$$ $$dv_t=\kappa(\bar{v}-v_t)dt+\eta\sqrt{v_t}dW^v_t,\quad d\langle ...
FunnyBuzer's user avatar
  • 1,012
2 votes
1 answer
330 views

Characteristic function of CGMY model

I have a basic question about the CGMY model which has characteristic function $$ \Gamma(-Y_p)\left((M-iu)^{Y_p}-M^{Y_p}\right)+\frac{C_n}{C_p}\Gamma(-Y_n)\left((G+iu)^{Y_n}-G^{Y_n}\right) $$ whith $...
lbf_1994's user avatar
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3 votes
1 answer
292 views

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 ...
Rodolfo Oviedo's user avatar
4 votes
2 answers
165 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 ...
David Nguyen's user avatar
4 votes
0 answers
91 views

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 ...
Ahmad's user avatar
  • 41
2 votes
1 answer
343 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 ...
srinivasan's user avatar
3 votes
0 answers
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 ...
mac13k's user avatar
  • 191
0 votes
1 answer
362 views

Understanding FFT's complex number result on option pricing

I have been using the Carr-Madan method to price caplets using the FFT. I have followed every step closely and (i believe) successfully. I understand the procedure theoretically but I cannot interpret ...
Sotiris Zampelis's user avatar
5 votes
1 answer
244 views

Heston ITM and OTM options pricing

In the Carr and Madan (1999) methodology exploiting the fast Fourier transform, the quasi-analytical price of a call is given by: $$C(t,T,K)=e^{-r(T-t)}\frac{e^{-\alpha \log (K)}}{\pi}Re\left[\int_0^\...
NSZ's user avatar
  • 511
20 votes
4 answers
6k views

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 ...
sets's user avatar
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