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)...
user34971
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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 ...
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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:
$$C(t,T,K)=e^{-r(T-t)}\frac{e^{-\alpha \log (K)}}{\pi}Re\left[\int_0^\...
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Why do we need approximation in option pricing?
We know that we can get a closed form for European option price. And we can calculate directly the normal distribution accumulation. But I saw that people use many approximation methods such as ...
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Change of the stock price dynamics while pricing using the Fourier transform techniques
Right now I am trying to understand how we can use the Fourier theorem in obtaining the formula for option pricing (from Zhu J., "Modular pricing of options").
While modeling the interest ...
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Zero-rebate barrier option pricing under the Heston model
I'm trying to derive an approximation for the zero-rebate barrier option under the Heston model:
$$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 ...
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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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1
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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 ...
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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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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 $...
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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 $...
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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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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\...
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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 ...
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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.
...
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2
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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 ...
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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 ...
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0
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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 ...
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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 ...
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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)}...
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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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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 ...
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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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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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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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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 ...