Questions tagged [fourier-transform]

The tag has no usage guidance.

12 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
4 votes
0 answers

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
4 votes
0 answers

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
4 votes
0 answers

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
3 votes
0 answers

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
1 vote
0 answers

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
1 vote
0 answers

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
1 vote
0 answers

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
  • 442
1 vote
0 answers

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
0 votes
0 answers

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
0 votes
0 answers

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
0 votes
0 answers

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
  • 326
0 votes
0 answers

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
  • 2,476