Questions tagged [fourier-transform]

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119 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, ...
2
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2answers
83 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. ...
1
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1answer
58 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 ...
1
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1answer
74 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 $...
4
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0answers
103 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 ...
2
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1answer
112 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 $...
3
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1answer
148 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 ...
4
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2answers
105 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 ...
4
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0answers
60 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 ...
1
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1answer
140 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 ...
3
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0answers
344 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 ...
0
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1answer
226 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 ...
3
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1answer
112 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^\...