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I was trying to solve european option pricing problem using Conv method (introduced by Lord in 2008 https://pdfs.semanticscholar.org/0632/460bd50b2151f74ac40028df4cc60e73a884.pdf).

The final step of this algorithm is to transform the solution on the frequency domain to the time domain by inverse fast Fourier transform, which means that I can retrieve approximations for all the grid points.

However, I noticed that only the solutions in the center of the time domain (in this case, x=40, and I used log grid points) are accurate. Here is the plot: the orange line represents the approximation using FFT, the blue line represents the real solution.

the orange line represents the approximation using FFT, the blue line represents the real solution

Moreover, the approximation looks periodic. So I was wondering what kind of situation will inverse FFT give a 'periodic-like' solution? I did some research on this topic, and foundthat DFT assumes the input is periodic, which may cause "time domain aliasing" (https://www.dspguide.com/ch10/3.htm).

I also found that "spectral leakage" may be related to my problem. Can anyone give me some advice on this? Thank you very much.

P.S. By periodic, I mean the solutions on the two ends are very close to each other. I changed lots of parameters, and this always holds.

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  • $\begingroup$ What do you mean by periodic? It doesn't look like it repeats to me ... Maybe try plotting the logarithm of the $x$-coordinate on the $x$-axis, and then it might be sinusoidal? $\endgroup$ Nov 12, 2019 at 4:37
  • $\begingroup$ @ZubinMukerjee By periodic, I mean the solutions on the two ends are very close to each other. I changed lots of parameters, and this always holds. $\endgroup$
    – Wenzel
    Nov 12, 2019 at 4:45
  • $\begingroup$ This is not an artifact of where you stop the plot? $\endgroup$ Nov 12, 2019 at 4:59
  • $\begingroup$ @ZubinMukerjee No, that’s the full time domain $\endgroup$
    – Wenzel
    Nov 12, 2019 at 5:08
  • $\begingroup$ maybe you should have a look at this question math.stackexchange.com/questions/2432207/… $\endgroup$ Nov 14, 2019 at 16:43

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