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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 the complex nature of my results. Is the modulus my answer? Or is it the real part? Am I doing something wrong to have a complex number as my result?

https://wwwf.imperial.ac.uk/~ajacquie/IC_Num_Methods/IC_Num_Methods_Docs/Literature/CarrMadan.pdf

Thanks in advance

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    $\begingroup$ Could you please cite the formula? If I remember correctly they end up with the real part only. First there is the integral from - infinity to + infinity, then you change variables, get the chf and the conjugate chf added which gives 2 times the real part. Then your result it not imaginary anymore. $\endgroup$ – Richard Jul 3 '17 at 20:23
  • $\begingroup$ wwwf.imperial.ac.uk/~ajacquie/IC_Num_Methods/… This is the paper. Do you need the formula for the characteristic function aswell? $\endgroup$ – Sotiris Zampelis Jul 4 '17 at 16:00
  • $\begingroup$ I've implemented this on my Github page github.com/phillyfan1138/FFTOptionPricing/blob/master/…. There is no complex output; your code must be wrong somewhere. $\endgroup$ – user9403 Jul 4 '17 at 22:19
  • $\begingroup$ Thank you very much! I will try to check it out! Any chance you can tell me the model whose characteristic function you used? $\endgroup$ – Sotiris Zampelis Jul 5 '17 at 20:00
  • $\begingroup$ @SotirisZampelis please incorporate your link in your question $\endgroup$ – SRKX Jul 23 '17 at 4:36
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As I figured after reading Stephane Crepey's Financial Modelling book the result is meant to be complex, we should only include the real part as the answer something not 100% clear (at least to me) from Carr-Madan's paper.

I also found a useful outline of the algorithm for a naive version of FFT at F.Rouah's book on the Heston Model.

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