Option Pricing with Fourier Transform and Exponential Lévy Models [pdf]

Re:Option Pricing with Fourier Transform and Exponential Lév... by tanderson92 on Saturday October 27, 2018 @05:28PM (#18317761)

The paper mentions (page 117) that there are accuracy concerns with the FT quadrature method used for equation 8.21 (and analogous ones for others) for "near maturity deep OTM and ITM calls (puts)". This is attributed to the highly oscillatory nature of the Fourier Transform kernel. Is performance important here? Like, would a better quadrature rule which didn't suffer due to the oscillatory kernel help in an important way?

I ask, of course, because there are better ways to treat Fourier-type integrals than trapezoidal rule (I even wrote a numerical analysis paper on such a method).

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Re:Option Pricing with Fourier Transform and Exponential Lév... by FabHK on Saturday October 27, 2018 @07:00PM (#18318178)

I've rarely used FT methods in the real world (one reason being the wrap-around boundary conditions), and not really followed them. And, not sure whether that paper reflects the current state of the art.

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Re:Option Pricing with Fourier Transform and Exponential Lév... by tanderson92 on Saturday October 27, 2018 @07:37PM (#18318303)

FT methods are different from Fourier-spectral methods which typically have periodic BC requirements. That was not what my question was about.

The method in the paper exactly represents the solution as a Fourier-type integral which must be computed numerically. The error in the quadrature rule is the sole source of pricing error.

I guess whether the extra computational cost in computing those integrals exactly with the method the author used would carry a corresponding financial cost.

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