Inverse characteristique function

[Julianlapoutre]

Hi everybody i'm working on Heston-Nandi and i have to show how they have found their probability q1 and q2 but they doesn't really show how. They said they have used Feller 1971 et Kendall and Stuart (1997) without details.

in fact, i have a problem with the last line it's looks like the fourier transform but i don't understand where the real part come from

thanks for help

 

[Polter]

See: http://pfadintegral.com/docs/Schmelzle2010 Fourier Pricing.pdf
In particular, 3.2 The Inversion Theorem; and work through, say, 4.1 The Black–Scholes Style Formula.

 

[Julianlapoutre]

A big thanks it's looks like to be exactly what i'm looking for !

 

[Julianlapoutre]

Another stupid question :

I don't understand the last line, i know that under Q it have to be egal to r. But with yt = ln(St)\ln(St-1) i don't understand where -1/2\sigma^{2} goes, i think it's egal to 0 but i don't understand why.

thanks for help