嗯，谢谢了

我的问题就是从这篇文章来的。。。它直接就是写由第一个式子化简得到第二个式子，但是没有中间化简的过程。我想问具体是如何化简得到的（中间这个定积分是如何求的）。谢谢

我的问题就是从那篇文章来的。。。它直接就是写由第一个式子化简得到第二个式子，但是没有中间化简的过程。我想问具体是如何化简得到的（中间这个定积分是如何求的）。你之前帮我解答过其它问题，都很有用，谢谢。

I don't think that integral can be evluated directly.
The Heston version of pricing option via Fourier transform utilize the Gil-Palaez Inversion as I have shown above.

I checked several other papers, they all use this type of inversion for derivation.

So, in my opinion, the author writes the probability in this form because he want to apply the Gil-palaez inversion. Otherwise it is useless to prove the inversion in the early part of the paper. I am not a mathematical guy, so my knowledge is a little limited in this area. Sorry for that.

best

Indeed, this formula is based on Formula (3.17) in the above paper, based on the meaning of \pi_2.

Agree

I know,thank you

there is a derivation in this book "the heston model and its extensions in matlab and c#", however, I do not have this book.

There is a post now. https://bbs.pinggu.org/thread-2543002-1-1.html