Hi,I have just derived an option pricing formula in the framework of Duffie/Pan/Singleton. I also need the delta, i.e. the first derivative with respect to the option price. Can I further simplify the formula attached to this tread. More precisely, I have seen Bakshi/Cao/Chen derive the delta of their formula (Call = S \Pi_1 - K \Pi_2) as Delta = Pi_1 in a similar context. However, currently I do not see why this is possible.Looking forwards to your comments. Thanks a lot in advance

Hi, I haven't looked at your attachment, but here isone approach that should work for you.Define the function f(t,S,theta) = delta = dC/dS, wheretheta is whatever you are calling your extra affine state variable(s).If you take the S-derivative of your original PDE, you will see thatf() satisfies an equation of the same form, except thatthere is no discounting term, and the r in front of the first partialhas become r + sig^2. Anyway, repeat your solution methodwith this (new affine) equation, which now has the payoff f(T,S,theta) = 1(S > K),and you should get what you need.regards, p.s. finally looked at the attachment. You 'could' do it that way, too,by changing integration variables: z -> z + i in your next-to-last equation. This is effectively a contour move, which is legal because there are nopoles crossed under the move.

Hi Alan,thanks a lot for your comments. I haven't seen the contour move. I will also try the alternative procedure though.Regards,Mucki