Question on the berrahoui's paper

pierrelefou · September 6th, 2007, 2:21 pm

I have a question on the berrahoui's paper.Let's consider two Forward rate F1,F2 We want to price the option: Max(F1(T)-F2(T)-K,0) where K is a strike and the maturity T of the option. In this paper, it is said that we can calculate the value of this option if we can calculate the value of Proba(F1(T)>x1) But this value is approximatively equal to: Proba(F1(T)>x1)=Call(F1(T),x1 - 1pb,Sig1,T) - Call(F1(T),x1 + 1pb,Sig1,T)where Call() is the value of the Call on F1(T).My question is: what is the value T in the call? Is it equal to the option maturity? Thank you

richbrad · September 6th, 2007, 2:25 pm

I think, from memory, yes....

pierrelefou · September 6th, 2007, 2:41 pm

Okmore precisely here is my pb: F1 and F2 are in fact CMS swap rates.Say F1 is the CMS30Y and F2 is the CMS2Y.1) If I understand well, if T is ten year, F1(T) must be the CMS30Y that starts is ten years.2) Now, what is Call(F1(T),x1 - 1pb,Sig1,T) ?? To me, this call on F1(T) is a Caplet, which maturity (T) is then year, which strike is x1-1bp, which volatility is Sig1.Since it is a Caplet, it only pays one cash flow. My question is: when does this caplet stat ? Is it one year before the maturity of the option?