Hi Yougy60,I do not get your point. What I see what you are doing is to use a Black model for Xt and use a DD model for Yt.In the Black world there is a flat volatility which when Xt seen as a DD it is not! There is skew.Thus, if you get the ATM vol you have to use the ATM strike in both models... I does not be a surprise if you calculate a Call value on X0+b. In fact what is flat in OIS (Xt) is not flat in Libor (Yt). We have a skew there. The formulae are actually some formulae from a paper by P. Jaeckel on Quanto Skew.Best, Lapsi

Hi,Thanks for replying.I found the article you refer to : http://www.pjaeckel.webspace.virginmedi ... pdfHowever, I do not find where the beta is defined. Do you know what he calls beta?

the beta might be forward/(basis+forward) and in your case the value of the beta is 0.5458 instead of 0.1677,not sure but bigger value might be helpful.

Hi Lapsilago,The formula you refer to (ie from Jaeckel quanto skew paper) is the formula for the following DD modelisation :dSt = ( S0*sigma*(1-beta) + sigma*beta*St ) dWtHowever, in our case, the DD modelisation is simply :dSt = sigma * (St + b) dWt (where S is the OIS and b the libor-ois spread) So with beta = S0/(S0+b) it leads to dSt = ( sigma*St + S0*sigma*(1-beta)/beta ) dWt which does not correspond.So, I think my formula is right for this modelisation. And it still don't work for my parameters.Do you agree?

Sorry for interupting...with beta = S0/(S0+b) it leads to dSt ={sigma*S0/(S0+b)}(St + b) dWt So sigma_DD=sigma*S0/(S0+b)=eta*beta in the Jorg's paperthen put eta in the analytical formulae in Jaeckel's paper as sigma.Strange but hope i am not wrong...

Hi wadwad.I am not sure to understand what you say.Let F be the OIS and b the libor-ois spread.By definition of beta, we have b=F0*((1-beta)/beta) , so that dFt = sigma*(Ft + F0*((1-beta)/beta)) dWtDo you agree with this?If yes, which formula do you use to convert sigma into a black volatility?

i have a doubt, starting from you formulaedSt = ( S0*sigma*(1-beta) + sigma*beta*St ) dWtyou divided beta on boths side,(switching to F case) (1/beta) dFt = sigma*(Ft + F0*((1-beta)/beta)) dWt

Ok if I understand, you have divided both sides by beta.And then?

just rewrite your functiondSt = ( S0*sigma*(1-beta) + sigma*beta*St ) dWtin terms of b by plug in beta = S0/(S0+b) and you will have dSt ={sigma*S0/(S0+b)}(St + b) dWt which is consistent with both papers.

No because in Joerg's paper it is :dSt = sigma * (St + b) dWt (where S is the OIS and b the libor-ois spread)

Joerg sees this sigma as sigma_DD which is beta*eta,eta is the sigma in the function i typed,maybe i am wrong...

He says that we may interpret sigma as a displaced diffusion volatility sigmaDD, where sigma is dSt = sigma * (St + b) dWt and S the OIS (see p. 10.)So, eta is not the sigma in the SDE you typed whereas sigma is the sigma in the SDE you typed.

maybe we can get rid of the meaning and just follow math.Joerg has sigma_DD which can not be used in analytical formular because analytical formular use another SDE,so he transformed sigma_dd to eta,and eta can be used as sigma in the analytical formular. Beta is used twice,for transforming and in the analytical formular. Strange enough,this sigma_DD actually can be directly used in the analytical formular because there is the term sigma*beta. In a word,sigma_DD is directly used but not that direct on why it is.hope this helps, maybe i find myself say something stupid tomorrow,as i always am. Anyway,nice discussion for today,maybe somebody else will help.

Personally, I use the methodology without basis when such a case happens (Displaced Diffusion vol cannot be converted to Black vol).It is pretty uncommon, but if anyone has any suggestion about this, you are welcome.