<t>My underlying is the LIBOR rate for USD, EUR and CHF.My first idea was to keep the same prices for k<alpha (shifted lognormal) and the same prices for k>beta (lognormal). And for k into [alpha, beta] to take some convex combination of the two pricers. One problem is that alpha and beta will be de...

<t>Hi,Thanks for replying. To be more precise on my requirements, I would like the prices (1) to be near the lognormal prices when strike is large AND (2) to be near the shifted-lognormal prices when strike is low.I think I stated all requirements now. Sorry for unclarity.So, Pimpel, your solution i...

<t>Hi,Thanks for replying.You are right, I forgot that I would like the prices to be near the old prices (ie lognormal prices) when the strike is >0,5% (ideally equal to the lognormal prices from a certain strike).So that the users of the pricer do not note any change in the prices for large strikes...

<t>Hi,I have a lognormal floor pricer and a shifted-lognormal floor pricer.The lognormal pricer is bad for low strikes, because the prices of the floor converges to 0 when strikes goes to 0% (ie it neglects the possibility of negative interest rates).So that for the moment I use the lognormal pricer...

Hi,If you speak french, you can read propostion 2.9 p.24http://fiquant.mas.ecp.fr/ioane_files/InterestRatesModels-LectureNotes2011.pdf

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.

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.

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

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

<t>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? <...

<t>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...

<r>Hi,Thanks for replying.I found the article you refer to : <URL url="http://www.pjaeckel.webspace.virginmedia.com/QuantoSkew.pdfHowever"><LINK_TEXT text="http://www.pjaeckel.webspace.virginmedi ... pdfHowever">http://www.pjaeckel.webspace.virginmedia.com/QuantoSkew.pdfHowever</LINK_TEXT></URL>, I ...

<t>You can anyway find an inconsistency when you look at the call arbitrage boundaries :Let Y be the libor, X the OIS. Then you have dXt = sigmaBLACK * Xt * dWtdYt = sigmaDD * (Xt+basis)* dWtYou want to egalize Call(Xt,K=X0) and Call(Yt,K=X0+b)Call(Yt,K=X0+b)=Y0 (2*N(0.5*sigmaDD*sqrt(T))-1)The arbit...

Hi,Thanks for replying.Could you please tell me where you found your formulaes?The one I used is from equating the black call price with the shifted black call price with strike K+shift.I don't understand how a beta can occur in argument of N(). Thanks

<t>Hi,As the approximation was not precise in this case, I already tried to use the analytical formula. However, it doesn't have a solution because the argument in N^{-1} (inverse cumulative normal distribution) is >1.The analitycal formula I used to convert Black vol into DD vol is :sigmaBLACK = (2...