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Hi, (1) Can't you get the ATM vol from the market? (3) I don't understand your issue with rho. Concerning equation (9) it only represents the equation you have to solve to find your short tenor volatilities. Assuming the short tenor volatilities are the same gives good results.

Thanks for replying(1) yes,i can get ATM cap vol,but i 'm asking the way to bootstrap caplet vol,(3)rho is a parameter,should i estimate it from historical data? or just set it to a number(like 0).Btw,assuming short tenor vol are the same is good advice.

(1) Ah ok, I did it with a linear interpolation between the known strikes, but if you find a more precise method, let me know.(3) I think the best is to use historical correlation

Currently i am trying to convert 6M cap vol to 1M cap vol using this transforming technique,and comparing to the data from Bloomberg VCUB cap vol.The outcome is not satisfying because what i see from bloomberg is that they have extremely high vol for 1yr maturity of 1M tenor. Do you know how they create them? probably a strange quesition....

Hi,I get a high vol for 1M tenor with this methodology...

Did you use the method including basis to achieve high vol , or is there a big difference between single curve and multi-curve ?I don't quite understand the technique of multi-curve,could you give me some instructions about it, particularly how(ideas,calculations) to get OIS vol from forward vol ?Another detail,how do you get the first six 1M vol,do you assume they are the same as the sixth 1M vol? but i think maybe they should be higher...

Yes I did use the method including basis.The idea is to find the black OIS vol from the DD distribution of the OIS, that you can write from the distribution of the libor (using libor-ois spread).Yes I assume the vols are the same.You should read in details this thread, it could be very helpful for you.

Hi Lapsilago, Did you notice that eq (22) gives very strange results when beta is small?For small betas (ie ois forward is much smaller than libor forward), I get anormally high vols with the methodology including basis, unlike the "without-basis" methodology...Do you have any idea about this?Thanks.

Hi,To be more precise, how would you do when it is impossible to convert Displaced Diffusion volatility to Black volatility?I am trying to find a solution which is not "use the methodology without basis" but I don't figure out how to do it...

Hi,you should use the analytic formula not the approx formula in this situation.I wonder if you tried that out. Do you have the analytic formula. Could you give me a hint on the parameter values you use? What is beta and what is the spread?I will look into this issue.Best, Lapsi

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/sqrt(T)) * N^{-1} (0.5 + (0.5 / beta) * (2 * N(0.5*sigmaDD*sqrt(T)) - 1))The parameter I used are :forward=0.002862basis=0.002382beta =(forward-basis)/forward = 0.1677T=0.088sigmaDD=1.43Thanks.

Hi Yougy,Trysigma_{BS} = 2/Sqrt(T) * N^{-1}(beta N(sigma_{DD}*beta*Sqrt(T))/beta+(1-beta)/(2beta))andsigma_{DD}=2/(beta Sqrt(T))N^{-1}(beta N(sigma_{BS}*Sqrt(T)/2)+(1-beta)/2)For me your parameters work fine!Best, Lapsi

Another hint when you calibrate the SABR.You have to notice that in the DD setting we already have a skew! Might be an idea to fit SABR such that you hit ATM + Skew around ATM.Best Lapsi

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

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 arbitrage boundary tells us that Call(Xt,K=X0) < X0So Y0 (2*N(0.5*sigmaDD*sqrt(T))-1) must be < X0With my parameters (forward=0.002862basis=0.002382beta =(forward-basis)/forward = 0.1677T=0.088sigmaDD=1.43)we haveY0 (2*N(0.5*sigmaDD*sqrt(T))-1) = 0.0004849 as Y0=forwardX0= 0.00048so Y0 (2*N(0.5*sigmaDD*sqrt(T))-1)>X0 and the arbitrage boundary is violated.