Suppose my broker quote par vol for a 5Y cap strike 3.5 on 6m euribor = 20.90%How can I price a 5Y cap strike 3.5 on 3m euribor? How can I adjust 20.90%?Doing boostrapping using broker screen are avaiable par vols for year 1-2 vs 3 mth, while for year 3-30 vs 6 mthUsing a method as shown "Hull 5° Edition" I will find spot vols on 3 mth for 1-2y and on 6 mth on 3-30;To price a 5Y cap vs 3 mth I should use spot vols form 0 to 5y on 3 mth but using the boostrapping I have 6 mth spot vol from 3y to 5y;How I can do?Germoz

6m EURIBOR can be written as a linear combination of 3m EURIBOR - using the market implied 3m instantaneous volatility term structure and correlation coefficients between the 3m forward rates. Details on how to combine these rates can be found in Brigo & Mercurio and in the attached paper (page 10).

Waht mutley said - If I understand what you're trying to do correctly, then you're missing an input - the correlation structure between the forward rates. AFAIK there is no liquidly traded set of IR instruments other than 3m and 6m caps that will allow you to back out correlations, so you would have to estimate these using historical data. The errors you would get between market prices and your prices would be ... significant. I'm sure there are many non-correlation based methods you can try and use to get some estimate, but correlation is what creates the basis between these things, so you'd just be fooling yourself.

What Geist said - apart from European swaptions (massively liquid in most markets). While these things are sensitive to the average off-diagonal correlation of the forward rates, the precise correlation structure will make little impact in the pricing of them (so they're not perfect but are a good start)If you take the attached paper (simple but easy to get a handle on the ideas) and use a parametric form for both the instantaneous volatilities (N parameters) and forward correlations (M parameters), you can do a numerical optimization over the N+M variables to fit your model swaption prices against the market swaptions prices (all ATM).From this you can construct both 3m and 6m vols. If they don't fit the 3m ones exactly, tweak the vol structure again (such that they do fit them) and then calc the 6m vols from this. (I know then the vol structure and the correlation structure will not be from the same source so really a joint calibration should be used but it's near enough)James EDIT: Unfortunately Geist, you mentioned the only (I think) IR derivatives (caps + floors) with no correlation sensitivity!

nice documents , mutley. thanx

I use a simple method for interpolating / exteapolating the Volatilities for 3m/6m caplets.For Example in EUR we have Vols and Smiles for 3M and 1Y (Via Swaption) out to 2 years. To get the 6m Vols simply intrapolate the Normalised Vol (Rate*Vol) of the 3M and 1Y. You then have all Vols out to 2 years for 6M tenors.Past 2 Years you have Vols for 6M and 1Y, and must extrapolte the Noramlised Vols to get the 3M vols.I work on ATM vols and then interpolte the smiles of the other tenors.Alternatively use a SABR Model and extrpolate SABR parmeters which is a more complete apraoach to the problem.

QuoteOriginally posted by: KookaI use a simple method for interpolating / exteapolating the Volatilities for 3m/6m caplets.For Example in EUR we have Vols and Smiles for 3M and 1Y (Via Swaption) out to 2 years. To get the 6m Vols simply intrapolate the Normalised Vol (Rate*Vol) of the 3M and 1Y. You then have all Vols out to 2 years for 6M tenors.Past 2 Years you have Vols for 6M and 1Y, and must extrapolte the Noramlised Vols to get the 3M vols.I work on ATM vols and then interpolte the smiles of the other tenors.Alternatively use a SABR Model and extrpolate SABR parmeters which is a more complete apraoach to the problem.With SABR, the normalised vol is at the first order