I have made some research on how to imply caplet vols from cap vols and I have encountered two ways of doing so:1)Use the functional form σ(t) = (a+bt)exp(-ct)+d for volatility structure;2)Use caps premiums and used them to imply caplet vols (ex. We have 1y and 2y caps. 1y cap has only one option with 6m expiry so if we invert the cap’s premium we get the 6m caplet vol. The 2y cap has 3 options with expiry dates 6m, 1y and 1.5y.If we invert the 2y cap’s premium we can imply the 1y and 1.5y caplet vol).Witch is the best method?I think the first one has the advantage of the possibility to use ATM and other strikes vols but I don’t know where that functional form came from.In the second method it’s not clear to me how to imply both the 1y and 1.5y caplet vols.Can someone pls give me some lights on this subject?Thanks

The first method is less precise, but it gives complete prices for all possible caplets (not necessarily correct prices, however). It's useful for many analytic purposes, but not accurate enough for trading in liquid markets.The second method requires a complete set of cap prices, that is one for every payment time. If you don't have that, you have to interpolate somehow, for example using the first method but only over the interval of missing data.The first method gives you a theoretical price in a simple expression. The second method gives you an actual market price, at least to the extent your prices are good. Sometimes we want to know what something should sell for, other times we want to know what it does sell for.

What I did was to calibrate a, b, c and d to the cap volatilities quoted in the market for different maturities and then use those parameters to obtain vols for other maturities that are not quote in the market. In this way do I get market prices for caplets of different maturities or just some vols that can’t be used for trading?Thanks for your help Aaron.Any other posts will be welcome

QuoteOriginally posted by: Aaron The second method requires a complete set of cap prices, that is one for every payment time. If you don't have that, you have to interpolate somehow, for example using the first method but only over the interval of missing data. Hello Aaron,could you or anyone give me an example of quotation page ( the font data house if private) that gives cap prices for every payment time? I'm interested in comparing Libor vols obtained interpolating cap prices with the real ones but I only have reuter's ICAP's feed . It would be kind from youPedroRaquel, where did you learn of the first method? any paper title you can give?bye & tnkx

Hello Aaron,could you or anyone give me an example of quotation page ( the font data house if private) that gives cap prices for every payment time? I'm interested in comparing Libor vols obtained interpolating cap prices with the real ones but I only have reuter's ICAP's feed . It would be kind from youPedroRaquel, where did you learn of the first method? any paper title you can give?bye & tnkxI think it was on "The Oxford Guide to Financial Modeling" but I can't be sure.How did you interpolate the Libor vols using cap prices? Did you use linear interpolation or other and more complex method?It's not clear to me how to invert a 2y cap to get the 1y and 1.5y vols. Do one use the 1y price quoted in the market and the 6m cap price obtained inverting the 1y cap price?Could someone explain it to me (maybe with an example)...Thanks

For the moment I'm using linear and cubical interpolation between different expiries. Tough beeing interested in comparing different interpolation techniques, including linear interpolation between different maturities following the changing money. However I'm still hearing of various more dense cap quotations, including Aaron's one. And I'm getting more and more anxious to catch one a happy day. together with the ICAP broker who compute the "compact" usual flat vol matrix. So that I can constrain him/her somehow until he give me his "compression" algorithm.In fact, I think that the main problem still be chosing the good IR / hybrid model, the one you will use after this confused first step.

As Aron said, I use the 2nd method with linear interpollation for the short term and cubic for the long maturities.To improve your vol you can adjust/fit with a function (with continuity and derivability).

Aaron apologise for your name

QuoteOriginally posted by: Stochastic44<brcould you or anyone give me an example of quotation page ( the font data house if private) that gives cap prices for every payment time?I get them from our trading desk and, of course, cannot distribute them. Whatever interpolation is necessary has already been done by the time I see it.

Dear Aaron,Shouldn't the interpolation be applied on variance rather than vols.

I assume you're saying that because local variance is hedgeable in theory, while local volatility is not. It doesn't make much difference in practice and, of course, the two can be made equivalent by using appropriate interpolation methods. So I wouldn't say there's a clear reason to prefer variance to volatility, but I could see why some people might choose it as the more natural expression.

Carol Alexander describes the procedure of backing out the caplet volatilities from the quoted flat volatilities in her articel "Common Correlation Structures for Calibrating the LIBOR Model" (Available at SSRN)It should give you the example you are looking for, and discusses the volatility/variance question.Her conclusion is that the flat volatility is a vega weighted average of the underlying caplet volatilities.If the vegas are not available, the unweighted average will do resonably well.Christian