I have implemented a Markov functional Libor Forward/Swap model as described in Hunt and Kennedy's book "Financial derivatives in theory and practice". Calibration works very well on an implied volatility surface for digital caplets / swaptions.However I'm not sure about how to obtain this kind of volatility surface from market data and this is not described in any book or article I've seen.For now, I have a per maturity Black calibration : for each caplet/swaption maturity, I extract the ATM Black volatility and use it to obtain prices for digital caplets/swaptions at any possible strike (which is what is required by the calibration process). Of course, this method does not account for the volatility smile that occurs in market data.Does it make sense to do a per maturity SABR calibration which would use the whole volatility smile ?Any idea on other ways to obtain these digital caplets / swaptions prices ?

Hi,With HK methodology the smile is perfectly fitted if the market digitals are Abitrage-Free. With Sabr Implied volatility formula, the digitals are not AF for long term maturities. Thus, an AF extrapolation is required. I suggest you, the RBS quants paper : An arbitrage-free method for smile extrapolation

QuoteOriginally posted by: lmzHowever I'm not sure about how to obtain this kind of volatility surface from market data and this is not described in any book or article I've seen.On creating the volatility surface from market data why don't you try as a start the volatility cube methodology that BBG has (if you have access to BBG)?

Thank you both for the insight.About the volatility cube, if others are interested, I found the following technical report.