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sdurkin
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Joined: November 9th, 2007, 6:38 pm

SABR and caplet smiles

November 27th, 2007, 6:20 pm

My understanding is that for liquid caps, such as USD on 3M LIBOR, you can very often get many away from the money volatilities quotes. For example, a page such as this http://www.tfici.com/live/tullettfinanc ... .aspAssume caplet stripping has been done and now we have a smile that reflects caplet implied volatilities. My question is in such a case, would one ever use SABR to refine the smile or just use the market data as a given smile and adjust from there? Is SABR only used for caplets when smile data is no available from the market (like for exotic currencies) ?My understanding is that for European swaptions, SABR is very popular because the market gives you no smile information (ie only ATM are quoted)thanks-Sean
 
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SABR and caplet smiles

December 2nd, 2007, 5:55 pm

With SABR, you calibrate (sigma, alpha, beta, rho) using market quoted vols (whatever you have). Once you calibrate to those vols and fit the smile, than you have to believe each price/vol from the model is right, including implied vols that are not explicitly quoted.In some cases, you might have to extrapolate the smile for better calibration, but generally SABR calibrates well with few data points (that is one reason why it is popular for rates). The market gives you the smile and the price. What it does not give you are the hedges you need for a particular instrument. So SABR ensures that you can recover vol quotes and prices from the market and in addition gives you the right hedges (insofar as you believe the model is right.)