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Question for the fixed income quants out there…Let’s say I had a grid of implied vols for 3m10yr swaptions with various strikes, let’s say ATMF and +/- 50 and 100bps. If I want to price an option that is 30bps out of the money, for example, what type of functional form would I assume to “connect my dots” to price this option? Is there any convention in the marketplace? Any recommendations from others?

The most popular FI skew model is SABR, look at the Wilmott article "Managing Smile Risk" by Hagan

If you have your OTM values already, then you can simply use some kind of splining... Many use cubic splines just because of their easyness in use. If you are interested in the behaviour of your skew as the market moves (e.g. how does the smile changes with chaning forward rates and atm volatilities), then as "Estcourt" suggests, you need to make some assumption about the rates and use a model to explain them. SABR is an excellent one and very widespread. If you don't wan't to get into that kind of complexity, CEV could also give you reasonable smirks for interest rates.gc

Thanks gc and estcourt. I downloaded the paper and took a quick look. A few follow-up questions for you both, if you don't mind ... I am trying to decide if I should attempt to implement.1. Does anyone have an opinion on the extra impact of adding higher order terms to equation 2.17a? Does it make a difference? The authors seem to imply not.2. What are some conventions to choosing the value of beta? The authors seem to imply that beta should be chosen a priori. 0 is for a stochastic normal, 1 for a stochastic lognormal, 1/2 is for a stochastic square-root process. Any practical guidelines in choosing these parameters?3. They mention typically that the ATM vol is input and then we can solve for alpha. This leaves us with two parameters to estimate (once ATM vol and beta are determined). What procedures would you recommend to solve for these parameters? I have some old code for Levenberg-Marquardt, perhaps this is one way to go, but are there practical methods which might be easier/better? 4. When they say that Greeks are determined from "finite differences" am I correct in assuming that they just shock the given parameter, then take the difference in the values and divide by the shock size (as opposed to setting up some type of finite difference grid)?5. Lastly, if I understand the model correctly, it is used to fit the skew or smile for a given option expiration date on a given asset only. For example, I could use it to calibrate to the prices of ITM/ATM/OTM 3m10y swaptions, but not if I wanted to simultaneously fit the prices of ITM/ATM/OTM 3m10y and 6m10y swaptions.Thanks for the help .... it is much appreciated!!Rgds