I want to interpolate the swaption volatility surface (fixed tenor) in the maturity dimension. I have volatility smiles at times T1 and T2, and would like to get the smile at time T with T1<T<T2 by interpolation. I didn’t find much discussion about what is the preferred interpolation method here. Linear interpolation seems like the most straightforward one but I haven’t found any reference yet.
Here are my questions:
- The strikes are quoted in terms of moneyness, so the value of strikes at the same moneyness are different at T1 and T2. Should I interpolate in moneyness or strike or is there a better method?
- In the equity world, people fit model to the smile at T1 and T2 first, then interpolate the model parameters to get modeled volatility at time T. Is this method also suitable for SABR model in interest rate world?
- Is there any good reference talking about interpolation in maturities in the rate world?