I have some ATM swaption volatilities with the following characteristics:
- (-IBOR) payment frequency: 1M
- Underlying swap maturities (tail): 1Y, 2Y, 5Y, 10Y, 15Y and 20Y
- Swaption expiries: 1M, 3M, 6M, 1Y, 2Y 5Y and 10Y.
I would like to compute volatilities for swaptions with shorter swap maturities (tails) (specifically 3M, 6M and 9M).
Is there any model/bibliography that I could check to extrapolate my market vols in such way?