# What is the definition of "co-terminal swaptions"? why they are important in the calibration process?

could anyone help me understand the definition of "co-terminal" swaptions? What are they? Can you provide an example to illustrate? And why such instruments are important in model calibration?

What does that mean for the calibration process? Some of these swaptions are actually traded e.g. 2y3y but for others you will need to find the closest match. What you end up with is a diagonal, or co-terminal, set of calibration instruments. You can see that the tenor of each swaption is decreasing as $$T_{bond} - T_j$$ for each expiry $$T_j$$ and fixed bond maturity $$T_{bond}$$. Often these are chosen to be ATMF (you can also include skew and calibrate diagonally to moneyness). The strike calibration depends a bit on the instrument/bond and its structure (e.g. amortizing, floating, fixed coupon).