# volatility of a mid curve option

Question:

When checking the volatility surface for, let's say, a swaption, where the the option expires in 1Y and the underlying starts in 1Y and ends in 5Y, one would check the volatility surface for the quoted volatilities and pick the volatility from Exp. 1Yx5Y ;

What happens to the volatility of a mid curve option? how do you relate/ interpolate the volatility in this case? let's say the option expires in 1Y, and the asset starts in 6Y and ends in 5Y after start? where on the volatility surface should the volatility of a mid curve option be situated? Or in other words howw do you get the volatility for the 6Y fwd 5Y swap for an option that expires in 1Y ?

• You mean, implied volatility? It doesn't matter when the underlying expires. It can be spot which never expires at all... All you care about is the option's expiration time itself, and the price of underlying. Jul 27, 2016 at 2:32
• Yes, implied volatility is what I mean; so, from what you are saying, the implied volatility of the two swaptions described above should be the same? Jul 27, 2016 at 9:34
• Volatilities will be the same only if the prices of your two swaps are the same, otherwise no. It's the same formula, only one number is different - forward price of the underlying contract (1Y or 6Y forward starting). Jul 27, 2016 at 23:34
• checked bbg yesterday. for the spot starting - i got an implied voll of about 40bps; for the fwd starting - got an implied vol of about 80 bps. the 40 bps could be tied to the surface of quoted vols. the other one is what i am after. Jul 28, 2016 at 7:36