# 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. Commented 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? Commented 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). Commented 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. Commented Jul 28, 2016 at 7:36

A swaption in which the underlying swap starts at a date materially after the expiration date is called a midcurve swaption. The implied volatilities of these can not be obtained from the regular swaption surface. Market makers calculate implied volatilities for midcurves in a number of ways. One popular method is to compute the volatility of the forward swap using the volatilities of two spot starting swaps, and the correlation between them. For example , consider a midcurve option expiring in 1 year into a swap which starts 5 years later and ends 10 years later. The correct volatility can be computed from the 1yrx5yr volatility, the 1yrx10yr volatility , and the correlation between 5yr and 10 yr swaps for the next year.

• This depends on being able to write the forward swap (the underlying of the mid-curve swaption) as a weighted (by annuities fractions) differences of vanillas, which is not necessarily possible in a multicurve framework. How does one do in a multi curve framework ? Commented May 11, 2018 at 18:46
• Or maybe all "vanilla" mid-curve swaption are such that the two vanilla swaps have same XIBORS of the same frequency ? Commented May 11, 2018 at 19:00
• When you say "The correct volatility can be computed from the 1yrx5yr volatility, the 1yrx10yr volatility" what strikes will be sample on 1Y5Y volatility and 1Y10Y volatility? How do you handle the vol skew? Commented Oct 24, 2019 at 14:57
• @TommyLin I think this enough material for a new question. Commented Oct 24, 2019 at 16:15
• @TommyLin One usually does this exercise for the ATM volatilities, and assumes a structurally similar formulation of the skew as of the 2 component swaptions; or the one the midcurve is 'closer' to in some sense (say underlying tenor). Commented Jun 15, 2020 at 23:25