# Swaption Vol surface

¿How can I get the implied vol from a swaption when I have a vol surface with the maturity of the option and the tenor of the swap? For example I want to know what is the volatility for a swaption that gives the holder the right to pay 6.2% in a 3-year swap starting in 5 years.

Swaption vol can have 3 dimensions: option expiry, underlying tenor and strike.

In your example, if nothing is said, then it's probably ATM (at the money) volatility which means it's the vol for a Swaption with a strike equal to the forward of the underlying.

So if you only have a surface, and not a cube, you probably don't have exactly the information you need.

If you do have vol data for multiple strikes, even if you don't have the 6.2% strike, you could fit SABR parameters to the smile to determine the vol for the strike you need.

Alternatively, if you have a cap surface and a Swaption ATM surface, you could also build other Swaption strike vols with a method called lifting from caps.

• Thanks a lot for your time David, I am new at swaption so, I'm trying to understand this. The exercise I want to solve is Suppose that the LIBOR yield curve (which we assume is used for discounting) is ﬂat at 6% per annum with continuous compounding. Consider a swaption that gives the holder the right to pay 6.2% in a 3-year swap starting in 5 years. The volatility of the forward swap rate is 20%. Payments are made semiannually and the principal is \$100 million. The answer from the book for vol is 0.20 so, I really don´t understand how i can get it. Feb 14, 2020 at 23:55
• The table you presented before and this question weren't really together, right? I think this simple exercise works on the assumption of flat vol. So you're given the volatility of the underlying (5y3y swap) and you're suppose to use it in the valuation (probably Black's model since the vol is in percentage and not bps) along with the other given inputs: strike, forward (flat curve), time to maturity and tenor. Feb 17, 2020 at 9:48
• You mention a flat curve @ 6% p.a. but the strike for your payer is 6.2% i.e. +20bp OTM. Most likely the vols in your table are ATMF so unless payer skew is flat (which is possible), I don't see how you have enough info to answer the question. Oct 31, 2020 at 21:38