# Which volatility input for in-arrear convexity correction?

When pricing a Libor-in-arrear swap, I am using the following formula (for the cashflow covering the period $[T_{i-1}, T_i]$, ie. paid at $T_i$ and resetting at $T_i$):

$V(t) = P(t,T_i)F(t;T_i,T_{i+1})\left(1 + \frac{\tau F(t;T_i,T_{i+1})}{1+\tau F(t; T_i, T_{i+1})}(\exp(\sigma T_{i}) - 1) \right)$

where $P(t,.)$ is the discount factor, $F(t;.,.)$ the forward rate, $\tau$ the year fraction. I'm just not sure where I should get the volatility $\sigma$ from?

I read it should be from capfloors surface, but can someone give a more concrete example?

It is the implied volatility of an instrument which has expiration $T_i$ with an underlying rate from $T_i$ to $T_i+1$. If $T_i+1 - T_i$ is a short period such as 3m or 6m, this is a cap volatility. If it is longer (1yr or more) then it is a swaption volatility.
• So if for example $T_i$ is one year from now, and $T_{i+1}-T_i$ is 3M and I have a standard cap volatility surface from BBG that has dimension expiry x strike, which point should I be looking at? Should this be the 1 year expiry and ATM? – TDC Mar 27 '18 at 13:48