### Bloomberg Volatility Swap fair vol under Black-Scholes

Posted:

**February 5th, 2022, 5:02 pm**Hi I a wondering if I can pick your brains on vol swap pricing...

Currently I am trying to match Bloomberg OVML Black-Scholes model, taking calculation date of 28 Jan 2022 on USDCAD, with first and last fixings to be 28 July 2022 and 30 Jan 2023 respectively, Bloomberg has a fair vol (ie vol strike with zero NPV) of 7.30229.

However, I arrive at a number that is a little lower at 7.30071. I have chosen the two dates above so that they coincide with the expiry of the 6M and 1Y options, which have ATM vols of 7.18 and 7.155 respectively. Taking a actual/365 day count from 28 Jan 2022, and with the assumption of linear accumulated variance, the accumulated variance accumulated between the two dates are 7.155*7.155*t2-7.18*7.18*t1=AV. The BBG implementation of the fair vol is given by SQRT(A*AV/N)*(1-1/(4*N)) where A is 252 and N in this case is 122 (the number of log returns between the two dates). This results in the 7.30071. t1 is 0.49589, t2 is 1.00548. (I did not round the intermediate values so it is unlikely to be due to rounding...)

I am wondering if anyone had experience with this?

Currently I am trying to match Bloomberg OVML Black-Scholes model, taking calculation date of 28 Jan 2022 on USDCAD, with first and last fixings to be 28 July 2022 and 30 Jan 2023 respectively, Bloomberg has a fair vol (ie vol strike with zero NPV) of 7.30229.

However, I arrive at a number that is a little lower at 7.30071. I have chosen the two dates above so that they coincide with the expiry of the 6M and 1Y options, which have ATM vols of 7.18 and 7.155 respectively. Taking a actual/365 day count from 28 Jan 2022, and with the assumption of linear accumulated variance, the accumulated variance accumulated between the two dates are 7.155*7.155*t2-7.18*7.18*t1=AV. The BBG implementation of the fair vol is given by SQRT(A*AV/N)*(1-1/(4*N)) where A is 252 and N in this case is 122 (the number of log returns between the two dates). This results in the 7.30071. t1 is 0.49589, t2 is 1.00548. (I did not round the intermediate values so it is unlikely to be due to rounding...)

I am wondering if anyone had experience with this?