Calculating a Two-Year Swap Rate from Eurodollar Futures

Summary

The document explains how to derive a two-year swap yield from a sequence of Eurodollar futures rates. It says Bloomberg’s displayed Rate column is already convexity adjusted, so the calculation can use those rates as period growth inputs rather than applying a separate adjustment again. The cited convexity discussion refers to Hull–White style modeling, with cap normal volatility and an uncalibrated mean reversion speed; it also notes an approximation intended to recover the Ho–Lee limit when mean reversion is zero.

To account for the schedule, the example uses ACT/360 accrual and includes a 29-day final stub so that the swap ends on its stated maturity date. The accumulated growth across the periods is then converted into an annualized yield using the total 731-day horizon. This is a brief tie-out explanation rather than a complete construction recipe: the source gives no full futures strip, market quote, or detailed treatment of the initial stub, and its convexity assumptions may differ from other systems.

Key ideas

• The Bloomberg Rate column in the example already includes a convexity adjustment.
• The cited adjustment uses cap normal volatility and an uncalibrated mean reversion speed.
• A final stub is needed to align the accrual schedule with the swap maturity.
• Convert cumulative period growth to a yield using ACT/360 over the full term.

Tags

# How does Bloomberg calculate the 2 year swap rate using the current eurodollar futures prices?


# How does Bloomberg calculate the 2 year swap rate using the current eurodollar futures prices?












I am getting hung up on the front and back stub periods and convexity adjustment. I've read a ton of similar posts but so far have not been able to tie out to this 2 Yr rate exactly. Any help is greatly appreciated!

Edited to include my quick math that does not have the convexity component, and the stub periods at the front and back end.

## Answer by AKdemy (score 3)

https://quant.stackexchange.com/a/73498

Convexity adjustment works like this

For references, see:

- Hull. 2002. Options, Future and Other Derivatives p. 566.

- Piterbarg and Renedo. 2006. Eurodollar Futures Convexity Adjustments in Stochastic Volalitiy Model. 2006

Note, cap normal vol is used (not caplet) and the mean reversion speed is not calibrated. Also, a slight approximation is made so that in the case of zero mean reversion (Ho-Lee model), the Hull White model reduces to Ho-Lee.

The 2yr value itself simply uses the Rate column, which is already convexity adjusted in your case. I am showing MMKt below, where you take ACT/360. The end is on 2022-10-17 which is 731 days, so you need 29 in the last period. It's the growth value over time for each period, turned into a yield measure,

where the green cell is computed as $(1099075.95/1000000-1)*360/731$.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.