Futures/Forward Convexity Adjustment
Computes the convexity adjustment between a futures rate and the equivalent forward rate, using the Ho-Lee approximation: forward = futures − ½·σ²·T1·T2. Interest rate futures and forwards don't carry the same rate because of the daily marking to market of futures, and the convexity adjustment corrects that difference, always pushing the forward rate below the futures rate. Enter the absolute short-rate volatility, the time to the futures maturity and the end of the rate period.
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Futures/Forward Convexity Adjustment
Computes the convexity adjustment between a futures rate and the equivalent forward rate, using the Ho-Lee approximation: forward = futures − ½·σ²·T1·T2. Interest rate futures and forwards don't carry the same rate because of the daily marking to market of futures, and the convexity adjustment corrects that difference, always pushing the forward rate below the futures rate. Enter the absolute short-rate volatility, the time to the futures maturity and the end of the rate period.
Why interest rate futures and forwards don't match
It seems an interest rate future and a forward contract on the same rate should have the same price, but they don't. The difference comes from a mechanical detail: the future is marked to market every day, with gains and losses settled immediately, while the forward only settles at the end. That daily marking creates an asymmetry that favors the rate-short side, and the market discounts it.
The convexity adjustment quantifies that difference. In the Ho-Lee approximation, the forward rate sits below the futures rate by an amount that grows with the square of volatility and with the product of the two terms involved. The longer the contract and the more volatile the rate, the larger the adjustment, which can reach several basis points over long horizons.
Enter the absolute short-rate volatility, the time to the futures maturity and the end of the rate period. The tool returns the adjustment in basis points, which you subtract from the futures rate to get the forward. It's an essential adjustment for anyone using interest rate futures to build forward curves.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.