What Drives Convexity Adjustments in Short-Rate Futures

Summary

The question compares convexity adjustments for three-month FRA or LIBOR futures, overnight indexed swap futures, and federal funds futures. It asks whether lower volatility in the overnight rate implies a smaller adjustment, and why federal funds futures adjustments can appear close to zero.

The reply expects LIBOR and federal funds futures with matching expirations to have broadly similar adjustments when their rate volatilities and correlations with the discount rate are similar. It suggests that near-zero federal funds adjustments may reflect contracts with short expirations, where there is insufficient time value for a material adjustment. These are qualitative explanations, not a numerical comparison or general proof. The excerpt does not resolve the overnight indexed swap comparison, establish that overnight rate volatility is always lower, or specify a pricing framework; those conclusions require market data and model assumptions.

Key ideas

• Futures convexity adjustments depend on rate volatility and its relationship to discounting rates.
• The reply expects similar adjustments for LIBOR and federal funds futures when their volatilities and relevant correlations are similar.
• An adjustment that appears small may reflect the short time to expiration.
• The excerpt does not establish a general ordering between overnight indexed swap and three-month rate adjustments.

Tags

# 3M FRA futures convexity vs 3M OIS futures convexity adjustment


# 3M FRA futures convexity vs 3M OIS futures convexity adjustment












Let’s say I can trade 3M FRA va 3M futures, this will give me th level of 3M convexity (off the 3M curve). On the other hand, I can trade a 3M OIS swap (Sonia for example) va 3M Sonia futures (which gives me the OIS convexity). How would these convexities compare? They depend on The 3m Rates volatilities (on 3M and Sonia). Can we say that we expect the OIS futures convexity adjustments to be lower than the 3M convexity adj as the corresponding vols are lower on SONIA?(is that even true?) And what about fed fund futures? Why is the convexity adjs of these futures almost 0?

Thank you.

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/40494

I would expect the convexity adjustment for 3m libor futures to be approximately the same as that of the fed funds futures with the same expiration. That's because the volatilities of fed funds and libor are very similar , and their correlations to the discount rate to the expiration date are also quite similar.

You ask why the convexity adjustments of Fed Funds futures are small/zero. I suspect you are looking at very short dated futures <2yrs where the time value is insufficient to create a meaningful adjustment.

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