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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.

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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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