Lesson 5 of 5 · 13 min
Convexity bias and the effect of central clearing
Interest rate futures pay a fixed amount per basis point, while an FRA's settlement is discounted at the new rate and so is non-linear; meanwhile central clearing has given OTC forwards futures-like margining, shrinking the gap between the two.
In short
- An FRA settles at A at the present value of the net interest: net payment ÷ . Futures settle at BPV × basis points, with no discounting.
- So the FRA's payoff is non-linear in MRR: it gains more when MRR falls than it loses when MRR rises by the same amount (for a receive-fixed FRA). This is the convexity bias.
- Convexity bias is larger for longer discounting periods.
- Central clearing requires OTC dealers to post margin to a CCP; dealers pass similar requirements to end users, so forward cash flows look more like futures.
- Result: smaller cash flow and price differences between futures and forwards, but end users must hold cash or eligible collateral and bear financing and administrative costs.
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