Why an OIS Fixed Leg Has Material Duration

Summary

The document answers whether the modified duration of an overnight index swap is zero or nearly zero. It explains that an OIS has a floating leg and a fixed leg, so the duration of the whole swap cannot be inferred from the behavior of the overnight floating payments alone.

The floating leg has duration close to zero because its rate resets frequently, leaving only the current overnight accrual period exposed to rate changes. The fixed leg retains duration comparable to that of a three-month swap with the same fixed-leg terms. Thus, an OIS can have meaningful rate sensitivity even though its floating leg is nearly insensitive. The explanation is concise and qualitative: it provides no formula, valuation convention, maturity-specific calculation, or discussion of how net swap duration depends on the relative present values of the two legs.

Key ideas

• An OIS contains both a floating leg and a fixed leg.
• Frequent overnight resets make the floating leg’s duration nearly zero.
• The fixed leg has duration comparable to a three-month swap with matching fixed-leg terms.
• The duration of the overall OIS cannot be assumed to be near zero based only on its floating leg.

Tags

# Modified Duration of Overnight Index Swaps


# Modified Duration of Overnight Index Swaps












Is the modified duration of an overnight index swap zero or close to zero?

## Answer by Phil H (score 2)

https://quant.stackexchange.com/a/8632

In short, no.

An OIS has 2 legs, like any other swap. The float leg duration will be nearly zero, because apart from the ON period the rates are floating. The fixed leg, however, has the same duration as a 3m swap with the same fixed leg specification.

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.