Interpreting Zero-Notional Legs in Interest Rate and Currency Swaps

Summary

The document considers whether a swap can have zero notional on one leg and what such a contract would represent. Its answer says that a leg with no effective payment stream generally removes the defining exchange of a swap. It distinguishes a zero swap rate from zero notional: in a fixed-for-floating interest rate swap, a zero fixed rate eliminates fixed coupon payments, while a zero floating leg leaves a stream of zero-coupon-bond-like cash flows. For a single-currency interest rate swap, the notional is shared by both legs, rather than set independently for each leg.

The answer also describes a theoretical cross-currency case in which one currency’s value collapses, making the notional exchange in that currency effectively worthless. This is an extreme scenario, not a standard use of a swap with independently zeroed leg principal. The explanation is brief and conceptual; it gives no contract terms, valuation example, or practical market convention beyond these distinctions.

Key ideas

• A zero-notional leg generally removes the cash flows that make a contract a swap.
• A zero fixed rate can eliminate fixed coupons even when the swap notional remains positive.
• Eliminating the fixed or floating payments produces cash-flow patterns comparable to FRAs or zero-coupon bonds, respectively.
• Single-currency interest rate swaps use a shared notional across both legs.
• A cross-currency notional can become economically worthless in an extreme currency-collapse scenario.

Tags

# Zero notional on swap leg


# Zero notional on swap leg












Can there be a swap with zero notional on one leg alone? If so, what is the swap used for ?

## Answer by Pontus Hultkrantz (score 2)

https://quant.stackexchange.com/a/59680

While mathematically anything is possible, it does not make any sense to have a swap with zero notional, as it no longer is a swap.

For fixed for float interest rate swaps, if the swap rate is zero, while notional is not, that would mathematically be equivalent to a zero notional on that leg, since the whole leg is killed. Killing the fixed leg equals a series of FRAs; killing the floating leg equals a stream of zero coupon bonds. However, for sinle ccy IRS, the notional is shared among the two legs.

For a cross currency swap, if one of the states that issues the currency got totally destroyed, meaning that the exchange rate for the notional went to zero, then sure.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.