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

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  • $\begingroup$ As @Pontus Hultkrantz has already pointed out, a swap with a zero-notional-leg is not really a swap anymore. Practically, I sometimes set leg nominals to zero for some internal risk calculations, i.e. as a workaround in my risk systems... But I think that is not what you had in mind, no? $\endgroup$ – Kermittfrog Dec 1 '20 at 10:03
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    $\begingroup$ Depending on which leg has null notional, such a swap is equivalent to either a fixed-rate bond or a floating-rate bond. In practice I don't think this happens. $\endgroup$ – Daneel Olivaw Dec 1 '20 at 10:17
  • $\begingroup$ I'm guessing that it might be a workaround for booking in a less than perfectly designed IT system. For example, suppose you really want to book just one leg. But the system insists that you book 2 legs, so you book the other leg with 0 notional. (I could also imagine specyfing 0-notional leg on a non-standard termsheet to indicate its absense.) Another possible guess is a "template" that can be cloned and edited instead of entering all fields from scratch. $\endgroup$ – Dimitri Vulis Dec 1 '20 at 15:38
  • $\begingroup$ Ideally a firm should have some "approximate booking" or "model extension" policy - requring that all instances where the IT systems force traders to "work around" limitations (for example, having to book a callable swap as a separate vanilla swap and swaption, or having to book an amortizing swap as a series of bullet swaps) be noted, tracked, and eventually remediated in the booking system. $\endgroup$ – Dimitri Vulis Dec 1 '20 at 15:42
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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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