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? $\endgroup$– KermittfrogDec 1, 2020 at 10:03
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1$\begingroup$ 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 OlivawDec 1, 2020 at 10:17
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$\begingroup$ 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 VulisDec 1, 2020 at 15:38
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$\begingroup$ 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 VulisDec 1, 2020 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.
answered Dec 1, 2020 at 9:45