Cross-Currency Forwards Use Each Currency Leg’s Own Day Count

# Which Day Count Convention applies in a Cross Currency Swap


# Which Day Count Convention applies in a Cross Currency Swap












What is the rule (assuming there is one) specifying which day count convention should prevail in a cross-currency swap?

For example, where EUR follows ACT/360 and GBP follows ACT/365, which of the two conventions would apply to the calculation of a EURGBP forward price?

Bloomberg DES function refuses to show a Day Count when called on a cross-currency ticker. I struggle to find a definitive answer, and as we're dealing with OTC markets here, I'm curious about the possibility of a counterparty requesting a different day count.

Thank you,

EDIT: Having tried SWPM as suggested made me realize my question is probably not narrow enough, in my initial bid to attract answers. The SWPM does leave it to the user to pick the Day Count.

So here is my exact business case instead:

A Gold forward is priced using simple interest (no coupon, no compounding, not matter how many years it might span): $$Forward = Spot \times (1+r_{swap} \times \frac{ACT}{DayCountConv})$$ with the swap rate (GoFo) defined as the difference between the USD rate (Libor or SOFR nowadays) and the Gold rate (aka "lease rate") $r_{GoFo} = r_{USD} - r_{Lease}$

With Gold and USD both using a 360 daycount convention, all is well.

But is there a rule when pricing, say Gold in GBP or AUD, where both those currencies conventions are ACT/365 ?

Thanks again,

## Answer by Chris Taylor (score 5, accepted)

https://quant.stackexchange.com/a/71158

Your pricing formula for the forward rate is incorrect. You should use

$$ \mathrm{Forward} = \mathrm{Spot} \times \frac{1 + r_{\rm dom}\times \frac{ ACT}{DayCount_{\rm dom}}}{1 + r_{\rm for}\times \frac{ ACT}{DayCount_{\rm for}}} $$

i.e. each leg uses the day count appropriate to the currency for that leg. The same is true for a cross-currency swap - each leg is valued using its own day count.

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/71095

Instead of DES, use SWPM on Bloomberg. Use different currencies on the two legs. Then SWPM will show you the market comventions for various currency pairs.

These may differ depending on whether a leg is fixed or floating.

Each leg has its own frequency, day count convention, etc, and hence its own pv. Not sure how you'd apply a day count to the entire trade.