# 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.

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,

• A gold forward like XAUUSD on BBG? That is unrelated to a XCCY swap and can neither be priced on SWPM nor does Gold pay interest. Gold forwards are quoted with rates (Rts on FRD in BBG) as opposed to points (Pts). In my opinion, any interest rate is purely a no arbitrage assumption and not how the market quotes them. The default of SWPM, as Dimitri Vulis pointed out, will correspond to the market convention (for interest rate swaps). SWPM is flexible enough to allow you to switch it though if needed. In any case, that is unrelated to XAU. Jun 3, 2022 at 8:09
• Thanks a lot @AKdemy for your comment, and never having been involved with bonds, I take your point on Rts v Pts and will research further. Re Gold not bearing interest, yes and no. Yes in the sense that there is no central bank overseeing it, but for all intent and purposes, precious metals do feature a cost of carry and, at times, a convenience yield. Again, thank you, Jun 7, 2022 at 4:00

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

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

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.

• That settles the question neatly from a pricing's perspective. I still can't fathom why market practice would, in effect, default to a 360 day count over a 365 one when valuing a XAUAUD for instance (maybe out of simplicity), but since the calculation of the swap rate embeds both type of day counts, I'm content with it. Thanks lot for this Chris! Jun 7, 2022 at 4:14

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.