How does one choose a discount curve in multi-currency deals?

pj · Post by pj » Mon Sep 14, 2020 9:38 am

Say you have a complicated FX swap in CHF/EUR.

You currency is CHF.

How does one choose the discount curve?

nikol · Post by **nikol** » Mon Sep 14, 2020 10:22 am

First, you work out each currency separately:

Each currency discount link to OIS (CHF OIS, EUR OIS)

Each currency payout link to its IBOR (be aware it will disappear)

The same ideas apply about collateral.

After that you involve CHF/EUR cross currency spread to account for exchange between the two legs.

ref papers: Fujii, Takahashi. somewhere there is thesis by Fujii.

UPD. Error fix: base spread to cross currency spread.

pj · Post by pj » Mon Sep 14, 2020 10:32 am

Thank you, nikol!

Just what i need.

Yes, I have heard that IBOR might disappear.

nikol · Post by **nikol** » Mon Sep 14, 2020 2:51 pm

U r welcome.

Be aware of my error (too quick) Hammertime

Bad me: not basis spread, but cross-currency spread.

IBOR comes as "3d party" benchmark which is used to fix payout. Hence you will have to change IBOR to the new index in the contract.

Main idea with discount per currency is that it's linked to that currency account and you should not have arbitrage with cash from other products in same currency, e.g. fix-float IRS, to avoid internal arbitrage.

One step further, market based discount linked to OIS will give you market price, but not YOUR fair price, as you very likely have different funding and you have to know how much you are different from the market. That come withing XVA (CVA, FVA, etc) and these sort of things.

pj · Post by pj » Mon Sep 14, 2020 3:03 pm

I was reading too quick and automatically parsed it as cross-currency

spread

Cool

nikol · Post by **nikol** » Mon Sep 14, 2020 3:35 pm

Double error information transmission problem.

We have proved that!!!

But 2 idiots dont make 1 wiseman. They rather kill him.)))