Valuing Dual-Currency Bonds with Curves, FX Basis, and Credit Risk

# Dual currency bonds valuation


# Dual currency bonds valuation












How does one price dual currency bonds/notes? which benchmark is used in such cases say for example Israel government issued bonds in:

- principal paid in USD but denominated in BRL, fix coupon BRL or

- principal paid in BRL, fix coupon USD?

## Answer by Dimitri Vulis (score 4, accepted)

https://quant.stackexchange.com/a/81616

In the past, there were more examples like what you describe and textbooks like to discuss - the principal is repaid in USD, and the coupons are e.g. JPY, and no optionality.

All the examples I've seen recently have optionality: typically, for each interest or principal cash flow, the issuer can choose to pay e.g USD 1 or ARS 300. :)

For fair value, you need a Monte Carlo if the note is Bermudan callable etc; else closed form for each cash flow. Figure which currency would be the cheapest for the issuer to deliver, add the (out of the money) fx options. Get the risk-neutral probability of default from CDS if needed.

The procedures that my desk used in the 1990s, when such instruments were more common, as were Brady-like guarantees:

We discounted with swap curve if the cash flow currency was the same as the valuation currency, usually USD, or swap curve plus cross curerncy basis, if they currencies differ, rather than treasury curve, because we assumed that we'd hedge with interest rate swaps or cross currency swaps, rather than with treasurys.

If the cash flow in USD/JPY is (Brady-like) guaranteed by US/Japanese government; or if the issuer is sovereign and the cash flow is in currency that the sovereign issuer can print at will, then there is no credit risk. Else, we used risk-neutral probability of default from issuer's CDS, and the recovery assumption of 0 for interest cash flow, and the same recovery assumption used for CDS, i.e. 25% for emerging markets, for principal cash flows. I can imagine using a higher recovery for highly collateralized debt, but never needed to.

So, in this example (thanks again!!!), to price in USD, we'd discount all ILS cash flows with ILS swap curve plus USDILS cross-currency basis, and assume that the government can't default on ILS debt. We'd discount BRL cash flows with (offshore) BRL swap curve plus USDBRL cross-currency basis times the risk-neutral probability of survival from Israel sovereign CDS; and for BRL principal cash flows, add some value for the recovery in default. The model price was just the sum of the prices of the cash flows.

If an observable price was available - not always, then we also calculated the basis spread between that and the model price, which tended not to be very wide or volatile when we did.

We calculated sensitivities - first order deltas, second order gammas and cross gammas - to all the inputs, including CDS spreads, basis spreads, time - and a Taylor expansion P&L explain.

Some design decisions were motivated by the desire to mollify the model validation team, and to minimize unexplained P&L based on observable market data.