# How to determine the default probability of a county in a bond that is not in its native currency?

Disclaimer: This post is cross posted in here also.

Consider the following case:

Country P uses the currency Euro and gives p percent interest on a one year bond issued in Euro.

Country Q uses the currency TL and gives q percent interest on a one year bond issued in Euro.

## Question:

How can we determine the probability of default of the country Q with respect to P ?

• The short answer is you bootstrap euro bond - derived hazard rates from the euro bond price. You will observe a basis between this and any TL-bond derived probabilities driven by (i) supply/demand differences in bond pricing caused by differential investor appetite for Country Q TL-bonds vs Euro-bonds (ii) any credit-fx correlation between Country Q hazard rates and TL-Euro FX (eg if Euro is a 'haven CCY' versus TL then the Euro-bond will be seen to appreciate in price terms vs the TL bond on Country Q credit deterioration <- volatility of the Euro-TL FX pair will magnify this. – Mehness Jun 8 '18 at 12:37
• This effect is called generally called Quanto basis. In CDS terms this manifests itself as the price of protection in USD denominated CDS typically trades wider than the equivalent EUR contract if USD is perceived as a haven CCY relative to EUR. – Mehness Jun 8 '18 at 12:37
• Very roughly the additional probability of default per year is going to be $q-p$, but this is subject to many qualifications. (We would have to also discuss liquidity premia, and other factors that may also affect the yield spread. So as given it is a very complicated question). – Alex C Jun 8 '18 at 13:13
• For the broad background, see Does Sovereign risk in local and foreign currency differ? BIS709 bis.org/publ/work709.pdf – noob2 Jun 8 '18 at 17:38