Bias Curve Construction: Cross-Currency Swaps

Cross Currency Swaps work exactly like Interest Rate Swaps except the two series of cash flows exchanged between counterparties are denominated in typically two different currencies. Currency basis swaps are all quoted against USD so that if one wanted to trade a EURZAR CCBS, one would have to trade a EURUSD CCBS and a USDZAR CCBS, so that the USD cash flows net out.

A reference spot rate is required to calculate the principal exchanges. Usually the same reference rate is used for the inception as well as the final exchange. The default case is to use the current spot rate. Other exchange rates can be used, but this will affect the value (and hence price or rate) of the swap.

Curve construction

A basis swap is quoted on the zero-rate spread of the basis leg as:

Retrieve your curves and clean as necessary i.e. standardising rates to NACC for example.Next, interpolate. Linear, log-linear and cubic spline are common methods- it’s up to you which method you decide but be able to support your decision/ methodology. I personally don’t do anything fancy as smoothing out the curve too much will result in the disappearance of market noise, meaning a mismatch to market quotes.

The next step is to retrieve the swap curve for the related currency and from this we calculate our biased curve by simply adding the interpolated rates of market spreads to the swap curve. Note that all country risk premia are measured relative to the US, which means that in FX markets a USD leg in a CCS transaction uses the swap zero curve to project LIBOR as well as to discount future USD cash flows.

Below, is an example of a biased ZAR curve: