# AUD Forward Rate Agreement and Forward Curve Bootstrapping

The pricing between an Australian Forward-Rate-Agreement is different compared to the US one. The question is whether this is somehow included already in the Quantlib? Also how does it compare to the Bootstrapping?

• The payoff settlement formula is different for AUD and NZD FRAs than for other currencies so the calculation of PV is different, but bootstrapping does not change as you can still interpret the FRA rate quotation as a forward IBOR rate. Only beware that the DCC is act/365 whereas USD Libor is act/360. – Antoine Conze Jan 16 '18 at 18:37
• Thanks a lot for the answer. But lets say it is collaterlized and I have to take care that the swap is priced to zero do I still have not to account for the new FRA pricing? – JonDoe Jan 16 '18 at 19:17
• The pricing formula is different, but for an FRA that trades today at zero price the FRA quoted rate is equal to the forward IBOR, so you can still use that property in the bootstrapping as you would for non AUD FRAs. – Antoine Conze Jan 17 '18 at 7:30
• Thanks a lot for the answer. Is there a mathematically equoation showing it? – JonDoe Jan 17 '18 at 8:19

• USD FRA: $\text{payoff} = N \frac{\delta (R - K) }{ 1 + \delta R}$ paid on the FRA start date, where $N$=notional, $\delta$= year fraction, $K$= fixed rate, $R$= floating rate;
• AUD FRA: $\text{payoff} = N (\frac{1}{1 + \delta K} - \frac{1}{1 + \delta R} )$ paid on the FRA start date.
Now $$N \left(\frac{1}{1 + \delta K} - \frac{1}{1 + \delta R} \right) = \frac{N}{1 + \delta K} \frac{\delta (R - K) }{ 1 + \delta R}$$ therefore AUD style FRA payoff with notional $N$ $\Leftrightarrow$ USD style FRA payoff with notional $\frac{N}{1 + \delta K}$
• Thanks a lot. But How did you derived $\frac{N}{1 + \delta K}$? That means that my notional still needs tobe adjusted with $1 + \delta K$ or do I misunderstand something? – JonDoe Jan 17 '18 at 15:40
• Yes as shown in my answer a AUD FRA payoff is equivalent to a USD FRA payoff with notional divided by $1 + \delta K$, and since you are bootstrapping on zero PV FRAs the notional has no impact so you can use Quantlib's USD FRA implementation for bootstrapping. – Antoine Conze Jan 22 '18 at 7:37