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?
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$\begingroup$ 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. $\endgroup$– Antoine ConzeJan 16, 2018 at 18:37
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$\begingroup$ 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? $\endgroup$– JonDoeJan 16, 2018 at 19:17
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$\begingroup$ 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. $\endgroup$– Antoine ConzeJan 17, 2018 at 7:30
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$\begingroup$ Thanks a lot for the answer. Is there a mathematically equoation showing it? $\endgroup$– JonDoeJan 17, 2018 at 8:19
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1 Answer
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- 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} $
answered Jan 17, 2018 at 12:40
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$\begingroup$ 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? $\endgroup$– JonDoeJan 17, 2018 at 15:40
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$\begingroup$ My other question is, as you said above in the bootstrapping and zero pricing there is no difference. So in Quantlib I should use the same way of bootstrapping an AUD IRS the same way as I would use e.g. bootstrapping an standard US IRS, independent of the different FRA pricer. $\endgroup$– JonDoeJan 19, 2018 at 15:41
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$\begingroup$ 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. $\endgroup$ Jan 22, 2018 at 7:37
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$\begingroup$ Thanks a lot! I think I will give it a shot. In case I see some differences, I willtry to post something new. $\endgroup$– JonDoeJan 24, 2018 at 18:05