Equivalence Between AUD and USD Forward Rate Agreement Payoffs

Summary

The document derives a relationship between Australian-style and US-style forward rate agreement (FRA) payoffs. It rewrites the AUD payoff as the USD-style payoff multiplied by a notional adjustment, showing that the two forms can be matched by scaling notional by the discounting factor associated with the contract rate.

This is an algebraic equivalence, not a discussion of curve bootstrapping or a comparison of software implementations. The document offers no market data, worked numerical example, or conditions for applying the relation across conventions. Readers should treat it as a payoff conversion identity and check the relevant contract definitions and accrual conventions before using it in pricing.

Key ideas

• The AUD-style FRA payoff can be rewritten in a form resembling the USD-style payoff.
• Matching the two payoff expressions requires adjusting the notional by the contract-rate discount factor.
• The discussion establishes a payoff identity but does not explain forward-curve bootstrapping.

Tags

# AUD Forward Rate Agreement and Forward Curve Bootstrapping


# 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?

## Answer by Antoine Conze (score 3, accepted)

https://quant.stackexchange.com/a/37774





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} $

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.