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Building an AUD Discount Curve Under USD Collateral

Article Quant Q&A · Author: dvar
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Summary

The document lays out a curve-construction problem: derive discount factors for Australian-dollar cashflows collateralised with US-dollar cash. It lists available Australian OIS, bank-bill swaps, basis swaps between bank-bill tenors and OIS, and cross-currency basis quotes against SOFR. It also describes an existing workflow for constructing an AUD OIS curve and an AUD three-month bank-bill forward curve from those instruments.

The author has additionally used the cross-currency basis to form a bank-bill discount curve under SOFR collateral, but questions whether that curve is appropriate for discounting AUD cashflows. They suspect the AUD bank-bill/OIS basis is needed, yet provide no answer or completed bootstrapping method. The instrument set and distinction between forwarding and collateral-specific discounting make this a useful framing of a multi-curve problem, but the document alone does not establish a solution or market conventions.

Key ideas

  • The instrument set combines AUD OIS, bank-bill swaps, tenor basis swaps, and cross-currency basis quotes against SOFR.
  • An AUD OIS curve and a three-month bank-bill forward curve can be built from the listed local-market instruments.
  • The question concerns how USD collateral changes the discount curve for AUD cashflows.
  • The document raises but does not resolve how the AUD bank-bill/OIS basis should enter the construction.

Tags

Fixed incomeForexMulti-assetDerivatives pricing
Full text
# Building an AUD discount curve collateralised with USD cash


# Building an AUD discount curve collateralised with USD cash












How do I produce a discount curve to discount AUD cashflows collateralised with USD cash?

I have the following data available from Bloomberg:

- AUD OIS up to 9m

- AUD 3 month bank bill (3mBB) swaps from 1y - 3y

- AUD 3mBB/AUD OIS basis swaps from 1y - 30y

- AUD 6mBB swaps from 4y - 30y

- AUD 6mBB/AUD 3mBB basis swaps from 4y - 30y

- XCCY basis quoted AUD 3mBB vs SOFR from 3m - 30y

Bloomberg build the AUD OIS market data using 1 - 5 i.e., AUD OIS up to 9m, (2) - (3) up to 3y, (4) - (5) - (3) up to 30y. Using this, I am able to build an AUD OIS curve collateralised under AUD cash, and can also build the 3mBB forward curve but I'm not able to figure out how to use the XCCY basis to get a discount curve collateralised with USD cash.

What I've done so far is use the 3mBB forward curve and the XCCY basis to get a 3mBB discount curve collateralised under USD cash (SOFR) but I don't think I can use this curve to discount AUD cashflows with USD cash as it's not the risk free curve. I'm thinking I need to use the 3mBB/OIS basis somewhere but it's not clear to me how to do that.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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