Bootstrapping AUD Swap Zero Rates and Choosing Curve Interpolation
Summary
The document asks how to bootstrap zero rates from Australian bank bill swap rates and interest rate swap quotes, including how coupon frequency conventions affect the bootstrap and whether the transition from short to longer maturities requires special treatment. The quoted conventions state that swaps are quarterly through three years and semiannual from four years onward, with intermediate maturities negotiated between counterparties.
The response says the key requirement is for the constructed curve to price the input instruments correctly. It recommends piecewise linear interpolation of log discount factors as a simple, robust alternative to cubic splines. It also advises matching the interpolation method to the bootstrap method, citing curve construction research to support that consistency. The excerpt does not supply the full AUD market conventions, day-count rules, payment calendars, or equations for each instrument, and its single-curve framing does not address more detailed modern multi-curve practice or counterparty credit adjustments.
Key ideas
- Swap coupon frequency conventions determine the cash-flow schedule used in bootstrapping.
- The cited convention uses quarterly payments through three years and semiannual payments from four years onward.
- A bootstrapped curve should reproduce the prices of the instruments used as inputs.
- Piecewise linear interpolation of log discount factors is presented as a simple robust choice.
- The bootstrap and interpolation methods should be consistent.
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Full text
# Bootstrapping zero-rates from AUD swap rates # Bootstrapping zero-rates from AUD swap rates I have a pay fixed / receive floating interest-rate-swap on the AUD BBSY that I'd like to price for the purposes of accounting. I understand the general process to be as follows (assuming single-curve theory): - Use the swap rates to bootstrap zero/spot rates. - Use the zero/spot rates to construct a yield curve (e.g.using cubic splines). - Use the yield curve to discount the future cash flows of the swap. - Adjust for the credit risk of the counterparties. Regarding the step 1 bootstrapping: the rates quoted in the market are 1, 2, 3, 4, 5, or 6 month "AFMA Bank Bill Swap Rates" and 1, 2, 3, 4, 5, 7, 10, and 15 year "AFMA Interest Rate Swaps". Two questions: 1) How can I tell what the coupon structure is for either reported rate (Bank Bill Swap Rates or Interest Swap Rates) so that I can construct the bootstrapping formula? 2) Do I need to do anything when I switch from the short-term to long-term rates other than recognize that in my coupon model in the bootstrapping? ## Answer by crunch (score 2, accepted) https://quant.stackexchange.com/a/16598 - Refer AFMA Interest Rates Conventions, paragraph 3.7 > Swaps are quoted on a quarterly basis for maturities out to 3 years and on a semi‐annual basis for maturities 4 years and greater. Swaps falling between the 3 and 4 year maturity will be negotiated between the two counterparties. - No. As long as your curve prices the input instruments correctly, you're good. Note: there's no need to use anything as complicated as splines for a simple bootstrap. I suggest sticking to raw interpolation (i.e. piecewise linear log-discount factor). This is simple to implement and robust. In fact, your interpolation and bootstrap method should be the same - refer Hagan & West, so you if you insist on using splines to interpolate, you should also use splines to bootstrap.
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