Choosing Zero Curves by Cash Flow Tenor and Credit Risk
Summary
The document explains why valuation may require different zero curves within one currency market. Its central rule is to choose discount rates that match both the cash flow’s timing and the risks of the entity making the payment. It illustrates this with a Treasury cash flow discounted from a government-bond curve and a bank swap payment discounted from a swap curve, using the relevant payment horizon in each case.
When traded instruments are insufficient to build a curve that reflects the obligor’s risk, the answer suggests adjusting a reference zero rate with a spread, such as a credit spread for a corporate payment. The discussion is a concise conceptual guide, not a full curve-construction or multi-curve pricing framework. It does not detail curve bootstrapping, collateral conventions, basis adjustments, or how to handle differences between forecast and discount curves. The examples therefore clarify the matching principle but do not settle every instrument-specific modeling choice.
Key ideas
- Select a zero curve that reflects the risk of the cash flow being discounted.
- Match the zero-rate horizon to the timing of the payment.
- Government and swap curves can differ because they represent different issuer or sector risks.
- When suitable traded instruments are unavailable, a spread can adjust a reference zero rate for obligor risk.
- The examples provide a principle for curve choice rather than a complete pricing framework.
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Full text
# When to use which zero curves # When to use which zero curves I have a very basic question. Why are there many different zero curves for a given currency/market? For example, there are zero curves constructed using gov bonds, swaps, STIR futures, OIS, Inflation, currency basis, etc. When would you use which zero curve? Furthermore, there are different tenors, e.g. 1M Zero, 3M Zero, etc. When would you use which? Will you use bond derived z curve when pricing bonds, and swap derived when pricing swaps? Will you use 1M Zero when pricing swaps where the reference rate is 1M rate? Thank you in advance! ## Answer by AlRacoon (score 2) https://quant.stackexchange.com/a/46044 Zero rates are interest rates from t=0 to the term of the zero rate. Zero rates are used to discount periodic cash flows in the valuation process. The appropriate zero rate to use should 1) be the same period in which the cash flow occurs and 2) incorporate the risks associated with the cash flow you are discounting. For example, if you are valuing a cash flow from the US Treasury in 1M, you would apply the 1M zero rate derived from the UST curve; If you are valuing a 6M cash flow from a bank (such as that from a periodic swap payment), you would use the 6M zero derived from the Swap Curve, which will reflect the credit risk associated with the banking industry. In some instances, there will not be enough traded instruments that reflect the risks of the obligor in order to derive a zero curve. In these cases, one would adjust the zero rate by adding a spread to reflect the risk of the obligor's payment at the time of payment (such as a credit spread to reflect a corporate obligation).
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.