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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!

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  • $\begingroup$ To discount a cash flow at time T, you need the discount rate $r(0,T)$. Zeros have a nice property. You know that from their pricing formula $YtM=r(0,t)$. Although, from a bullet bond, the yield to maturity cannot be mapped to a discount rate. Because it's YtM is an "imaginary" metric since you cannot reinvest in it $\endgroup$ – Bougias A. Jun 11 at 11:47
  • $\begingroup$ It definitiely depends on what you are pricing and for which kind of investors. This means that factors such as demand segmentation and market liquidity play a role in the choise. Gov bonds are usually the most liquid. Many corporate bonds price against the average spreads of a comparable group based on rating, sector. Others, such as Middle East Gov bonds are much more investors concerned and price against the swap curves because of their higher liquidity. $\endgroup$ – Vitomir Jun 11 at 11:53
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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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