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Yield Curve Interpolation and No-Arbitrage Term Structure Models

Article Quant Q&A · Author: noob-mathematician
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Summary

The document asks how to infer shorter-maturity annualized spot rates from a sparse set of observed term-structure points. It gives three observations at maturities of three, six, and nine months, then asks for rates at two and four months and whether a standard no-arbitrage interpolation method applies.

The response does not calculate either missing rate or recommend a particular interpolation rule. Instead, it directs readers toward yield curve models, including affine term structure models, as background for understanding how rates across maturities can be represented. The material therefore frames the modeling question but leaves the choice of curve construction, no-arbitrage constraints, and numerical estimation unresolved.

Key ideas

  • The question concerns estimating spot rates at maturities between observed curve points.
  • The example supplies annualized spot rates for three-, six-, and nine-month horizons.
  • The response points to yield curve models and affine term structure models for further study.
  • No interpolation formula or missing rate is derived in the exchange.

Tags

Fixed incomeStatistics
Full text
# yield curve basics


# yield curve basics












Suppose we observe the following term structure (of annualised spot rates):

- 0-3 Months $\rightarrow$ 4.0%.

- 0-6 Months $\rightarrow$ 4.2%.

- 0-9 Months $\rightarrow$ 4.4%.

Question1) How can we infer (compute) the rates for the period 0-2M and 0-4M. Is there any standard way (interpolation) to do that in the context of no-arbitrage? Any reference?

Thanks!

## Answer by user24980 (score 1)

https://quant.stackexchange.com/a/54185

there are several types of yield curve models, have a read at https://link.springer.com/chapter/10.1057/9780230513747_3

you might also have a look at https://en.wikipedia.org/wiki/Affine_term_structure_model

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