Why Sparse LIBOR Quotes Cannot Determine a Full Forward Curve

Summary

The question asks whether four quarterly LIBOR spot and forward rates can be derived from a one-year spot rate and a one-year-forward-one-year rate. The responses explain that a limited set of quoted maturities can support some equivalent rate calculations, but it does not uniquely reveal every shorter spot or forward rate. Building a curve from only a few points requires additional assumptions or market observations.

An overnight rate could provide a starting point for imputing a three-month rate, while conventions such as linear interpolation or a constant-forward assumption would shape the inferred values. Forward rates at other start dates would also be estimates from the curve construction. The central caveat is that an imputed rate is conditional on the method: financial equivalence does not establish the actual market rate at an unquoted maturity. The exchange provides no numerical example or preferred interpolation method, so it illustrates an identification limitation rather than a complete curve-building procedure.

Key ideas

• A small number of quoted maturities does not uniquely determine a full interest-rate curve.
• Equivalent rates for other maturities can be calculated without knowing the actual rates traded at those maturities.
• An overnight observation can help anchor an imputed three-month rate.
• Interpolation or forward-rate assumptions affect inferred spot and forward rates.

Tags

# Calculating 3 month libor from 1 year libor?


# Calculating 3 month libor from 1 year libor?












Is there a way to calculate the four 3-month LIBOR rates (spot and forward) given a 1-year spot LIBOR rate and a 1y1y forward LIBOR rate?

## Answer by Will Gu (score 1, accepted)

https://quant.stackexchange.com/a/31590

You can calculate the risk-free 2-year LIBOR rate based on what you have. You can impute the 3-month LIBOR rate if you have an overnight rate to start with. Then the 3-month LIBOR rate would depend on your assumptions (linear, constant forward, etc)

For the 3-month forward LIBOR (forward starting point within 21 months), it's gonna be the result of imputation as well.

You are basically trying to generate a curve based on two points.

## Answer by Bravo Zulu (score 0)

https://quant.stackexchange.com/a/31586

From 1 year interest rates you can calculate financial equivalent interest rates for other maturities, but not the interest rate of those maturities.

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