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Why Forward Rates Change: Fixed Dates Versus Rolling Tenors

Article Quant Q&A · Author: user34785
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Summary

The document distinguishes a forward rate tied to specific calendar dates from a forward rate quoted for a rolling tenor. If the start and end dates remain fixed, the rate observed on a later valuation date reflects changes in the market’s forecast curve; absent market movement, it would be unchanged. The answer uses a three-month interbank rate example to explain that a curve represents market pricing for future fixings, not a guaranteed forecast of what those fixings will be.

A generic forward such as a three-month period beginning three months from now moves forward as the valuation date advances. Its start and end dates therefore differ from one day to the next, so the new quote describes a different accrual period even if the curve has not otherwise moved. The distinction also helps explain why futures linked to fixed settlement dates are easier to compare across valuation dates. The discussion is conceptual and provides no curve construction, discounting formula, or treatment of conventions and basis; it concerns historical IBOR-style forecasting curves rather than establishing details for every modern benchmark.

Key ideas

  • A forward rate for unchanged calendar dates changes when the market curve reprices those dates.
  • Without market movement, a fixed-date forward rate remains the same from one valuation day to the next.
  • A rolling-tenor forward shifts its accrual dates as the valuation date advances.
  • Comparing forward quotes requires checking whether they refer to the same underlying dates.

Tags

Fixed incomeDerivatives pricingFutures
Full text
# Does Foward Rate on Libor change depending on which day you calculate it at?


# Does Foward Rate on Libor change depending on which day you calculate it at?












Based on this article: https://en.wikipedia.org/wiki/Forward_rate

If we were to calculate forward rate on libor 3M at times T1,T2 (ie, forward rate at T1, going forward T2), does that value change if we compute it today vs tomorrow, assuming T1 and T2 does not change.

My guess that it does, because our calculation of spot rate at T1 would change from day to day, as market conditions change, right?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/40487

The IBOR forecast curve is the market's expectation of the evolution of IBOR fixings. If today is 1-Jan-2018 and you have a curve that prices 27-April-2018 for 3M as 1% then if the market evolves as predicted and there is no (exogenous supply/demand) market movement between today and tomorrow then on the 2-Jan-2018 the 3M rate priced to start at 27-April-2018 is the same as it was yesterday, i.e. 1%. This is precisely what you will observe on futures markets, since the futures contract settle to fixed dates (IMM dates). Any fluctuation in those rates is market movement, i.e. change in expectations.

However if your dates are generic maturities, i.e. start-3M-end-3M, then the rates will change since a forward rate that is priced as 3M3M from 1-Jan-2018 has dates 1-April-2018 to 1-Jul-28, whereas a 3M3M priced from 2-Jan-2018 has dates 2-April-18 to 2-Jul-18, and therefore it does not represent the same price as yesterday.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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