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How Short-Rate Models Differ from Forward Curves

Article Quant Q&A · Author: VVKK77
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Summary

The document distinguishes forward rates read from a yield curve from rates generated by a short-rate model. At the current date, a yield curve is a fixed term structure from which one can calculate future rates for chosen short tenors. Those curve-implied forwards are deterministic given the curve.

A short-rate model instead describes possible behavior of the instantaneous short rate over time. Forward rates derived from that model depend on its parameters and need not match the forwards implied by the observed yield curve. The distinction clarifies that a curve supplies market-implied rates at a point in time, while a model represents dynamics for projecting rates. The brief answer does not explain calibration, model selection, or how to reconcile differences between model-generated and curve-implied forwards, so it is a conceptual distinction rather than a practical modeling procedure.

Key ideas

  • A yield curve at the current date implies deterministic forward rates for selected tenors.
  • A short-rate model projects the behavior of an instantaneous rate through time.
  • Forward rates derived from a short-rate model depend on its parameters.
  • Model-generated forwards are not necessarily equal to forwards implied by the observed yield curve.

Tags

Fixed incomeFuturesStatistics
Full text
# What's the difference between the short rate model projection and the 3M forward curve?


# What's the difference between the short rate model projection and the 3M forward curve?












A term structure has a forward curve

So what is it that the short rate model is projecting exactly?

Why is it needed?

How are they different?

## Answer by Kiann (score 0, accepted)

https://quant.stackexchange.com/a/44598

A yield curve is a deterministic function as set and seen at time T=0. One can project any short-term (e.g. 1 mth, 1 wk or 1 day) forward rates from the curve and they are deterministic.

A short rate model only projects the behaviour of the instantaneous short rate (again can be defined as any tenor). The forward rates from this model are generated from the model parameters and might not necessarily match the yield curve.

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.