Skip to content
All library documents

Limits of CIR Rate Simulations for Forecasting

Article Quant Q&A · Author: ColinJ
Read the original

Summary

The document asks how to evaluate a calibrated Cox-Ingersoll-Ross short-rate model against historical observations, noting that the ordinary R-squared from a linearized parameter fit may not provide a meaningful goodness-of-fit measure. The response does not offer a statistical fit test or compare calibration procedures such as ordinary least squares and maximum likelihood.

Instead, it cautions that simulated paths can vary substantially because of their random draws and the model’s parameter dependence. It argues that CIR simulations may have limited economic value as point forecasts of rates, while still being useful for pricing or modeling securities and derivatives. This is a qualitative warning, not a demonstrated result: the excerpt provides no dataset, diagnostics, or alternative forecasting benchmark. It also does not resolve how to test historical fit before simulation, so a researcher would need separate diagnostics suited to the model and forecasting objective.

Key ideas

  • A linear regression R-squared may not adequately assess a CIR model fit.
  • CIR simulated paths can differ because they depend on stochastic draws and calibrated parameters.
  • The answer cautions against treating simulated paths as reliable rate forecasts.
  • It identifies security and derivative pricing as more natural uses for simulated paths.
  • No formal goodness-of-fit procedure or empirical comparison is provided.

Tags

Fixed incomeStatisticsBacktestingDerivatives pricing
Full text
# CIR calibration


# CIR calibration












I'm using a CIR short rate model to forecast interest rate paths. I've been thinking and also searching online about different ways of estimating its parameters (a, b and sigma). While there are a number of relatively intuitive ways with their pros and cons (e.g. reshape into a linear regression and do OLS or MLE), I cannot find anywhere how to actually calibrate them and fit them. Is there a way to measure the goodness of fit? From my calculations, the R-squared from the linear regression is meaningless. In what way can you test that your fitted values are similar to your observed values?

To clarify, this question is not about term structures. I'm only interested to see how well it fits to the observed historical time series values before I run simulated paths.

Thanks for any advice!

## Answer by Kch (score 1)

https://quant.stackexchange.com/a/43031

CIR can be used to simulate paths, although forecasting with a model of that class is a bit unintuitive. Why? The results are highly dependent on the stochastic parameters of the equation. So, let's say you obtained a calibrated model and simulated it 5 times. You would (most likely) get very different results with the same model but with different random numbers. You could average the numbers, but then all you're getting is a mean-reversion result based on historic parameters that are calibrated on a random walk (w/ drift). Overall, the parameters are really just an extension of a random walk and won't describe time series data well.

Therefore, the economic value of a CIR simulation is limited if forecasting. But, using the paths to price and model a security or derivative is indeed a very useful tool and you can likely see why.

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.