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Estimating LIBOR Rates with a Vasicek Model

Article Quant Q&A · Author: Bard
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Summary

The document considers forecasting daily three-month and one-month LIBOR over a long horizon by treating observed rates as instantaneous short rates and estimating Vasicek model parameters with regression. The proposed use is forecasting rather than derivative valuation, so the author accepts that the model would not fit the current yield curve.

The response cautions that the model’s limited parameterization may not describe real yield-curve behavior and that parameter estimates can depend on whether they are fitted across maturities or through time. In particular, cross-sectional regression may produce estimates of mean reversion and volatility that differ from those useful for time-series dynamics, while the long-run rate may be difficult to estimate stably. The exchange offers conceptual cautions, not empirical results or a validated forecasting procedure; it does not establish whether this approach will forecast either LIBOR series well.

Key ideas

  • The proposed forecast treats realized three-month and one-month LIBOR as instantaneous short rates.
  • Regression could be used to estimate the Vasicek model parameters from historical rates.
  • The proposed use is forecasting, so matching the current yield curve is not required by the author.
  • A one-factor Vasicek model may not capture actual yield-curve dynamics.
  • Parameter estimates may differ between cross-sectional and time-series fitting.

Tags

Fixed incomeStatisticsBacktesting
Full text
# LIBOR 3M and 1M from Vasicek model


# LIBOR 3M and 1M from Vasicek model












I would like to discuss my approach toward modelling of interest rates with respect to its downsides and advantages.

My problem is to forecast daily LIBOR 3M and LIBOR 1M over a particular time horizon, let say 10Y.

I was thinking about applying Vasicek interest rate dynamics and treating realized historical LIBORS for 3M and 1M as instaneous rates and calibrating the model to them via regression approach.

This simplified apprach won't be used for any derivative valuations, therefore I am accepting some limitations, like no fit to current interest rate curve.

Do you think that my approach is acceptable in the light of the aim of this analysis?

Thanks, Bart

## Answer by Foster Boondoggle (score -1)

https://quant.stackexchange.com/a/25859

"Calibrating the model to them via regression"... Vasicek has just three parameters: $\sigma$ (vol), $r_L$ (long rate) and $a$ (mean reversion) and a time-dependent short rate $r_0$. Can you specify what you are thinking of in terms of a regression model to estimate these? Obviously $r_0$ will not be a stable parameter. If you want to estimate $\sigma$, $r_L$and $a$, you have to contend with the fact that actual yield curves & dynamics are not well explained by a one factor model (here $r_0(t)$ parameterizes the factor), so it's going to be tricky to use regression without having the fact that the model is wrong mess up the estimates. E.g., if you do cross-sectional regressions, the apparent values of $a$ and $\sigma$ will be much larger than the ones that do a good job of describing time-series dynamics. And $r_L$ won't be easy to stably estimate with small values of $a$ and $\sigma$ corresponding to the apparent time-series behavior.

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.