What Stochastic Interest Rate Models Can and Cannot Forecast
Summary
The document distinguishes the forecasts implied by stochastic interest rate models from their common use in pricing derivatives. A random walk model keeps the expected future short rate at its current level, while a Vasicek model makes the expected rate revert toward a long-term level. More elaborate models can represent a whole yield curve. Since bond prices depend on rates, these model paths can also be translated into bond price scenarios.
The answers caution against treating the average simulated path as a reliable trading forecast. Many models are risk-neutral and therefore omit real-world duration risk premia; model choice may also be wrong, and the framework may exclude policy, economic, sentiment, and market-structure information. Models calibrated to market forwards or a user’s forecast may simply reproduce those inputs in their average path. Their scenario distributions are useful for understanding rate variability and pricing rate derivatives, but a pure model is not a dependable crystal ball for bond prices.
Key ideas
- Stochastic rate models imply distributions and expected paths for future rates.
- Mean reversion models pull expected short rates toward a long-term level.
- Rate scenarios can be translated into bond price scenarios because bond prices depend on rates.
- Risk-neutral calibration, missing risk premia, model error, and omitted external information limit real-world forecasting.
- Simulated paths are often more useful for derivative pricing and variability analysis than as standalone bond trading signals.
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Full text
# Do stochastic interest rate models forecast future interest rate?
# Do stochastic interest rate models forecast future interest rate?
And if so, can they be used to estimate the future price of bonds?
## Answer by Chris Taylor (score 4, accepted)
https://quant.stackexchange.com/a/35761
Yes, every stochastic interest rate model makes a forecast for the future interest rate. For example, the random walk model
$$ dr_t = \sigma dW_t $$
predicts all future interest rates to be equal to the current rate. The Vasicek model,
$$ dr_t = a(\bar{r} - r_t)dt + \sigma dW_t $$
predicts that the future interest rate reverts to the long-term rate $\bar{r}$, i.e.
$$ E(r_t) = \bar{r} + (r_0 - \bar{r})e^{-at} $$
More complex models might make forecasts for the entire maturity structure of interest rates, rather than just for the short rate.
Every interest rate forecast can be converted into a forecast for bond prices, since bond prices are (more or less) a function of interest rates. However, you should note that
- You can't be sure that you have the right interest rate model.
- Even if you have an accurate model, most interest rate models are risk-neutral, i.e. they don't take the risk premium associated with duration into account. You can't expect them to give accurate forecasts of real-world interest rates.
- Stochastic models generally don't take external information into account (e.g. government monetary policy, risk sentiment, business cycle, bond market microstructure). They are potentially discarding valuable information.
For these reasons I would be very careful when using a pure stochastic interest rate model to make forecasts for bond prices.
## Answer by nbbo2 (score 2)
https://quant.stackexchange.com/a/35765
Yes, they do forecast the interest rate. But that is not really what they are used for. They are used to forecast the variability of interest rates (i.e. various outcomes for interest rates that we could have) and therefore allow the pricing of interest rate derivatives (not of the bonds themselves).
In other words these models generate a set of interest rate paths (thousands of them). The mean (expected) interest rate path from the model is not particularly interesting or useful for trading bonds. The model is generally calibrated so the mean outcome is derived from the forward structure in the market, or from the forecast of the person running the model. So you "learn nothing new" by averaging the model's predictions, you are just getting back what you put in.
So a stochastic interest rate model is a machine for automatically generating plausible i.r. scenarios, not a crystal ball that tells you what interest rates will be.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.