IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates
A Hull-White one-factor model, an extension of Vasicek, replaces the constant long-run mean with a time-dependent function θ(t). What is the main purpose of this change?
The time-dependent mean level in Hull-White is chosen so the model reproduces the observed current yield curve exactly. Vasicek with constant parameters generally cannot do this. The model still has mean reversion, randomness and the possibility of negative interest rates.
- ATo make the short rate non-random
- BTo fit the model exactly to the currently observed yield curveCorrect
- CTo prevent the short rate from ever being negative
- DTo remove mean reversion from the model
- To make bond prices independent of volatility
Explanation
The time-dependent drift θ(t) is chosen so that model zero-coupon prices match today's observed term structure. It does not remove mean reversion, nor prevent negative rates, since the model is still Gaussian.
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