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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

An actuary wants a one-factor short-rate model that reproduces today's observed market zero-coupon bond prices exactly, so that it can be used to price interest rate derivatives consistently with the market. Which feature of the model makes this possible?

A time-dependent drift fitted to today's yield curve, as in the Hull-White model, lets the model reproduce observed zero-coupon bond prices exactly. Models with constant parameters, like basic Vasicek or CIR, have too few degrees of freedom to match an arbitrary market curve.

  1. AA constant long-run mean rate and constant volatility, as in the basic Vasicek model
  2. BA time-dependent drift parameter fitted to the current yield curve, as in the Hull-White modelCorrect
  3. CA rate process that can never become negative, as in the Cox-Ingersoll-Ross model
  4. DA requirement that all bond yields are equal at every maturity
  5. A random walk for the short rate with no mean reversion and no drift

Explanation

Models with a time-dependent drift, such as Hull-White (extended Vasicek), can be calibrated so the model prices match the observed zero-coupon curve exactly. Basic Vasicek and CIR have a small number of constant parameters, so they generally cannot fit an arbitrary observed curve. Non-negativity or a flat curve does not give an exact fit.

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