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

In a continuous-time term structure framework, the instantaneous forward rate f(t,T) is best described as:

The instantaneous forward rate is the rate fixed at time t for borrowing over an infinitesimally short period beginning at future time T. It is the negative derivative of the log zero-coupon bond price with respect to maturity, not an average yield.

  1. AThe rate agreed at time t for borrowing over the infinitesimal interval starting at future time TCorrect
  2. BThe average spot rate earned between t and T
  3. CThe yield on a coupon bond maturing at T
  4. DThe expected future short rate under the real-world measure
  5. The rate on a zero-coupon bond of term T−t minus the short rate

Explanation

The instantaneous forward rate f(t,T) is the rate contracted at t for borrowing over a very short period starting at T. It equals -∂/∂T ln P(t,T). The average spot rate is the yield, not the forward rate, and forwards are not in general expectations of future short rates under the real-world measure.

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