IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates
Which statement about implied forward rates derived from an upward-sloping spot rate curve is correct?
On an upward-sloping spot curve, the one-year forward rate from t-1 to t is higher than the t-year spot rate. The t-year spot is a geometric average of earlier forwards, so a rising average requires the latest forward to exceed it.
- AThe one-year forward rate for a future year is below the spot rate for that maturity.
- BThe forward rate from t-1 to t is above the t-year spot rate.Correct
- CForward rates equal spot rates whenever spot rates differ by maturity.
- DForward rates are always below the one-year spot rate.
- Forward rates cannot be obtained from spot rates.
Explanation
Since (1+y_t)^t = (1+y_{t-1})^{t-1}(1+f), if y_t > y_{t-1} then f exceeds y_t. So on a rising curve forwards lie above the spot rates. The other options contradict this.
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