Consider a One-Factor HJM Model Where the Initial Forward Curve $T$

Consider a one-factor HJM model where the initial forward curve is given as 6% for one year and 7% between one and two years. The evolution of continuously-compounded one-year forward rates beginning at time $T$ , is given by the following binomial process: $f ( t + 1 , T ) = f ( t , T ) + \alpha \pm 0.02$ , where the up and down movements are equiprobable. What is the price of a $100 notional one-year cap on the one-year forward rate at a strike rate of 7%.

A) 0.87
B) 0.95
C) 1.05
D) 1.10

Correct Answer:

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