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. Consider the price of one-year call and put options on a two-year 6.5% coupon bond, with a strike price of $100 ex-coupon. The difference between the call and put prices will be

A) $6.5 e ^ { - 0.06 } + 106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 }$
B) $6.5 e ^ { - 0.06 } + 106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 } + 6.5 e ^ { - 0.06 }$
C) $106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 } - 6.5 e ^ { - 0.06 }$
D) $106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 }$

Correct Answer:

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