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

Consider a two-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 with two shock terms: $f ( t + 1 , T ) = f ( t , T ) + \alpha \pm 0.01 \pm 0.01$ , where the forward rate movements are equiprobable. What this means is that the forward rate may move up by either 0.02 with probability 1/4, or move down by 0.02 with probability 1/4, or remain the same with probability 1/2. What is the price of a put option on a $100 notional, 6.5% coupon bond, with a strike price of $100?

A) 0.25
B) 0.54
C) 0.77
D) 0.96