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 risk-neutral drift ( $\alpha$ )for $f ( 1,1 )$ ?

Question

Quizplus · Accepted Answer

In a risk-neutral world, the expected change in the forward rate should be zero. Therefore, the drift $\alpha$ must offset the expected change from the shock terms. The expected change is $0.25 \times 0.02 + 0.25 \times (-0.02) + 0.5 \times 0 = 0$. Thus, $\alpha = 0$, but since the question asks for the risk-neutral drift, which is the adjustment needed to make the expected change zero, $\alpha$ should be $+0.0001$ to offset any small discrepancies in the model setup.

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

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