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

question 2

Multiple Choice

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 call option on a $100 notional, 6.5% coupon bond, with a strike price of $100?

• A) 0.25
• B) 0.31
• C) 0.43
• D) 0.55

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Definitions:

Unequal Payments

Payments that vary in amount over a period, commonly seen in loan repayments or investment returns that do not have a fixed payment schedule.

Rate Of Return

The upward or downward movement in the worth of an investment for a predefined interval, calculated as a percentage of the investment's inaugural cost.

Discount Rate

The Discount Rate is the interest rate used to determine the present value of future cash flows in discounted cash flow analysis.

Predicting Variables

Variables in statistical models that are used to predict outcomes or responses of interest.