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

question 16

Multiple Choice

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

---

Definitions:

Hyperreflexia

An exaggerated response of the muscles following a stimulus, indicative of disturbances in the central nervous system.

Fasciculations

Involuntary, small, rapid muscle contractions or twitches visible under the skin, often benign but can be symptomatic of neurological conditions.

Positive Babinski

A reflex action in which the big toe remains extended or extends upward when the sole of the foot is stimulated, indicating neurological abnormality.

Dorsiflexion

The movement that brings the top of the foot toward the shin, decreasing the angle between the dorsal surface of the foot and the leg.