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

question 8

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 one-year call option on a two-year 6.5% coupon bond, with a strike price of $100 ex-coupon?

• A) 0.50
• B) 0.55
• C) 0.60
• D) 0.65

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Definitions:

Futures

Agreements that enforce a commitment from the buyer to acquire, or from the seller to divest, an asset at a specific price and time decided beforehand.

Jet Fuel

A type of aviation fuel designed for use in aircraft powered by gas-turbine engines.

Hedge

An investment made to reduce the risk of adverse price movements in an asset, typically involving derivatives contracts like futures and options.

American Call Option

A type of options contract that gives the holder the right, but not the obligation, to buy an asset at a set price at any time before the expiration.