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

question 9

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.Consider the price of one-year call and put options on a two-year 6.5% coupon bond,with a strike price of $100 ex-coupon.The difference between the call and put prices will be

• A) \(6.5 e ^ { - 0.06 } + 106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 }\)
• B) \(6.5 e ^ { - 0.06 } + 106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 } + 6.5 e ^ { - 0.06 }\)
• C) \(106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 } - 6.5 e ^ { - 0.06 }\)
• D) \(106.5 e ^ { - 0.06 - 0.07 } - 100 e ^ { - 0.06 }\)

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Definitions:

Ammonification

The process by which microorganisms decompose organic nitrogen from dead organisms and waste products into ammonia.

Nitrogenous Organic Compounds

Organic compounds that contain nitrogen as part of their molecular structure, including proteins, nucleic acids, and more.

Inorganic Nitrogen-containing Ions

Nitrate, nitrite, and ammonium ions that are crucial for plant nutrition but can cause environmental issues in excess.

Organic Molecules

Compounds primarily made of carbon atoms bonded with hydrogen, often containing oxygen and nitrogen, and forming the basis of all life forms.