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:

Average Number

A basic statistical measure represented by the sum of all values divided by the count of values, commonly used to describe the central tendency of data.

Probability

The measure of the likelihood that an event will occur, quantified as a number between 0 and 1.

System

A group of interacting or interrelated entities that form a unified whole, used to analyze or study a specific domain or set of procedures.

Expected Number

The calculated average or mean value of a numeric dataset, predicting the central value around which other values tend to cluster.