Option risk*
- a. In Section 21-3, we calculated the risk (beta) of a six-month call option on Amazon stock with an exercise price of $900. Now repeat the exercise for a similar option with an exercise price of $750. Does the risk rise or fall as the exercise price is reduced?
- b. Now calculate the risk of a one-year call on Amazon stock with an exercise price of $750. Does the risk rise or fall as the maturity of the option lengthens?
a)
![Check Mark](/static/check-mark.png)
To determine: Value of option when the option beta at an exercise price of $750.
Explanation of Solution
Given information:
Current stock selling price (P) is $900
Exercise price (EX) is $750
Standard deviation (σ) is 0.25784
Risk free rate (rf) is 0.01 annually,
t = 0.5
Stock beta is 1.5 and risk free loan beta is 0
Calculation of value of option:
The value of
The value of
Therefore,
Hence, the value of call option is $165.51
Person X has investing $781.48 and he borrows $615.98,
Calculation of option beta:
Therefore, the option beta is $7.082
The lower exercise price decreases the beta of call option ($10.95 to $7.08)
b)
![Check Mark](/static/check-mark.png)
To determine: Value of option when the option beta at an exercise price of $750 and time period is 1 year.
Explanation of Solution
Given information:
Current stock selling price (P) is $900
Exercise price (EX) is $750
Standard deviation (σ) is 0.25784
Risk free rate (rf) is 0.01 annually,
t = 1
Stock beta is 1.5 and risk free loan beta is 0
Calculation of value of option:
The value of
The value of
Therefore,
Hence, the value of call option is $185.15
Person X has investing $728.20 and he borrows $543.05,
Calculation of option beta:
Therefore, the option beta is $5.8995
The risk also decreases from $7.08 to $5.90 as the maturity is extended.
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Chapter 21 Solutions
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