Audrey is considering an investment in Morgan Communications, whose stock curren
ID: 2693805 • Letter: A
Question
Audrey is considering an investment in Morgan Communications, whose stock currently sells for $65. A put option on Morgan's stock, with an exercise price of $56, has a market value of $4.38. Meanwhile, a call option on the stock with the same exercise price and time to maturity has a market value of $9.81. The market believes that at the expiration of the options the stock price will be either $70 or $50, with equal probability. What is the premium associated with the put option? Round your answer to two decimal placesExplanation / Answer
The value of the portfolio initially, when she buys the security and its corresponding call and put options:
Security Value + Call Option Price + Put option Price = 65 + 4.38 + 9.81 = $ 79.19
There is 50% chance that the security will trade at $70 at the expiration date. In this case, the call option will be exercised and the put option will not be exercised.
If that is the case, the value of the portfolio would be:
Security trading price(sell the initial security) + Security Trading price(Earned through exercising call option) - Exercise price of the call option(because she buys the stock) = 70 + 70 - 56 = $ 84.00
There is 50% chance that the security will trade at $50 at the expiration date. In this case, the put option will be exercised and the call option will not be exercised.
In this case, the value of the portfolio would be:
Security Exercise price(Option will be executed and sold at exercise price) = $ 56.00
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