Question

Suppose that a stock price is currently $$\$ 20$$ and that a call option with an exercise price of $$\$ 25$$ is created synthetically using a continually changing position in the stock. Consider the following two scenarios: (a) Stock price increases steadily from $$\$ 20$$ to $$\$ 35$$ during the life of the option; (b) Stock price oscillates wildly, ending up at $$\$ 35 $$. Which scenario would make the synthetically created option more expensive? Explain your answer.

   Suppose that a stock price is currently $$\$ 20$$ and that a call option with an exercise price of $$\$ 25$$ is created synthetically using a continually changing position in the stock. Consider the following two scenarios: (a) Stock price increases steadily from $$\$ 20$$ to $$\$ 35$$ during the life of the option; (b) Stock price oscillates wildly, ending up at  $$\$ 35 $$. Which scenario would make the synthetically created option more expensive? Explain your answer.
 
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Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
John C. Hull 10th Edition
Chapter 19, Problem 9 ↓

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This means that the synthetic option is created by buying the stock at $20 and holding it until the stock price reaches $35. In this case, the synthetic option would be more expensive because the investor would have to hold the stock for a longer period of time  Show more…

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Suppose that a stock price is currently $$\$ 20$$ and that a call option with an exercise price of $$\$ 25$$ is created synthetically using a continually changing position in the stock. Consider the following two scenarios: (a) Stock price increases steadily from $$\$ 20$$ to $$\$ 35$$ during the life of the option; (b) Stock price oscillates wildly, ending up at $$\$ 35 $$. Which scenario would make the synthetically created option more expensive? Explain your answer.
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