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Answer: II. and III. (call on a put; put on a call)
A compound option is an option on another option. Let the value of the underlying option move with the stock price: - A **call** value increases when the underlying asset price increases. - A **put** value decreases when the underlying asset price increases. Now evaluate each compound type: 1. **Call on a call**: call value rises as the stock rises, so this compound option is **increasing**. 2. **Call on a put**: put value falls as the stock rises, so the call-on-put value is **decreasing**. 3. **Put on a call**: call value rises as the stock rises, so the put-on-call value is **decreasing**. 4. **Put on a put**: put value falls as the stock rises, so the put-on-put payoff rises, making it **increasing**. Therefore, the compound option values that are **decreasing** in the underlying asset price are **II and III**. So the correct answer is **C**.
Author: Manit Arora
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Consider the four main types of compound options:
I. call on a call,
II. call on a put,
III. put on a call,
IV. put on a put
With respect to the value of the compound option as a function of the underlying asset price, which of these compound option's value is (are) a DECREASING function of the underlying asset price?
A
None, the compound values are all (each) an increasing function of asset price
B
IV. only (put on a put)
C
II. and III. (call on a put; put on a call)
D
III. and IV. (put on a call; put on a put)
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