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Answer: A put option after a downward price movement
**Explanation:** - **Option A (Incorrect):** The payoff for a put option after an upward price movement is calculated as \(\text{Max}(0, X - S_u)\), where \(X\) is the exercise price and \(S_u\) is the price after the up move. Here, \(S_u = €26 \times 1.10 = €28.60\). Thus, the payoff is \(\text{Max}(0, €22 - €28.60) = €0\), which is lower than the payoff for Option B. - **Option B (Correct):** The payoff for a put option after a downward price movement is \(\text{Max}(0, X - S_d)\), where \(S_d = €26 \times 0.75 = €19.50\). The payoff is \(\text{Max}(0, €22 - €19.50) = €2.50\), which is the highest among the given options. - **Option C (Incorrect):** The payoff for a call option after a downward price movement is \(\text{Max}(0, S_d - X)\). Here, \(S_d = €19.50\), so the payoff is \(\text{Max}(0, €19.50 - €22) = €0\), which is also lower than Option B. This question tests the understanding of payoff calculations in a one-period binomial model for derivatives.
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An analyst gathers the following data for a stock: current price €26, gross return for an up move 1.10, and gross return for a down move 0.75. The exercise price for both call and put options is €22. Using a one-period binomial pricing model, which of the following options yields the highest payoff?
A
A put option after an upward price movement
B
A put option after a downward price movement
C
A call option after a downward price movement