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Answer: Floating lookback put (lowest) and floating lookback call (highest)
**Correct answer: B** Compute each payoff from the path: - **Floating lookback call** = \(S_T - S_{\min}\) = \(53 - 39 = 14\) - **Floating lookback put** = \(S_{\max} - S_T\) = \(61 - 53 = 8\) - **Fixed lookback call** with \(K=50\) = \(S_{\max} - K\) = \(61 - 50 = 11\) - **Fixed lookback put** with \(K=50\) = \(K - S_{\min}\) = \(50 - 39 = 11\) So the **lowest** payoff is the **floating lookback put** at 8, and the **highest** payoff is the **floating lookback call** at 14.
Author: Manit Arora
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Question-413.3. Assume a stock starts the year priced at $50.00, then drops to a low of $39.00, then subsequently increases up to a high of $61.00, before dropping to finish the year at $53.00; i.e., S(0) = 50 and S(1.0) = 53 with interim low of 39 and high of 61. Now consider four lookback options with lives corresponding exactly to the year: each option life begins when the stock trades at $50.00 and expires at the end of the year when the stock trades at $53.00. Two of the options are floating lookback options, which do not require strike prices; the fixed lookback options have strike prices equal to the initial $50.00. Which lookback option has, respectively, the lowest and highest final payoff?
A
Fixed lookback call (lowest payoff) and floating lookback put (higest payoff)
B
Floating lookback put (lowest) and floating lookback call (highest)
C
Floating lookback call (lowest) and floating lookback put (highest)
D
Fixed lookback call (lowest) and fixed lookback put (highest)
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