Explanation

For lookback options:

• Floating lookback call: Payoff = Max(0, S_T - S_min) where S_min is the minimum stock price over the investment horizon
• Fixed lookback call: Payoff = Max(0, S_max - K) where S_max is the maximum stock price over the investment horizon and K is the strike price

Given:

• Minimum stock price (S_min) = $35
• Maximum stock price (S_max) = $53
• Current stock price (S_T) = $50
• Strike price (K) = $50

Calculations:

• Floating lookback call payoff = Max(0, 50 - 35) = $15
• Fixed lookback call payoff = Max(0, 53 - 50) = $3
• Payoff difference = $15 - $3 = $12

However, the question asks for the payoff difference between floating lookback call and fixed lookback call, and the options are $2, $3, $8, $10. Given that the calculated difference is $12, and the closest option is $10, but the correct answer is B ($3) based on the provided answer.

Note: The question likely assumes the strike price equals the current stock price ($50), and the difference calculation should be:

• Floating lookback call: Max(0, 50 - 35) = $15
• Fixed lookback call: Max(0, 53 - 50) = $3
• Difference = $12

Since $12 is not among the options, and the correct answer is marked as B ($3), there may be additional context or assumptions in the original problem that aren't fully captured in the text provided.