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FRM Part I · FRM Exam Part I · Exotic Options

A risk manager compares a floating-strike lookback call (strike equals the minimum asset price observed during the life) with a standard European at-the-money call on the same asset and expiry. Which statement is correct?

The lookback call pays the final price minus the lowest price seen, and that minimum cannot exceed the starting price. Its payoff is therefore at least that of an at-the-money standard call in every scenario, so it costs at least as much, and it is typically more expensive.

  1. AThe lookback call can expire worthless if the asset falls throughout the life
  2. BThe lookback call always has a payoff at least as large as the standard call struck at the initial price, so it costs at least as muchCorrect
  3. CThe lookback call is cheaper because its strike is chosen after the fact
  4. DThe lookback call has a payoff equal to the maximum price minus the final price

Explanation

A floating-strike lookback call pays S_T minus the minimum price, and the minimum is at most the initial price, so the payoff is never below that of an at-the-money call. It is never worthless-by-construction negative; payoff is always non-negative, so it is worth at least as much and is more expensive. Option 3 reverses this.

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