FRM Part I · FRM Exam Part I · Exotic Options
A risk manager compares a floating-strike lookback call with a standard European call on the same underlying, with the same maturity and the strike of the European call equal to the initial spot price. Which statement is correct?
A floating-strike lookback call pays the final price minus the minimum price observed, which is never negative and is at least the payoff of a call struck at the initial price. It therefore is worth at least as much as that European call, and is typically more expensive.
- AThe floating-strike lookback call pays S_T minus the minimum price over the life, so it is never worth less than the European call struck at the initial priceCorrect
- BThe floating-strike lookback call pays the maximum price minus S_T, so it can finish out of the money
- CThe lookback call is cheaper because it has a lower expected payoff
- DThe lookback call can expire worthless if the asset falls throughout its life
Explanation
Floating-strike lookback call payoff is S_T - S_min, always nonnegative. Since S_min <= S_0 (the minimum includes the initial price), S_T - S_min >= S_T - S_0, and it is also >= 0, so it dominates the European call payoff. Hence it costs at least as much.
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