Consider a Floating-Strike Lookback Put Option Written on a Stock $S ^ { \max }$

Consider a floating-strike lookback put option written on a stock. Let $S ^ { \max }$ and $S ^ { \min }$ denote the maximum and minimum prices of the stock over the option's life. Then, the payoff to the option holder is given by $\max \{ X - Y , 0 \}$ , where

A) $X = S ^ { \max }$ and $Y = K$ , the given strike price of the option.
B) $X = K$ and $Y = S ^ { \min }$ .
C) $X = S ^ { \max }$ and $Y = S _ { T }$ , the price of the underlying at maturity.
D) $X = S _ { T }$ and $Y = S ^ { \min }$ .