I found a good answer in my library (short answer = YES)
"These [lookback options] are probably the most discussed and least used of the standard exotic options. The problem is that on the one hand they have immense intuitive appeal and pricing presents some interesting intellectual challenges; but on the other hand they are so expensive that no-one wants to buy them... The form of the payoff is unusual in that it does not involve an expression of the form max[0,...], since (ST - Smin) can never be negative; it has therefore been suggested that this is not really an option at all, although this is largely a matter of semantics." - Peter James, Option Theory
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