In the book of De Weert he approximates the price with a strip of knock-outs. For example the lookback call with fixed strike pays the (max(S) - K)+, is approximated by a strip of knockout calls with a rebate. So whenever the stock sets a new high, another call knocks out and you receive your rebate. In his example the rebates are 1 cent apart. So if the stock moves from $\$45$ to $\$50$, you will have collected $\$5$ in rebates. Anyways: - do you agree that a knock-out call while it is a live is long gamma? - do you agree that a barrier option that is knocked out has no gamma? - do you agree that a barrier option has more gamma when spot is closer to the strike? Assuming you agree with the 3 bullets above. you can see that once the stock goes up and knocks out a few barrier options. and then spot drops, the strip of barriers will have less gamma.