As said in my book, there exists a kind of barrier option which has negative gamma. I tried the knock in and knock out option, their gamma are positive. Could anyone provide an example where a barrier option has negative gamma? Thanks for any help!
As Quantuple said, you haven't looked too carefully:) For example:
You can download the app above here and play around to see gamma and other sensitivity plots when in doubt. For example, how does the above gamma plot change when the barrier monitoring is discrete? Can you have negative gamma for up and in options? (Yes you can.)