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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!

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  • $\begingroup$ You most probably did not generate the Gamma profile for a wide enough range of spot levels see emanuelderman.com/media/insoutbarriers1.pdf (pdf pp.9-12, document pp.63-66). It is particularly clear that for the up-and-out call and down-and-out put the Gamma becomes negative close to the barrier. $\endgroup$ – Quantuple Feb 9 '18 at 8:03
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How about a digital call option struck at usd 100 expiring tomorrow with today's stock price at usd101. This has negative gamma, since any volatility is potentially bad.

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As Quantuple said, you haven't looked too carefully:) For example:

enter image description here

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.)

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