Negative Gamma in Digital and Barrier Options

Summary

The document asks which barrier options can have negative gamma after the questioner finds positive gamma in the knock-in and knock-out options they examined. One response gives a nearby example rather than a barrier structure: a digital call near its strike, with the underlying above the strike and expiration approaching. The reply states that this option has negative gamma in the described setup because added volatility can be unfavorable.

A second response suggests exploring gamma profiles under different barrier features, including discrete monitoring, and notes that an up-and-in option can also exhibit negative gamma. The exchange therefore points to the dependence of option gamma on payoff shape, moneyness, time to expiry, and barrier monitoring. It provides no payoff derivation or sensitivity plots, and the digital-call example alone does not establish the behavior of every barrier contract. Further analysis would need to specify the structure and valuation assumptions.

Key ideas

• Option gamma can be negative for some payoff structures and market conditions.
• The response describes a near-expiry digital call just above its strike as an example of negative gamma.
• Barrier gamma behavior can depend on the barrier direction and monitoring schedule.
• The exchange gives examples but no derivation, so conclusions require analysis of the specific contract.

Tags

# Which barrier option has negative gamma?


# Which barrier option has negative gamma?












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!

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/38149

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.

## Answer by Yian Pap (score 0)

https://quant.stackexchange.com/a/38156

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.)

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.