Can gamma of an option be greater than 1?

[[email protected]]

Hi,

I am beating my head around this. I have seen certain atm options whenre Gamma is greater than 1? I felt if delta is bounded between 0 and 1, so should gamma?

 

[David Harper CFA FRM]

Hi @[email protected] Gamma theoretically can exceed one, but i think the intuition is much more difficult than delta. Option delta bound by [0,1] is intuitive--or at least, can be intuitive; e.g., a deeply in the money option cannot increase in value by more than the stock price change. But gamma is the second partial derivative; as the rate of change of delta, gamma can be viewed as the slope of delta's tangent line, so I'm not sure why we would expect it to be bound by 1.0 if we can imagine a steep delta. If you want to experiment, here is a greeks page from our learning XLS https://www.dropbox.com/s/u86nxrd6jylunf3/0815-gamma.xlsx?dl=0

... screenshot below. This is for a 1-year ATM option. These are somewhat "typical" Gammas in the sense that they are 0.0x or 0.00x or even 0.000x. Due to the units implied by the 2nd derivative, it's not unusual to see gamma - 0.0026. In fact, gamma of 0.3 would look strangely high to me. However, if you decrease the term of this ATM, you can dial up the gamma. I hope that's helpful!