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Knud45
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Posts: 1
Joined: April 16th, 2018, 8:56 pm

Option gamma greater than 1 intuition

April 16th, 2018, 9:14 pm

Hello,

Mathematically, I understand that a bounded function can have an unbounded derivative, so that gamma can be greater than 1. But how would an option trader intuitively think about this and hedge his delta and gamma? Or is this modelled away so that gamma never exceeds 1?
 
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bearish
Posts: 2961
Joined: February 3rd, 2011, 2:19 pm

Re: Option gamma greater than 1 intuition

April 16th, 2018, 11:10 pm

I don't really see 1 as being a magic number when it comes to gamma. For delta, yeah - traditional put and call deltas generally stay in the (-1,1) range, at least if suitably defined. For standard options, gamma goes to infinity as time to maturity goes to zero and you are at the money. No way to model that away, nor a way to hedge it (aside from outright taking the opposite side of the option trade). The good news is that it doesn't happen too often, although if you search for "pinning risk options" it appears to be more common than Black-Scholes would suggest. 
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