I'm a bit confused about the relationship between volatility and gamma for ITM and OTM options. I was reading the article below and it states high volatility results in a reduction in gamma for ITM and OTM options (Highlighted in the screenshot). However when I look a the diagram on the same page it appears the opposite is occurring... Gamma of the OTM options is higher when volatility is high compared to same strike options during low volatility (Circled in green on the screenshot). https://www.optionseducation.org/advancedconcepts/gamma As a tie breaker I decided to use the options model on my brokers software (Analyze tab on Thinkorswim). I used the Dec 20 275 Put as a sample position. When I modify the volatility higher or lower by 15% the gamma goes down in both scenarios! (I have attached 3 screenshots detailing this). I know you probably can't speak to the specifics to the broker software but I am curious to know why this is occurring and what is the correct behavior of gamma in OTM options as volatility changes.
You are looking for Zomma. It is a third order greek and a derivative of an options value. But to give the most simple answer, when IV increases gamma will also increase. To know the relationship between IV, Gamma and Delta, you need to know Zomma. And gamma is greatest ATM.
I am not sure how this is possible given The formula for Gamma. The only place a volatility term has a major effect is in the denominator (the numerator effect is significant but hand-waving here it is likely overshadowed by the effect in the denominator). Volatility is scaled with the square root of time (typically sqrt(252)). This term alone will be some number greater than or equal to 1 (sqrt(252) is approximately 16 or so). This is then multiplied by the stock price resulting in number that will be greater than or equal to 1. So, with this, naturally as you increase volatility gamma will go down in a proportional amount when everything else is held constant which is precisely what the OP experienced. I don't have any examples of zomma off the top of my head, but you'd probably expect it to be negative. I am not sure how it could be made reliably positive (im not doubting it could be, im just unsure).
If Zomma is 1 that means gamma will increase by 1 unit for every 1% IV increase. Why would gamma go down if the IV is increasing and increasing the likelyhood that further OTM strikes will be ITM? Think about it.
If Gamma is the rate of change of delta given a movement in price then Zomma is the rate of change of Gamma given a movement in volatility.
Don't need to look. My bet is that the low vol OTM options no longer have optionality(premium) in them. Vol 0, gamma 0, theta 0. Anything else would make no sense. 2 - Gamma increases as vol goes lower. This is not debatable.
From images.google.com: As can be seen from the chart above, all other things equal, higher volatility causes gamma to decline ATM and increase DOTM.
That makes sense So then the answer is both depending on how far OTM you are. The curve flattens so near the money gamma gets lower and far OTM gamma goes higher.
Cool, thanks for the image. Confirms what I said. The extreme wings exhibit no optionality - no extrinsic. Greeks are all move towards zero with the exception of delta which is 100 or 0.