I just don't understand why ATM gamma increases (ITM/OTM gamma decreases) when vol decreases or time passes. After re-reading the Natenberg section on gamma about 5 million times, I have realized that he just doesn't explain why the above happens (it's him not me ).

The reason that ATM Gamma increases (OTM/ITM Gamma decreases) as time passes is because the uncertainty of whether ATM options will expire ITM/OTM increases, but the uncertainty of ITM/OTM options decreases. You can think of Gamma as the amount of uncertainty of whether the option will expiry ITM/OTM. A decrease in volatility has a similar effect to the decrease in the amount of time to expiry. Hence a decrease in volatility causes ATM Gamma to rise and OTM/ITM Gamma to fall.

Why would uncertainty increase - about whether an ATM expiring ITM/OTM - as time passes? Isn't it just as uncertain 80 days away as it is 5 days away from expiration? As a real-life example, I'm not any more certain today that an ATM GOOG June call will expire ITM/OTM than I am on June 15th, assuming on June 15th the option is ATM. I must be missing something here.

Think of it this way - implied volatility shows how much the underlying is expected to change (non-directionally) per unit of time. So, if you have less time, you going to have less time to effect these changes.

Think of it this way, if an option only has 1 min to expiry and it is right ATM. Even a slight move in the underlying one way or the other could mean that it expires either ITM or OTM, so the uncertainty of what's gonna happen is really great. It's a somewhat extreme example, but I hope you see the point. Here's a different example, say you're watching a basketball game, where one team leads by 20 points and there's only 5 min to the end. Now, what if the lead is only 1 point. Which game would be more uncertain and thus more interesting to watch?

Gamma is the rate of change of delta. On the day of expiration, delta will be either 0 or 100. The further out in time, delta just doesn't move that much, hence lower gamma. Volatility is time. More time, you have a greater chance of being in the money. Look at some simulations. Take an atm leap and change the underlying by .10 or .20 cents. The delta will not budge. Same with vol. Move the vega numbers around, see how the delta changes.

Gamma is the rate of change of delta. If you have a 50 level call and only 10 seconds til expiration and the stock is trading as follows... 49.99... Delta = 100 50.01... Delta = 0 But if that happens with 1 year til expiry, then the delta is unchanged.

Ok finally makes sense. Thanks guys. I've been studying options for about 6 weeks, so I don't know if I'm retarded and not getting it, or if my questions are expected for someone at my stage of learning. Things are clicking I feel, but once in a while a concept comes up that I just can't find an answer to. You guys should charge me for advice