My understanding: gamma is largest when option is at the money and close to expiration. Now CFAI tells me that gamma is larger when there is more uncertainty about whether the option will expire in or out of the money. If the option is at the money and close to expiration, wouldn’t there be less uncertainty about the option and therefore reflect a large gamma? My head is going to explode.
At the money = more uncertainty…think about it as being balanced on the fence. Deep out and Deep in would be more certain because your well on one side of the fence already. At least that is my thinking.
Maybe… When you’re at the money and near expiry a slight change (up or down) will push you to at the money or out of the money, and you’re likely to expire in one of those, therefore this is consistent with gamma being large when it is at the money.
There is MOST uncertainty when the option is at the money. When the option is well in the money, there is little uncertainty that it will end in the money. Same with if it’s far out of the money. When it’s at the money, you don’t know where it will end up.
I think I have it. I think what screws me up is that in my mind, as you get closer to expiration, one would think that uncertainty would be removed. I like the fence analogy - throw in a timeclock and I see how uncertainty increases.
at the money=high uncertainty = higher value
This doesn’t even make sense.
It should.
If the strike price of a call option is, say, $25 on an option that expires tomorrow, then:
- If the underlying price is $5, there’s no uncertainty: the option’s going to expire out of the money, and delta will be 0.
- If the underlying price is $50, there’s no uncertainty: the option’s going to expire in the money, and delta will be +1.
- If the underlying price is $25, there’s a world of uncertainty: a movement of ±$0.01 is the difference between expiring in the money (with a delta of +1) or out of the money (with a delta of 0).
Right, thank you!
No worries, mate.