"Call and put options on the same underlying asset with the same exercise price and time to maturity will have equal gammas. Long positions in calls and puts have positive gammas."
What this says (which is a bit strange but I'm not too sure of that) is that if the stock goes up by $1, then both the call and the put will change by the same amount (not percentage either)! That's what gamma says: change in delta/change in stock.
If stock price is $10, strike =$20, call price = $0.10, put price =$10....are they saying that if stock goes up to $11, both the call and the put will change by same amount? The put has just dropped $1...so that can't be true.
> Long positions in calls and puts have positive gammas."
This is fine because the deltas move in the same direction as the underlying price.
are they basically just saying that the rate of change of delta with a given change in stock price is the same for both calls and puts (with puts being the opposite direction)?
i guess this makes sense since the graphs of the two (pg 84 schweser book 5) look the same.