The following exhibit shows the relationship between the option price and the underlying stock price, and the relationship between the Gamma and the underlying stock price. (X = 50, r(c) = 0.0488, T = 0.75, σ = 0.35).
A. the underlying price must be very large.
Gamma measures how sensitive the delta is to a change in the underlying.
II. For a call option, delta increases the greater the underlying value.
For a call option, option price increases the greater the underlying value.
Gamma is large when the option is near-the-money (or close to at-the-money).
A. there will be a large change in the option price for a small change in the underlying price.
Gamma measures how sensitive the delta is to a change in the underlying, and delta measures the change rate of the option price for a small change in the underlying price.
I. For a call and a put that have the exact same parameters, their gammas will be equal.
A. I and III
II is incorrect because when the call is deep in-the-money, the call value will be moving one to one with the underlying asset price. Hence, the rate of change, which is gamma, is very low.
III is correct because when a put is deep out-of-the-money, the rate of change in its value, which is gamma, will be very low.
IV is incorrect because the gamma for both a long put and a long call option may take on some negative values.