To clarify it’s actually the second derivative of the options price w.r.t the underlying price, whereas “delta” is the first derivative of the same. (So gamma is the rate of change of delay w.r.t the options price since delta is not constant)
Gamma is the rate of change of delta w.r.t the underlying price. For example OTM calls have a delta close to 0. As the underlying price increases the delta will increase. When the underlying price reaches the call strike price (ATM) the delta will typically be 0.5. As the underlying price continues to rise and the call becomes deep ITM the delta will approach 1.0.
