In the Black$-$Scholes framework, computeExplain, intuitively, why the delta$-$hedging of European ATM options near expiry is diffi$-$

cult. Then, using the Black$-$Scholes framework, discover $($analytically$)$ what happens to the

gamma of a European ATM option as the time to expiry goes to zero.

$\frac{\text{d}\text{e}\text{l}\text{C}}{\text{d}\text{e}\text{l}\text{K}}$ and $\frac{de{l}^{2}C}{del{K}^2}.$

Then, use the Put$-$Call parity to compute $\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{K}}$ and $\frac{de{l}^{2}P}{del{K}^2}.$