2) Let $p(t, s)=C(t, s, K, r, \sigma, T)$ be the price function of the European call option. Namely $$ p(t, s)=s N\left(d_{1}(t, s) ight)-e^{-r(T-t)} K N\left(d_{2}(t, s) ight) $$ where $$ \begin{aligned} & d_{1}(t, s)=\frac{1}{\sigma \sqrt{T-t}}\left\{\ln \left(\frac{s}{K} ight) \left(r \frac{1}{2} \sigma^{2} ight)(T-t) ight\} \\ & d_{2}(t, s)=d_{1}(t, s)-\sigma \sqrt{T-t} \end{aligned} $$ Compute $\frac{\partial p}{\partial \sigma}$ to check that $\frac{\partial p}{\partial \sigma}(t, s)>0$, for all $(t, s) \in[0, \infty) \times[0, \infty)$