a) Compute the "optimal call option" prices $\mathbb{E}\left[\left(M_{0}^{T}-Kight)^{+}ight]$estimated by optimally exercising at the maximum value $M_{0}^{T}$ of $\left(S_{t}ight)_{t \in[0, T]}$ before maturity $T$.

b) Compute the "optimal put option" prices $\mathbb{E}\left[\left(K-m_{0}^{T}ight)^{+}ight]$estimated by optimally exercising at the minimum value $m_{0}^{T}$ of $\left(S_{t}ight)_{t \in[0, T]}$ before maturity $T$.