$($iii$)$ Explain why the market price for the put might differ from that calculated in $($ii$).1$

Q$5)$

$5-1$ You are given the following stock price process:

$S(t)=2(2(t){)}^2+4t^2-2t+5$

where $Z(t),$ is Browniam motion.

a$)$ Is $S(t)$ a Martingale with respect to $Z(t)?.(05$ marks$)$

$5-2$ If you are given the following stock price process:

$S(t)=e^{aZ(t)-4},$

where $Z(t),$ is Bromnian motion.

b$)$ Find a such that $S(t)$ is a Martingale with respect to $Z(t)?.(10$ marks$)$