$($a$)$ Calculate the value of this option at time $0.$

Note: The payoff of the compound option at time $t$ is $(C(S_t,K,T-t)-x{)}_{+}$

$($b$)$ If we wanted a call$-$on$-$put option that allows its holder the ability to purchase at time $xKt(C(S_t,K,T-t)-x{)}_{+}t$ a put for a fixed

$x$ premium with strike $K,$ agreeing the strike price $at110$ and leaving all other data unchanged, what would the

price $be?$

Note: The payoff $of$ the compound option $at$ time $tis(C(S_t,K,T-t)-x{)}_{+}.$