Let $A(t)$ be the value of a risk$-$free asset at time $t$ and $S(t)$ be the value of a risky asset at time $t.$ Additionally let $A(0)=100,A(1)=102,S(0)=10$ and

$S(1)=\{\begin{array}{ccc}12& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& p\\ 8& \text{w}\text{i}\text{t}\text{h}\text{p}\text{r}\text{o}\text{b}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}& 1-p\end{array}$

where $C(0)t=0K=10C(0)t=0K=11P(0)t=0K=10P(0)t=0K=110.$

$(a)$ Compute, $C(0),$ the value $of$ a call option $at$ time $t=0of$ the strike price $isK=10.$

$(b)$ Compute, $C(0),$ the value $of$ a call option $at$ time $t=0of$ the strike price $isK=11.$

$(c)$ Compute, $P(0),$ the value $of$ a put option $at$ time $t=0of$ the strike price $isK=10.$

$(d)$ Compute, $P(0),$ the value $of$ a put option $at$ time $t=0of$ the strike price $isK=11.$