Problem $8.$ Consider a two period case where we have three nodes $N_{0,0},N_{1,0},N_{1,1}.$ If we know the

state price of node $N_{1,0}$ to be $P_{1,1}^e,$ what is the price at time $t=0$ of a security that pays $S_{1,0}$ at $N_{1,0}?$

Denote this price as $P.$

$($a$)$ Compute the value of zero coupon bond, $Z_0^3,$ that pays $1$ dollar at maturity $t=3,$ evaluated at

$t=0.($Round your answer to the fourth decimal place$).$

$($b$)$ Compute the forward price for $t=2$ of a zero coupon bond with face value $100$ and maturity $t=3,$

evaluated at $t=0.($Round your answer to the fourth decimal place$).$

$[$ Hint: $\frac{E_0^Q[\frac{Z_2^3}{B_2}]}{E_0^Q[\frac{1}{B_2}]}]$