Question $4(25$ marks$)$

Consider the interest rate tree table below. You estimated the risk neutral probability to move up

the tree to be $p=\frac{1}{2}.$

a$)(5$ marks$)$ Compute the value of the two zero coupon bonds $($assume $$100$ face value$)$

maturing at

period $i=1$ and at $i=2.$

b$)(5$ marks$)$ Compute the continuously compounded yields $($yield to maturity$)$ for both

bonds.

c$)(8$ marks$)$ Compute the value of an asset with payoff

Asset payoff $i=1=100$max$(r_1-4\%,0)$

d$)(7$ marks$)$ Set up the replicating portfolio that uses the bond prices determined in Part $($a$),$

that can replicate the asset's payoff. Check that this portfolio in fact replicates the asset's

payoffs. Consider the interest rate tree table below. You estimated the risk neutral probability to move up

the tree to be p $=(1)/(2).$