Consider the interest rate tree table below. You estimated the risk neutral probability to move up the tree to be p = 12.

Interest rate tree on January 8, 2002

Periodi=0 i=1 Time inyearst=0 t=0.5

r0=4%

r1,u=6%

r1,d=3%

with risk neutral probability p = 1/2

with risk neutral probability 1-p = 1/2

1. a)Compute the value of the two zero coupon bonds (assume $100 face value) maturing at period i = 1 and at i =2.
2. b)Compute the continuously compounded yields (yield to maturity) for both bonds.
3. c)Compute the value of an option with payoff
4. Option payoffi=1= 100 x max (r1- 4%, 0)
5. d)Set up the replicating portfolio that uses the bond prices determined in Part (a), that is able to replicate the option's payoff. Check that this portfolio in fact replicates the option.