Question 4 Consider the interest rate tree table below. You estimated the risk neutral probability to move up the tree to be p = . Interest rate tree on January 8, 2002 Period i = 0 i = 1 Time in years t = 0 t = 0.5 r1,u=6% with risk neutral probability p = 1/2 r0=4% r1,d=3% with risk neutral probability 1-p = 1/2

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