Problem 10 (Pricing a callable bond with interest rate trees). Suppose you have the following interest rate tree 6-month spot rate at time 0 is 8% In each 6-month period, the 6-month spot rate can either go up by 25%, or down by 25% The risk-neutral probabilities of the spot rate going up or down are both 50% Assume semi-annual compounding (a) What is the price of a $100 par zero-coupon bond maturing in 18 months? (b) What is the 18 month zero-coupon rate? (c) What is the value of a call option that allows the issuer to redeem the zero-coupon bond in 6 months at $92?