3. The one-period interest rate follows the following binomial tree. Each period is 0.5 year, assuming semi-annual compounding. The risk neutral probability for the rate to go up at any node is 0.5. r(0,1)= 10% r(1,2;u) = 12% r(1,2;d) = 8% r(2,3;uu) = 14% r(2,3;ud) = 10% r(2,3;dd) = 6% (a) Price a callable 1.5-year 10s. The bond can be called back at par (after the coupon payment) at period 1 or 2. (b) Price an interest swap that pays 0.5*face amount*(One-period spot rate - 8%) at period 1 and 2. (c) If the market price for the swap in (2) suggests a -100 bps OAS from the model, what is the market price?