Question #11

A. 97.17

B. 98.29

C. 99.01. Explanation The callable bond price tree is as follows: 100.00 A → 98.67 98.29 100.00 99.00 100.00 As an example, the price at node A is obtained as follows: PriceA = min[(prob × (Pup + (coupon / 2)) + prob × (Pdown + (coupon/2)) / (1 + (rate / 2)), call price] = min[(0.5 × (100 + 2.5) + 0.5 × (100 + 2.5)) / (1 + (0.0776 / 2)), 99} = 98.67. The bond values at the other nodes are obtained in the same way. (Module 27.2, LOS 27.f) Kate Inka is a new hire for Maya Incorporated, a fixed income fund manager. On her first week on the job, she is asked to prepare a presentation on valuation and analysis of bonds with embedded options. Inka starts her presentation with the following three statements: Statement 1: "In times of increased expectations of interest rate volatility the value of callable bonds will fall." Statement 2: "When trying to analyze the return for credit and liquidity risk on a corporate callable bond relative to a government bond, the Z-spread must be calculated. The Z-spread can be viewed as the constant spread added to treasury spot rates such that the present value of the callable bonds coupons and principal equate to its market price." Statement 3: "When analyzing the interest rate risk of a callable bond it is worth keeping in mind that its effective convexity will be less than or equal to the equivalent option free bond." Inka is analyzing a three-year, 6% annual coupon, $100 par callable bond. The bond has a European call feature allowing it to be called at 101% of par in two years' time. Inka uses a binomial tree assuming interest rate volatility of 20% as shown in Exhibit 1. Exhibit 1: Binomial Lattice T0 T1 T2 6.34% 5.45% 3% ????? 3.65%