The semi-annually compounded swap rates are as shown in Figure 1 below: Period Swap Rate 0.5 1.800% 1 2.098% 1.5 2.346% 2 2.543% 2.5 2.719% 3 2.884% 3.5 3.038% 4 3.182% 4.5 3.315% 5 3.437% 5.5 3.458% 6 3.551% Figure 1 1. Calculate the term structure of interest rates. 2. An AA-rated firm issues a 3.6% p.a. six-year semi-annual pay bond. Calculate the bonds a. Price, b. Yield, c. Duration, and d. Convexity. 3. If interest rates exhibit volatility of 12% p.a. across the yield curve, calculate the arbitrage-free interest rate grid using the Black-Derman-Toy (BDT) methodology. 4. If the bond is callable at par in two years or anytime thereafter, calculate the bonds a. Price, b. Yield, c. Duration, and d. Convexity using the BDT model. 5. Calculate the price of a four-year 4% interest rate cap starting in two years using the BDT model. 6. Calculate the price of a four-year 4% receive-fixed interest rate swaption starting in two years using the BDT model. 7. Calculate the price of a four-year 4% receive-fixed interest rate swaption starting in two years using Blacks model.