1. The yield reported by the website are reported as yearly (and corresponding to annual compounding). Please convert the data into continuous compounding. 2. Lets consider the July 20, 2020. Please derive the prices of the corresponding zerocoupon bonds, with a face value of $1,000. Double check that you can compute the numbers also with a scientific calculator. 3. Lets consider the maturities between 1 and 10 years, on July 1, 2020. There are some missing maturities: 4, 6, 8 and 9. There are many ways to interpolate between these maturities, but we are going to proceed with a linear interpolation. Lets say that you know the rates corresponding to maturity (t) and (t + j), and you are trying to compute the rate for maturity (t + i), where i has to be lower than j, then rt+i = rt + (rt+j rt) (t + i) t (t + j) t so for example, say that you wanted to get the 4 year maturity (t+1), then you would interpolate between the 3rd (t), and the 5th (t+j): r4 = r3 + (r5 r3) 4 3 5 3 4. Once you have calculated the rates for all 10 maturities, compute the price of a 10-year coupon bond with face value of $1,000 and annual coupons of 5%. Compute also the yield to maturity, the duration and the convexity. 1 5. Price now the same 10 year bond everyday of the month. You will also compute yield to maturity, duration and convexity. You should have in the end a price, ytm, duration and convexity for each day of the month. We are going to forget about the fact that this is not the same bond because we are keeping maturity constant at 10 years. So technically speaking the bonds are all different because their due-dates are all different (i.e., the bond you price on July 1, 2020 is due on June 30, 2030 while the bond you price on July 23 is due on July 22 of 2030). 6. Now we are going to check the volatility estimates implied by duration and convexity against actual changes in prices. On each day, from July 1 to July 31, compute the bond volatility (i.e., the expected change in price for a change in interest rates), corresponding to the actual change in yield-to-maturity from one day to the next. So say that you wanted to compute the expected change in price from July 14 to July 15: in the formula for the expected bond price change, you would use the duration and convexity computed on July 14 and as y the actual change in the yield-to-maturity from July 14 to July 15. Please plot, the expected change (remember there are two of those, one based on duration and one based on duration and convexity) against the actual change (in the example above, the percentage difference in the bond price from July 14 to July 15. What do you see? Are the points exactly on the 45 degree line?

Use Treasury Data for question