Any way to solve this in excel or show calculations?

2. Risk Measurement, Risk Management, Duration - 30 points Dollar duration and convexity are used to characterize and to control the riskiness of fixed income securities. However, several examples were presented in the lectures to exhibit the limitations of these measures. One way we might attempt to improve these measures is by making them more robust to non-uniform shifts in the term structure. For a fixed income security that makes annual payments over four years, P(R1, R2, R3, R.) = K e-t-Re, t=1 1 -ART. where R4 is short for the spot rate R(0,t), we can perform a Taylor expansion to arrive at an expression relating the change in price of the bond to changes in the zero coupon term structure by (1) aR Consider an 8% coupon bond maturing in four years with a face value of $1000. You are given the following information about the current state of the continuously compounded zero yield curve, and four possible scenarios that might occur instantaneously. Yield Yr. 1 Yield Yr. 2 Yield Yr. 3 Yield Yr. 4 Current 6.25% 7.00% 7.50% 8.00% Scenario 1 7.00% 7.75% 8.25% 8.75% Scenario 2 6.25% 7.50% 8.00% 8.50% Scenario 3 5.00% 6.00% 7.50% 7.00% Scenario 4 7.00% 6.50% 6.25% 6.00% Scenario 5 7.25% 7.25% 7.25% 8.20% For each scenario, compute the following: (a) The actual price change of this bond. (b) The price change of this bond as approximated by the duration method As. This is by assuming that the bond price depends on a single risk factor, the yield-to- maturity. Comment on your findings. (c) The price change of this bond as approximated by the first-order changes in the underlying five spot rates. 2. Risk Measurement, Risk Management, Duration - 30 points Dollar duration and convexity are used to characterize and to control the riskiness of fixed income securities. However, several examples were presented in the lectures to exhibit the limitations of these measures. One way we might attempt to improve these measures is by making them more robust to non-uniform shifts in the term structure. For a fixed income security that makes annual payments over four years, P(R1, R2, R3, R.) = K e-t-Re, t=1 1 -ART. where R4 is short for the spot rate R(0,t), we can perform a Taylor expansion to arrive at an expression relating the change in price of the bond to changes in the zero coupon term structure by (1) aR Consider an 8% coupon bond maturing in four years with a face value of $1000. You are given the following information about the current state of the continuously compounded zero yield curve, and four possible scenarios that might occur instantaneously. Yield Yr. 1 Yield Yr. 2 Yield Yr. 3 Yield Yr. 4 Current 6.25% 7.00% 7.50% 8.00% Scenario 1 7.00% 7.75% 8.25% 8.75% Scenario 2 6.25% 7.50% 8.00% 8.50% Scenario 3 5.00% 6.00% 7.50% 7.00% Scenario 4 7.00% 6.50% 6.25% 6.00% Scenario 5 7.25% 7.25% 7.25% 8.20% For each scenario, compute the following: (a) The actual price change of this bond. (b) The price change of this bond as approximated by the duration method As. This is by assuming that the bond price depends on a single risk factor, the yield-to- maturity. Comment on your findings. (c) The price change of this bond as approximated by the first-order changes in the underlying five spot rates