Problem 4 (8 points): Consider the Key Rates model with keys equal to 2, 5, 10, and 30 year forward rates. Assume that currently all forward interest rates are equal to 6%. The KR01s for 5, 7, 10, 16, and 30-year zero-coupon bonds are given in the table below. All bonds have $100 face values. Keep at least 6 decimal digits for all calculations!!!

Bond KR012 KR015 KR0110 KR0130 5-year 0 0.036121 0 0 7-year 0 0.026958 0.017972 0 10-year 0 0 0.053755 0 16-year 0 0 0.042227 0.018097 30-year 0 0 0 0.049437

a) (1.5 points) Find KR01s of a 2-year zero-coupon bond b) (2 points) Find KR01s of a 14-year zero-coupon bond c) (2 points) Using 2, 5, 10, and 30-year zero-coupon bonds, find the optimal hedging portfolio to hedge a portfolio that consists of 1,000 of 7-year zero-coupon bonds d) (2.5 points) Using 2, 5, 16, and 30-year zero-coupon bonds, find the optimal hedging portfolio to hedge a portfolio that consists of 1,000 of 7-year zero-coupon bonds

Problem 4 (8 points): Consider the Key Rates model with keys equal to 2, 5, 10, and 30 year forward rates. Assume that currently all forward interest rates are equal to 6%. The KROIs for 5, 7, 10, 16, and 30-year zero-coupon bonds are given in the table below. All bonds have $100 face values. Keep at least 6 decimal digits for all calculations!!! Bond KR012 KRO15 KRO1 10 KRO130 5-year 0 0.036121 0 0 7-year 0 0.026958 0.017972 0 10-year 0 0 0.053755 0 16-year 0 0.042227 0.018097 oo 30-year O 0 0.049437 a) (1.5 points) Find KROIs of a 2-year zero-coupon bond b) (2 points) Find KROIs of a 14-year zero-coupon bond c) (2 points) Using 2, 5, 10, and 30-year zero-coupon bonds, find the optimal hedging portfolio to hedge a portfolio that consists of 1,000 of 7-year zero-coupon bonds d) (2.5 points) Using 2, 5, 16, and 30-year zero-coupon bonds, find the optimal hedging portfolio to hedge a portfolio that consists of 1,000 of 7-year zero-coupon bonds