Consider a multi-factor key rate model with key rates being YTM on 2, 5, 10, and 30-year par ponds. Assume also that cur

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Consider a multi-factor key rate model with key rates being YTM
on 2, 5, 10, and 30-year par ponds. Assume also that currently YTM
on 2, 5, 10, and 30-year bonds are 4%, 5%, 6%, and 7% respectively.
Assume all bonds have a $100 face value. Keep at least 6 decimal
digits.
a) (2 points) Find KR012 for 2-year par bond; KR015 for 5-year
par bond; KR0110 for 10-year par bond; and KR0130 for 30-year par
bond
b) (1 point) Find all key rates (KR012, KR015, KR0110, and
KR0130) for a 15-year par bond if YTM for this bond is 6.25%
c) (1 point) Find all key rates (KR012, KR015, KR0110, and
KR0130) for a 20-year par bond if YTM for this bond is 6.5%
d) (1 point) Find all key rates (KR012, KR015, KR0110, and
KR0130) for an 8-year par bond if YTM for this bond is 5.6%
e) (1 point) Find all key rates (KR012, KR015, KR0110, and
KR0130) for a 6-year par bond if YTM for this bond is 5.2%
f) (6 points) You would like to hedge your portfolio that
consists of a thousand 6-year par bonds using 2, 8, 15, and 20
bonds. How would you do it? Please, specify the number of each
bonds (number of bonds for every type of bonds) you should buy or
sell (note you may end up using only some of these bonds). Use the
KR01 rates you found earlier and make sure to write the system of
equations you want to solve before trying to solve it.