Problem 3 (9 points): The price of a risky 10-year zero-coupon bond depends on two parameters: risk-free 10-year spot rate r'(10) (to simplify notations, denote r'(10) by r), and the $1.000.000 Today r=0.05 and s=0.12, so, (1+0.5r+2rs 20' = $483.53 1.61. You want to estimate the change in the bond risk factor 5 and it is given by P(r, s) = _ $1,000,000 100's) _ (1+0.5:.=0.05+2:.=0.05*0.12)20 price using first-order Taylor series approximation, i.e., write the change in price AP as a linear function of the change in interest rate Ar and risk factor As as AP=A*Ar+B*As, where A and B are some constants. a) (5 points) Find A and B. Round to the nearest integer number. $1,000,000 (1+0.5r+2rs)2' by 0.01, by how much the interest rate should change to keep the price unchanged? c) (2 points) Using the Taylor series approximation, if the risk factor increases by 0.01 , how much the interest rate should change to keep the price unchanged? b) (2 points) Using the original price function, P (r, S) = if the risk factor increases