The price of a risky 10-year zero-coupon bond depends on two parameters: risk-free 10-year spot rate...

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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 Today r=0.05 and s=0.12, so, risk factors and it is given by P(r,s) = P(r,s) = = $1,000,000 (1+0.5*0.05+2*0.05*0.12)20 $1,000,000 (1+0.5r+2rs) 20° = $483,531.61. You want to estimate the change in the bond 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. b) (2 points) Using the original price function, P(r,s) = $1,000,000 if the risk factor increases (1+0.5r+2rs) 20' 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? 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 Today r=0.05 and s=0.12, so, risk factors and it is given by P(r,s) = P(r,s) = = $1,000,000 (1+0.5*0.05+2*0.05*0.12)20 $1,000,000 (1+0.5r+2rs) 20° = $483,531.61. You want to estimate the change in the bond 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. b) (2 points) Using the original price function, P(r,s) = $1,000,000 if the risk factor increases (1+0.5r+2rs) 20' 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?

Answer rating: 100% (QA)

To find the constants A and B in the linear function AP A Ar B As we need to differentiate the bond price function Pr s with respect to r and s Pr s 1000000 1 05r 2rs20 a Calculating A and B Taking th... View the full answer