Question
please help
A bank owns a portfolio of bonds whose value P(r) depends on the interest rate r (measured in percent; for example r = 5, means a 5% interest rate). The bank's quantitative analyst determines that P(5) = 140000 ,dp/d|r-5 = - 35000, d2/dr2|r = 5 = 45000 . In finance, this second derivative is called bond convexity. Find the second Taylor polynomial of P(r) centered at r = 5 and use it to estimate the value of the portfolio if the interest rate moves to r = 5.5%. (Use decimal notation. Give your answer to two decimal places.) If the interest rate moves to r = 5.5%, the value of the portfolio would be help (fractions).
Explanation / Answer
P = P(5) + dP/dr *(r-5) + (d^2P/dr^2)*(r-5)^2/2
P(5.5) = 140000 - 35000*0.5 + 45000*0.5^2/2 =128125
