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Prentice Hall Frank Fabozzi Bond Markets Analysis_1

Tham khảo tài liệu 'prentice hall frank fabozzi bond markets analysis_1', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 0 BHR ER 4RSS Price ffllity s approximation. It should be apparent that the accuracy of the approximation depends on the convexity of the price-yield relationship for the bond. Measuring Convexity Duration modified or dollar attempts to estimate a convex relationship with a straight line the tangent line . Is it possible to specify a mathematical relationship that provides a better approximation to the price change of the bond if the requứed yield changes We can use the first two terms of a Taylor series to approximate the price change as follows5 dP r-dy ịị dy 2 error 4.15 dy 2 dy Dividing both sides of èquation 4.15 by p to get the percentage price change gives us dP _ dPl 1 d2P 1Z_ _A2 error p pdy 2dfp dy P 4-16 Thejirst term on the right-hand side of equation 4.15 is equation 4.14 that is it is the dollar price change based on dollar duration. Thus the first term in equation 4.15 is our approximation of the price change based on deration. In equation 4.16 5A Taylor series discussed in calculus textbooks can be used to approximate a mathematical function. Here the mathematical function to be approximated is the price function. F l CHAPTER 4 Bond Price Volatility 71 the first term on the right-hand side is the approximate percentage change in price based on modified duration. The second term in equations 4.15 and 4.16 includes the second derivative of the price function equation 4.1 . It is the second derivative that is used as a proxy measure to correct for the convexity of the price-yield relationship. Market participants refer to the second derivative of price equation 4.1 as the dollar convexity measure of the bond that is dollar convexity measure 2 4.17 The product of the dollar convexity measure and the square of the change in the required yield indicates the estimated price change due to convexity. That is the approximate change in price due to convexity is dP dollar convexity measure dy 2 4.18 The second derivative divided by price is a measure of .