Chapter 9 Examples.pdf

Chapter 9 Examples.pdf - Lecture 36 Chapter 9 Examples...

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Lecture 36: Chapter 9 Examples ACTSC 231 — Introductory Financial Mathematics Spring 2019 Chapter 9 Examples 1 / 8

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Duration and Convexity Summary Duration Macaulay: D ( i , ) = - dP / d δ P ( i ) Modified: D ( i , m ) = - dP / di ( m ) P ( i ) Convexity Macaulay: C ( i , ) = d 2 P / d δ 2 P ( i ) Modified: C ( i , m ) = d 2 P / di ( m ) 2 P ( i ) The Simple Case: Annual CFs and Annual Effective rate i D ( i , ) = t C t v t P ( i ) D ( i , 1 ) = t C t v t + 1 P ( i ) = vD ( i , ) C ( i , ) = t 2 C t v t P ( i ) C ( i , 1 ) = t ( t + 1 ) C t v t + 2 P ( i ) = C ( i , )+ D ( i , ) ( 1 + i ) 2 Chapter 9 Examples 2 / 8
Duration and Convexity Summary CFs More Frequent than Annual: Consider m payments per year and nominal rate i ( m ) . If we use j = i ( m ) m and do everything in terms of interest/payment periods: D ( j , ) = t C t ( 1 + j ) - t P ( j ) for t in interest periods Then, would convert to years by dividing by m . C ( j , ) = t 2 C t ( 1 + j ) - t P ( j ) for t in interest periods Then, would convert to years by dividing by m 2 . Chapter 9 Examples 3 / 8

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Duration and Convexity Summary CFs More Frequent than Annual: Consider m payments per year
• Fall '19
• Bond duration, Zero-coupon bond, t Ct v t, Convexity Summary

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