HW3 Solution - MIE375H1F - Financial Engineering - HW2...

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Unformatted text preview: MIE375H1F - Financial Engineering - HW2 Solutions Nick Yeung October 6, 2010 Question 3.10 Assuming Semi-Annual Coupon Payments. F = 100, = 0 . 1, C = 8, m = 2, n = 20: Price = F (1 + m ) n + C 1- 1 (1 + m ) n = 100 (1 + . 1 2 ) 20 + 8 . 1 1- 1 (1 + . 1 2 ) 20 = 87 . 54 Duration = 1 + m - 1 + m + n ( c m- m ) c ( (1 + m ) n- 1 ) = 1 + . 1 2 . 1- 1 + . 1 2 + 20( . 08 2- . 1 2 ) . 08 ( (1 + . 1 2 ) 20- 1 ) = 6 . 84 years Question 3.11 From Sensitivity Analysis of the Price of a bond, we have dP d =- D M P and D M = D 1+ m . For a perpetuitiy, P = A Hence: dP d =- A 2- A 2 =- D M P- A 2 =- D 1 + m A D = 1 + m D M = 1 1 or Duration = 1 + m - 1 + m + n ( c m- m ) c ( (1 + m ) n- 1 ) As n , the second term goes has an indeterminate form. Using LHopitals Rule, we get the second term being 0: lim n 1 + m + n ( c m- m ) c ( (1 + m ) n- 1 ) = lim n d dn 1 + m + n ( c m-...
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This note was uploaded on 04/20/2011 for the course MIE 375 taught by Professor R.kwon during the Spring '11 term at University of Toronto- Toronto.

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HW3 Solution - MIE375H1F - Financial Engineering - HW2...

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