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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, λ = 0 . 1, C = 8, m = 2, n = 20: Price = F (1 + λ m ) n + C λ 1- 1 (1 + λ m ) n = 100 (1 + . 1 2 ) 20 + 8 . 1 1- 1 (1 + . 1 2 ) 20 = 87 . 54 Duration = 1 + λ m λ- 1 + λ m + n ( c m- λ m ) c ( (1 + λ 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 dλ =- D M P and D M = D 1+ λ m . For a perpetuitiy, P = A λ Hence: dP dλ =- A λ 2- A λ 2 =- D M P- A λ 2 =- D 1 + λ m · A λ D = 1 + λ m λ D M = 1 λ 1 or Duration = 1 + λ m λ- 1 + λ m + n ( c m- λ m ) c ( (1 + λ m ) n- 1 ) As n → ∞ , the second term goes has an indeterminate ∞ ∞ form. Using L’Hopital’s Rule, we get the second term being 0: lim n →∞ 1 + λ m + n ( c m- λ m ) c ( (1 + λ m ) n- 1 ) = lim n →∞ d dn 1 + λ m + n ( c m- λ...
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HW3 Solution - MIE375H1F Financial Engineering HW2...

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