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Tutorial 8

# Tutorial 8 - 07/08 Semester II THE UNIVERSITY OF HONG KONG...

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07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Tutorial 8 April 11, 2008 1 Review 1.1 Book Value Book value is the present value of the remaining coupon payments and redemption value. B k = ( Fr ) a n - k | i + Cv n - k = v ( Fr + B k +1 ) . ⇒ 4 B k = B k +1 - B k If 4 B k > 0, i.e., B k +1 > B k , then writing up or accumulation of discount. If 4 B k < 0, i.e., B k +1 < B k , then writing down or accumulation of premium. We remark here that |4 B k | is the amount of writing-up/writing-down in the ( k + 1)th coupon. 1.2 Bond Amortization Schedule Every coupon consists of interest and principal adjustment amount (writing-up or writing- down). Fr = I k +1 + P k +1 Interest at time k + 1 is based on the book value at time k , that is, I k +1 = B k i = Fra n - k | + Cv n - k · i = Fr - C ( g - i ) v n - k (1) and the writing-up or writing-down is the remainder of the coupon. P k +1 = Fr - I k +1 = C ( g - i ) v n - k = 4 B k . (2) Therefore, we have the following relationship P k +1 = -4 B k . 2 Exercise 1. A \$1000 par value 3 - year bond with annual coupons of \$50 for the first year, \$70 for the second year and \$90 for the third year is bought to yield a force of interest

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