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Unformatted text preview: Problem Set 8: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. We need to find the worst case to the investor for calculating the price of the callable bond. Let T denotes the number of coupons up to a call date. Then the possible range of T is 20 , 21 , , 30. To have the effective semi-annual yield rate of j , the price of the bond for a redemption date of T is P = C + C ( g- j ) a T e j , T = 20 , 21 , , 30 . The modified coupon rate ( g ) is 8%/2 = 4% since the redemption amount ( C ) is equal to the face value ( F ). Depending on the yield (effective interest rate) for the coupon period, the worst case is determined. (a) Given j = 6% / 2 = 3%, g > j thus the worst case to the investor is the earliest redemption with T = 20, i.e. the borrower (issuer) calls a bond at the end of year 10. Then, the callable bond price is P = 1 , 000 + 1000(4%- 3%)a 20 e 3% = 1148 . 775 . (b) Given j = 10% / 2 = 5%, g < j which is the opposite situation to (a). So, the worst case to the investor is the latest redemption with...
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- Fall '09