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Mathematics and Statistics for Financial Risk Management by Michael B. Miller

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Answers

CHAPTER 1

1. a. y = 5

a. y = ln(1) – ln(e) = 0 – 1 = –1

b. y = ln(10) + ln(e) = ln(10) + 1 = 3.3026

2. Annual rate = 5.12%; semiannual rate = 5.05%; continuous rate = 4.99%.

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8. ln(ln(10)) = 0.8340.

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11. The bond will pay 10 coupons of $2, starting in a year's time. In addition, the notional value of the bond will be returned with the final coupon payment in 10 years. The present value, V, is then:

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We start by evaluating the summation, using a discount factor of δ = 1/1.05 ≈ 0.95:

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Inserting this result into the initial equation we obtain our final result: ...

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