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**Unformatted text preview: **Interest Rates Chapter 4 1 Types of Rates Treasury rates LIBOR rates Repo rates 2 Measuring Interest Rates The compounding frequency used for an interest rate is the unit of measurement The difference between quarterly and annual compounding is analogous to the difference between miles and kilometers 3 Continuous Compounding (Page 77) In the limit as we compound more and more frequently we obtain continuously compounded interest rates $100 grows to $ 100e RT when invested at a continuously compounded rate R for time T $100 received at time T discounts to $ 100e- RT at time zero when the continuously compounded discount rate is R 4 Conversion Formulas (Page 77) Define R c : continuously compounded rate R m : same rate with compounding m times per year 5 ( 29 R m R m R m e c m m R m c = + = - ln / 1 1 Zero Rates A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T 6 Example (Table 4.2, page 79) 7 M aturity (years) Zero R ate (% cont com p) 0.5 5.0 1.0 5.8 1.5 6.4 2.0 6.8 Bond Pricing To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate In our example, the theoretical price of a two- year bond providing a 6% coupon semiannually is 8 3 3 3 103 98 39 0 05 0 5 0 058 1 0 0 064 1 5 0 068 2 0 e e e e- - - - + + + = . . . . . ....

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