Ch04HullOFOD6thEd - Options, Futures, and Other Derivatives...

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Unformatted text preview: Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.1 Interest Rates Chapter 4 Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.2 Types of Rates Treasury rates LIBOR rates Repo rates Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.3 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 Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.4 Continuous Compounding (Page 79) 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 Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.5 Conversion Formulas (Page 79) Define R c : continuously compounded rate R m : same rate with compounding m times per year ( 29 R m R m R m e c m m R m c = + = - ln / 1 1 Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.6 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 Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.7 Example (Table 4.2, page 81) M aturity (years) Zero Rate (% cont com p) 0.5 5.0 1.0 5.8 1.5 6.4 2.0 6.8 Options, Futures, and Other Derivatives 6 th Edition, Copyright John C. Hull 2005 4.8 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 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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Ch04HullOFOD6thEd - Options, Futures, and Other Derivatives...

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