4.1 Interest Rates and duration(久期) Chapter 4 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.1 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Interest Rates and Duration(久期) Chapter 4
4.2 Types of rates Treasury rates(国债利率)- regarded as risk-free rates LIBOR rates(London Interbank Offer ate)(伦敦银行同业放款利率) generally higher than Treasury zero rates Repo rates(回购利率) -slightly higher than the Treasury rates Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.2 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Types of Rates • Treasury rates（国债利率）—regarded as risk-free rates • LIBOR rates (London Interbank Offer rate) (伦敦银行同业放款利率)–generally higher than Treasury zero rates • Repo rates (回购利率)—slightly higher than the Treasury rates
4.3 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. In practice. it is usually called zero-coupon interest rate(零息票利率) Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.3 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 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. In practice, it is usually called zero-coupon interest rate (零息票利率)
4.4 Example (Table 4.1, page 89) Maturity Zero Rate (years)(% cont comp) 0.5 5.0 1.0 58 1.5 64 2.0 68 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.4 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Example (Table 4.1, page 89) Maturity (years) Zero Rate (% cont comp) 0.5 5.0 1.0 5.8 1.5 6.4 2.0 6.8
4.5 Bond pricing To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate In our example (page 89), the theoretical price of a two-year bond with a principal of $100 providing a 6% coupon semiannually is Be 0.05×0.5 +3e005800+3e-04.5 +103e 0.068×2.0 $98.39 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
4.5 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Bond Pricing • To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate • In our example (page 89), the theoretical price of a two-year bond with a principal of $100 providing a 6% coupon semiannually is 103 $98.39 3 3 3 0.068 2.0 0.05 0.5 0.058 1.0 0.064 1.5 + = + + − − − − e e e e