Ch04HullOFOD10thEdition期权期货及其他衍生品
Chapter 4 Interest Rates,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,1,Types of Rates,Treasury rate LIBOR Fed funds rate Repo rate,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,2,Treasury Rate,Rate on instrument issued by a government in its own currency,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,3,LIBOR,LIBOR is the rate of interest at which a AA bank can borrow money on an unsecured basis from another bank For 5 currencies and 7 maturities ranging it is calculated daily by the from submissions from a number of major banks There have been some suggestions that banks manipulated LIBOR during certain periods. Why would they do this?,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,4,The U.S. Fed Funds Rate,Unsecured interbank overnight rate of interest Allows banks to adjust the cash (i.e., reserves) on deposit with the Federal Reserve at the end of each day The effective fed funds rate is the average rate on brokered transactions The central bank may intervene with its own transactions to raise or lower the rate Similar arrangements in other countries,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,5,Repo Rate,Repurchase agreement is an agreement where a financial institution that owns securities agrees to sell them for X and buy them bank in the future (usually the next day) for a slightly higher price, Y The financial institution obtains a loan. The rate of interest is calculated from the difference between X and Y and is known as the repo rate,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,6,LIBOR swaps,Most common swap is where LIBOR is exchanged for a fixed rate (discussed in Chapter 7) The swap rate where the 3 month LIBOR is exchanged for fixed has the same risk as a series of continually refreshed 3 month loans to AA-rated banks,Fundamentals of Futures and Options Markets, 9th Ed, Ch 4, Copyright © John C. Hull 2016,7,OIS rate,An overnight indexed swap is swap where a fixed rate for a period (e.g. 3 months) is exchanged for the geometric average of overnight rates. For maturities up to one year there is a single exchange For maturities beyond one year there are periodic exchanges, e.g. every quarter The OIS rate is a continually refreshed overnight rate,Fundamentals of Futures and Options Markets, 9th Ed, Ch 4, Copyright © John C. Hull 2016,8,The Risk-Free Rate,The Treasury rate is considered to be artificially low because Banks are not required to keep capital for Treasury instruments Treasury instruments are given favorable tax treatment in the US OIS rates are now used as a proxy for risk-free rates in derivatives valuation,Fundamentals of Futures and Options Markets, 9th Ed, Ch 4, Copyright © John C. Hull 2016,9,Impact of Compounding,When we compound m times per year at rate R an amount A grows to A(1+R/m)m in one year,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,10,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 10th Edition, Copyright © John C. Hull 2017,11,Continuous Compounding (Page 82-83),In the limit as we compound more and more frequently we obtain continuously compounded interest rates $100 grows to $100eRT 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 10th Edition, Copyright © John C. Hull 2017,12,Conversion Formulas (Page 83),Define Rc : continuously compounded rate Rm: same rate with compounding m times per year,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,13,Examples,10% with semiannual compounding is equivalent to 2ln(1.05)=9.758% with continuous compounding 8% with continuous compounding is equivalent to 4(e0.08/4 -1)=8.08% with quarterly compounding Rates used in option pricing are nearly always expressed with continuous compounding,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,14,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 10th Edition, Copyright © John C. Hull 2017,15,Example (Table 4.2, page 84),Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,16,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,Options, Futures, and Other Derivatives 10th Edition, Copyright © John C. Hull 2017,