期权、期货和衍生证券（Options，FuturesandOtherDerivatives）Chapter 4 Interest Rates

Chapter 4 Interest rates Options, Futures, and Other Derivatives 8th Edition Copyright o John C Hull 2012

Chapter 4 Interest Rates Options, Futures, and Other Derivatives 8th Edition, Copyright © John C. Hull 2012 1

Types ofrates Treasury rates e LIBOR rates Repo rates Options, Futures, and other Derivatives 8th Edition Copyright O John C Hull 2012

Types of Rates Treasury rates LIBOR rates Repo rates Options, Futures, and Other Derivatives 8th Edition, Copyright © John C. Hull 2012 2

Treasury Rates o Rates on instruments issued by a government in its own currency Options, Futures, and other Derivatives 8th Edition Copyright O John C Hull 2012 3

Treasury Rates Rates on instruments issued by a government in its own currency Options, Futures, and Other Derivatives 8th Edition, Copyright © John C. Hull 2012 3

lBOR and BD e liBOR is the rate of interest at which a bank is prepared to deposit money with another bank. (The second bank must typically have a aa rating) LIBOR is compiled once a day by the british Bankers association on all major currencies for maturities up to 12 months o LIBid is the rate which a aa bank is prepared to pay on deposits from anther bank Options, Futures, and other Derivatives 8th Edition Copyright O John C Hull 2012

LIBOR and LIBID LIBOR is the rate of interest at which a bank is prepared to deposit money with another bank. (The second bank must typically have a AA rating) LIBOR is compiled once a day by the British Bankers Association on all major currencies for maturities up to 12 months LIBID is the rate which a AA bank is prepared to pay on deposits from anther bank Options, Futures, and Other Derivatives 8th Edition, Copyright © John C. Hull 2012 4

R epo rates Repurchase agreement is an agreement Where a financial institution that owns securities agrees to sell them today for X and buy them bank in the future for a slightly higher price, Y e The financial institution obtains a loan e 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 8th Edition Copyright O John C Hull 2012 5

Repo Rates Repurchase agreement is an agreement where a financial institution that owns securities agrees to sell them today for X and buy them bank in the future 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 8th Edition, Copyright © John C. Hull 2012 5

The risk-free rate The short-term risk-free rate traditionally used by derivatives practitioners is LIBOR o The Treasury rate is considered to be artificially low for a number of reasons (See Business Snapshot 4.1) o As will be explained in later chapters a Eurodollar futures and swaps are used to extend the LIBOR yield curve beyond one year s The overnight indexed swap rate is increasingly being used instead of libor as the risk-free rate Options, Futures, and other Derivatives 8th Edition Copyright O John C Hull 2012

The Risk-Free Rate The short-term risk-free rate traditionally used by derivatives practitioners is LIBOR The Treasury rate is considered to be artificially low for a number of reasons (See Business Snapshot 4.1) As will be explained in later chapters: Eurodollar futures and swaps are used to extend the LIBOR yield curve beyond one year The overnight indexed swap rate is increasingly being used instead of LIBOR as the risk-free rate Options, Futures, and Other Derivatives 8th Edition, Copyright © John C. Hull 2012 6

Measuring Interest Rates o 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 8th Edition Copyright o John C. Hull 2012 7

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 8th Edition, Copyright © John C. Hull 2012 7

Impact of compounding When we compound m times per year at rate r an amount a grows to A(1+ r/mym in one year Compounding freguency Value of $100 in one year at 10%0 Annual(m=1) 110.00 Semiannual(m=2) 11025 Quarterly(m=4) 11038 Mont thly(m=12) 0.47 Weekly(m=52) 11051 Daily(m=365) 11052 Options, Futures, and other Derivatives 8th Edition Copyright o John C. Hull 2012

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 8th Edition, Copyright © John C. Hull 2012 8 Compounding frequency Value of $100 in one year at 10% Annual (m=1) 110.00 Semiannual (m=2) 110.25 Quarterly (m=4) 110.38 Monthly (m=12) 110.47 Weekly (m=52) 110.51 Daily (m=365) 110.52

Continuous Compounding Page 79 e In the limit as we compound more and more frequently we obtain continuously compounded interest rates o $100 grows to $100ert when invested at a continuously compounded rate R for time T e $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 8th Edition Copyright o John C. Hull 2012 9

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 8th Edition, Copyright © John C. Hull 2012 9

Conversion Formulas (Page 79) Define Rc: continuously compounded rate Rm: same rate with compounding m times per ear R R=mIn 1+m R/m Options, Futures, and other Derivatives 8th Edition Copyright o John C. Hull 2012 10

Conversion Formulas (Page 79) Define Rc : continuously compounded rate Rm: same rate with compounding m times per year Options, Futures, and Other Derivatives 8th Edition, Copyright © John C. Hull 2012 10 ( ) R m R m R m e c m m Rc m = +       = − ln / 1 1