《金融期货与期权》（英文版） Chapter 3 Determination of Forward and Futures Prices

3.1 Determination of Forward and Futures prices Chapter 3 Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.1 Determination of Forward and Futures Prices Chapter 3

3.2 Consumption vs Investment Assets Investment assets are assets held by significant numbers of people purely for investment purposes(EXamples: gold silver) Consumption assets are assets held primarily for consumption(Examples copper, oil) Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.2 Consumption vs Investment Assets • Investment assets are assets held by significant numbers of people purely for investment purposes (Examples: gold, silver) • Consumption assets are assets held primarily for consumption (Examples: copper, oil)

3.3 Short selling (Page 41-42 Short selling involves selling securities you do not own Your broker borrows the securities from another client and sells them in the market in the usual way Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.3 Short Selling (Page 41-42) • Short selling involves selling securities you do not own • Your broker borrows the securities from another client and sells them in the market in the usual way

3.4 Short selling (continued At some stage you must buy the securities back so they can be replaced in the account of the client You must pay dividends and other benefits the owner of the securities receves Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.4 Short Selling (continued) • At some stage you must buy the securities back so they can be replaced in the account of the client • You must pay dividends and other benefits the owner of the securities receives

3.5 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, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.5 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

3.6 Continuous Compounding (Page 43) In the limit as we compound more and more frequently we obtain continuously compounded interest rates $100 grows to $100eR/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, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.6 Continuous Compounding (Page 43) • 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

3.7 Conversion formulas (Page 44) Define R: continuously compounded rate Rm: same rate with compounding m times per year R R=mIn 1+ R=ml e Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.7 Conversion Formulas (Page 44) Define Rc : continuously compounded rate Rm: same rate with compounding m times per year ( ) R m R m R m e c m m Rc m = +       = − ln / 1 1

3.8 Notation o: spot price today Fo: Futures or forward price today T. Time until delivery date r. Risk-free interest rate for maturity T Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.8 Notation S0 : Spot price today F0 : Futures or forward price today T: Time until delivery date r: Risk-free interest rate for maturity T

3.9 Gold Example(From Chapter 1) For gold F0=S0+r)7 (assuming no storage costs) If r is compounded continuously instead of annually Fo= soe Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.9 Gold Example (From Chapter 1) • For gold F0 = S0 (1 + r ) T (assuming no storage costs) • If r is compounded continuously instead of annually F0 = S0 e rT

3.10 Extension of the Gold Example (Page 46, equation 3.5) For any investment asset that provides no income and has no storage costs Fo= soer/ Options Futures, and other Derivatives, 5th edition C 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 3.10 Extension of the Gold Example (Page 46, equation 3.5) • For any investment asset that provides no income and has no storage costs F0 = S0 e rT