ch03期權期貨與衍生證券（第五版）

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

2、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 consum

3、ption (Examples: copper, oil),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 ownYour broker borrow

4、s the securities from another client and sells them in the market in the usual way,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.4,,,Short Selling(continued),At some stage you must

5、buy the securities back so they can be replaced in the account of the clientYou must pay dividends and other benefits the owner of the securities receives,Options, Futures, and Other Derivatives, 5th edition © 2002

6、 by John C. Hull,3.5,,,Measuring Interest Rates,The compounding frequency used for an interest rate is the unit of measurementThe difference between quarterly and annual compounding is analogous to the difference betwe

7、en miles and kilometers,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

8、 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

9、,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.7,,,Conversion Formulas(Page 44),DefineRc : continuously compounded rateRm: same rate with compounding m times per year,Options, Fut

10、ures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.8,Notation,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.9,,,Gold Example (From Chapter 1),For gold

11、 F0 = S0(1 + r )T (assuming no storage costs)If r is compounded continuously instead of annually F0 = S0erT,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.10,,,Exten

12、sion of the Gold Example(Page 46, equation 3.5),For any investment asset that provides no income and has no storage costs F0 = S0erT,Options, Futures, and Other Derivatives, 5th edition © 2002 by

13、John C. Hull,3.11,,,When an Investment Asset Provides a Known Dollar Income (page 48, equation 3.6),F0 = (S0 – I )erT where I is the present value of the income,Options, Futures, and Other Derivatives, 5th edition &#

14、169; 2002 by John C. Hull,3.12,,,When an Investment Asset Provides a Known Yield (Page 49, equation 3.7),F0 = S0 e(r–q )T where q is the average yield during the life of the contract (expressed with continuous

15、 compounding),Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.13,,,Valuing a Forward ContractPage 50,Suppose that K is delivery price in a forward contract F0 is forward pr

16、ice that would apply to the contract todayThe value of a long forward contract, ?, is ? = (F0 – K )e–rT Similarly, the value of a short forward contract is (K – F0 )e–rT,Options, Futures, and

17、Other Derivatives, 5th edition © 2002 by John C. Hull,3.14,,,Forward vs Futures Prices,Forward and futures prices are usually assumed to be the same. When interest rates are uncertain they are, in theory, slightly

18、different:A strong positive correlation between interest rates and the asset price implies the futures price is slightly higher than the forward priceA strong negative correlation implies the reverse,Options, Futures,

19、and Other Derivatives, 5th edition © 2002 by John C. Hull,3.15,,,Stock Index (Page 52),Can be viewed as an investment asset paying a dividend yieldThe futures price and spot price relationship is therefore

20、 F0 = S0 e(r–q )T where q is the dividend yield on the portfolio represented by the index,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.16,,,Stock Index(continue

21、d),For the formula to be true it is important that the index represent an investment assetIn other words, changes in the index must correspond to changes in the value of a tradable portfolioThe Nikkei index viewed as a

22、 dollar number does not represent an investment asset,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.17,Index Arbitrage,When F0>S0e(r-q)T an arbitrageur buys the stocks underlying

23、the index and sells futuresWhen F0<S0e(r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.18,,,In

24、dex Arbitrage(continued),Index arbitrage involves simultaneous trades in futures and many different stocks Very often a computer is used to generate the trades Occasionally (e.g., on Black Monday) simultaneous trades

25、are not possible and the theoretical no-arbitrage relationship between F0 and S0 does not hold,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.19,,,A foreign currency is analogous to a

26、 security providing a dividend yieldThe continuous dividend yield is the foreign risk-free interest rateIt follows that if rf is the foreign risk-free interest rate,Futures and Forwards on Currencies (Page 55-58),Opti

27、ons, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.20,,,Futures on Consumption Assets(Page 59),F0 ? S0 e(r+u )T where u is the storage cost per unit time as a percent of the asset value.

28、 Alternatively, F0 ? (S0+U )erT where U is the present value of the storage costs.,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.21,,,The Cost of Carry (Page 60),

29、The cost of carry, c, is the storage cost plus the interest costs less the income earnedFor an investment asset F0 = S0ecT For a consumption asset F0 ? S0ecTThe convenience yield on the consumption asset, y, is de

30、fined so that F0 = S0 e(c–y )T,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,3.22,,,Futures Prices & Expected Future Spot Prices (Page 61),Suppose k is the ex

31、pected return required by investors on an assetWe can invest F0e–r T now to get ST back at maturity of the futures contractThis shows that F0 = E (ST )e(r–k )T,Options, Futures, and Other Derivatives, 5th edit

32、ion © 2002 by John C. Hull,3.23,,,Futures Prices & Future Spot Prices (continued),If the asset has no systematic risk, thenk = r and F0 is an unbiased estimate of STpositive systematic risk, then k &