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. Hull,3.2,Consumption vs Investment Assets,Investment assets are assets held by significant numbers o
2、f 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 2002 by John C. Hull,3.3,Short Selling (Page 41-42),Short selling involves selling securities you
3、do not ownYour broker borrows 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 buy the securities back so they can be replaced in the account
4、of the clientYou must pay dividends and other benefits the owner of the securities receives,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 measurementThe difference between quar
5、terly and annual compounding is analogous to the difference between 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 compounded interest rates
6、$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, 5th edition 2002 by John C. Hull,3.7,Conversion Formulas(Page 44),
7、DefineRc : continuously compounded rateRm: same rate with compounding m times per year,Options, Futures, 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 F0 = S0(1
8、 + 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,Extension of the Gold Example(Page 46, equation 3.5),For any investment asset that provides no income and has no storage co
9、sts F0 = S0erT,Options, Futures, and Other Derivatives, 5th edition 2002 by 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 2002 by John C
10、. Hull,3.12,When an Investment Asset Provides a Known Yield (Page 49, equation 3.7),F0 = S0 e(rq )T where q is the average yield during the life of the contract (expressed with continuous compounding),Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,3.13,Valuing a Forward Co
11、ntractPage 50,Suppose that K is delivery price in a forward contract F0 is forward price that would apply to the contract todayThe value of a long forward contract, , is = (F0 K )erT Similarly, the value of a short forward contract is (K F0 )erT,Options, Futures, and Other Derivatives, 5th edition 2
12、002 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 different:A strong positive correlation between interest rates and the asset price implies the futures price is slightly h
13、igher than the forward priceA strong negative correlation implies the reverse,Options, Futures, 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 F0
14、 = S0 e(rq )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(continued),For the formula to be true it is important that the index represent an investment assetIn other words, changes i
15、n the index must correspond to changes in the value of a tradable portfolioThe Nikkei index viewed as a 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 F0S0e(r-q)T an arbitrageur buys the stocks underlying the index and sells futuresWhen F0 r and F0 E (ST ),
