ch10期權(quán)期貨與衍生證券（第五版）

1、Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.1,Introduction toBinomial TreesChapter 10,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.2,A S

2、imple Binomial Model,A stock price is currently $20In three months it will be either $22 or $18,,,Stock Price = $22,Stock Price = $18,Stock price = $20,Options, Futures, and Other Derivatives, 5th edition © 2002 b

3、y John C. Hull,10.3,,,Stock Price = $22Option Price = $1,Stock Price = $18Option Price = $0,Stock price = $20Option Price=?,A Call Option (Figure 10.1, page 200),A 3-month call option on the stock has a strike price o

4、f 21.,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.4,Consider the Portfolio:long D sharesshort 1 call optionPortfolio is riskless w

5、hen 22D – 1 = 18D or D = 0.25,Setting Up a Riskless Portfolio,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.5,Valuing the Portfolio(Risk-Free Rate is 12%),The riskless portfoli

6、o is: long 0.25 sharesshort 1 call optionThe value of the portfolio in 3 months is 22´0.25 – 1 = 4.50The value of the portfolio today is 4.5e – 0.12´0.25 = 4.3670,Options, Futures, and Other D

7、erivatives, 5th edition © 2002 by John C. Hull,10.6,Valuing the Option,The portfolio that is long 0.25 sharesshort 1 option is worth 4.367The value of the shares is 5.000 (= 0.25´20 )The

8、value of the option is therefore 0.633 (= 5.000 – 4.367 ),Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.7,Generalization (Figure 10.2, page 202),A derivative lasts for time T and

9、 is dependent on a stock,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.8,Generalization(continued),Consider the portfolio that is long D shares and short 1 derivative

10、The portfolio is riskless when S0uD – ?u = S0d D – ?d or,,S0 uD – ?u,S0dD – ?d,,,S0– f,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.9,Generalization(continued),Value o

11、f the portfolio at time T is S0u D – ?uValue of the portfolio today is (S0u D – ?u )e–rTAnother expression for the portfolio value today is S0D – fHence ? = S0D – (S0u D – ?u )e–rT,Options, Futures, and Othe

12、r Derivatives, 5th edition © 2002 by John C. Hull,10.10,Generalization(continued),Substituting for D we obtain ? = [ p ?u + (1 – p )?d ]e–rTwhere,Options, Futures, and Other Derivatives, 5th edit

13、ion © 2002 by John C. Hull,10.11,Risk-Neutral Valuation,? = [ p ?u + (1 – p )?d ]e-rTThe variables p and (1 – p ) can be interpreted as the risk-neutral probabilities of up and down movementsThe value of a deri

14、vative is its expected payoff in a risk-neutral world discounted at the risk-free rate,p,(1 – p ),Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.12,Irrelevance of Stock’s Expected Re

15、turn,When we are valuing an option in terms of the underlying stock the expected return on the stock is irrelevant,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.13,Original Example

16、Revisited,Since p is a risk-neutral probability20e0.12 ´0.25 = 22p + 18(1 – p ); p = 0.6523Alternatively, we can use the formula,,,S0u = 22 ?u = 1,S0d = 18 ?d = 0,S0 ?,p,(1 – p ),Options, Futures, and Other Der

17、ivatives, 5th edition © 2002 by John C. Hull,10.14,Valuing the Option,The value of the option is e–0.12´0.25 [0.6523´1 + 0.3477´0] = 0.633,Options, Futures, and Other Derivatives, 5th edition

18、 © 2002 by John C. Hull,10.15,A Two-Step ExampleFigure 10.3, page 205,Each time step is 3 months,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.16,Valuing a Call OptionFigure

19、 10.4, page 206,Value at node B = e–0.12´0.25(0.6523´3.2 + 0.3477´0) = 2.0257Value at node A = e–0.12´0.25(0.6523´2.0257 + 0.3477´0) = 1.2823,201.2823,22,18,24.23.2

20、,19.80.0,16.20.0,2.0257,0.0,A,B,C,D,E,F,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.17,A Put Option Example; K=52Figure 10.7, page 208,,Options, Futures, and Other Derivatives,

21、 5th edition © 2002 by John C. Hull,10.18,What Happens When an Option is American (Figure 10.8, page 209),,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,10.19,Delta,Delta (D) is

22、the ratio of the change in the price of a stock option to the change in the price of the underlying stockThe value of D varies from node to node,Options, Futures, and Other Derivatives, 5th edition © 2002 by John