文档介绍：Introduction to Binomial Trees Chapter 10
1
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
A Simple Binomial Model
A stock price is currently $20
In three months it will be either $22 or $18
Stock Price = $22
Stock Price = $18
Stock price = $20
2
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Stock Price = $22
Option Price = $1
Stock Price = $18
Option Price = $0
Stock price = $20
Option Price=?
A Call Option (Figure , page 200)
A 3-month call option on the stock has a strike price of 21.
3
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Consider the Portfolio: long D shares short 1 call option
Portfolio is riskless when 22D – 1 = 18D or
D =
22D – 1
18D
Setting Up a Riskless Portfolio
4
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Valuing the Portfolio (Risk-Free Rate is 12%)
The riskless portfolio is:
long shares short 1 call option
The value of the portfolio in 3 months is 22´ – 1 =
The value of the portfolio today is – ´ =
5
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Valuing the Option
The portfolio that is
long shares short 1 option
is worth
The value of the shares is (= ´20 )
The value of the option is therefore (= – )
6
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Generalization (Figure , page 202)
A derivative lasts for time T and is dependent on a stock
S0
ƒu
S0d
ƒd
S0
ƒ
7
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Generalization (continued)
Consider the portfolio that is long D shares and short 1 derivative
The portfolio is riskless when S0uD –ƒu = S0d D –ƒd or
S0 uD –ƒu
S0dD –ƒd
S0– f
8
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Generalization (continued)
Value of the po