Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.1
Properties of
Stock Option Prices
Chapter 8
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.2
Notation
? c, European call
option price
? p, European put
option price
? S0, Stock price today
? K, Strike price
? T, Life of option
? ?,Volatility of stock
price
? C, American Call option
price
? P, American Put option
price
? ST,Stock price at option
maturity
? D, Present value of
dividends during option’s
life
? r, Risk-free rate for
maturity T with cont comp
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.3Effect of Variables on Option
Pricing (Table 8.1,page 168)
c p C PVariable
S0
K
T
?
r
D
+ + –+
+ ++ + + +
+ – + –
–– – +
– + – +
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.4
American vs European Options
An American option is worth
at least as much as the
corresponding European
option
C ? c
P ? p
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.5Calls,An Arbitrage
Opportunity?
? Suppose that
c = 3 S0 = 20
T = 1 r = 10%
K = 18 D = 0
? Is there an arbitrage opportunity?
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.6Lower Bound for European Call
Option Prices; No Dividends
(Equation 8.1,page 173)
c ? S0 –Ke -rT
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.7Puts,An Arbitrage
Opportunity?
? Suppose that
p = 1 S0 = 37
T = 0.5 r =5%
K = 40 D = 0
? Is there an arbitrage
opportunity?
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.8Lower Bound for European Put
Prices; No Dividends
(Equation 8.2,page 174)
p ? Ke-rT–S0
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.9
Put-Call Parity; No Dividends
(Equation 8.3,page 174)
? Consider the following 2 portfolios:
– Portfolio A,European call on a stock + PV of the
strike price in cash
– Portfolio C,European put on the stock + the stock
? Both are worth MAX(ST,K ) at the maturity of the
options
? They must therefore be worth the same today
– This means that
c + Ke -rT = p + S0
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.10Arbitrage Opportunities
? Suppose that
c = 3 S0 = 31
T = 0.25 r = 10%
K =30 D = 0
? What are the arbitrage
possibilities when
p = 2.25?
p = 1?
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.11
Early Exercise
? Usually there is some chance that an
American option will be exercised
early
? An exception is an American call on a
non-dividend paying stock
? This should never be exercised early
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.12
? For an American call option:
S0 = 100; T = 0.25; K = 60; D = 0
Should you exercise immediately?
? What should you do if
1 You want to hold the stock for the next 3
months?
2 You do not feel that the stock is worth holding
for the next 3 months?
An Extreme Situation
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.13Reasons For Not Exercising a
Call Early
(No Dividends )
? No income is sacrificed
? We delay paying the strike price
? Holding the call provides
insurance against stock price
falling below strike price
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.14
Should Puts Be Exercised
Early?
Are there any advantages to
exercising an American put
when
S0 = 60; T = 0.25; r=10%
K = 100; D = 0
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.15The Impact of Dividends on
Lower Bounds to Option Prices
(Equations 8.5 and 8.6,page 179)
c S D Ke
p D Ke S
rT
rT
? ? ?
? ? ?
?
?
0
0
Options,Futures,and Other Derivatives,5th edition ? 2002 by John C,Hull
8.16
Extensions of Put-Call Parity
? American options; D = 0
Equation 8.4 p,175
? European options; D > 0
c + D + Ke -rT = p + S0
Equation 8.7 p,179
? American options; D > 0
Equation 8.8 p,179
rTKeSPCKS ?????? 00
rTKeSPCKDS ??????? 00