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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

Properties of StockOptions

Chapter 10

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

Notation

c: European calloption price

p: European put

option price

S0: Stock pricetoday

K: Strike price

T: Life of option

: Volatility of stock

price

C: American Calloption price

P :American Put option

price

ST:Stock price at optionmaturity

D: Present value of

dividends during options

life r: !isk"free rate for

maturity T#ith cont$

comp$

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

Effect of Variables on Option

Pricing (Table 10.1, page 233)

c p C P Varia%le

S0KT

rD

& & '&( ( & &

& & & && ' & '

'' ' &

' & ' &

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

!erican "s E#ropean Options

An American option is #orth

at least as much as the

corresponding Europeanoption

Cc

P

p

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

$alls% n rbitrage Opport#nit&'

Suppose that

c) * S0) +0

T) 1 r) 10,

K) 1- D) 0

.s there an ar%itrage opportunity(

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

oer *o#n+ for E#ropean $all

Option Prices No -i"i+en+s (E#ation10./, page 23)

cma/S0 KerT, 0)

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

P#ts% n rbitrage Opport#nit&'

Suppose that

p ) 1 S0 ) * T )

0$2 r )2,K ) 30 D ) 0

.s there an ar%itrageopportunity(

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

oer *o#n+ for E#ropean P#t

Prices No -i"i+en+s(E#ation 10., page 2/0)

pma/Ke rT S0, 0)

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

P#t$all Parit& No -i"i+en+s

Consider the follo#ing + portfolios:

Portfolio A: European call on a stock & 4ero"

coupon %ond that paysKat time T

Portfolio C: European put on the stock & the stock

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Val#es of Portfolios

Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

ST> K ST< K

Portfolio A Call option ST K 0

5ero"coupon %ond K K6otal ST K

Portfolio C Put 7ption 0 K ST

Share ST ST

6otal ST K

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Te P#t$all Parit& 4es#lt (E#ation10.5, page 2/1)

8oth are #orth ma/ST,K9 at the maturity

of the options

6hey must therefore %e #orth the same

today$ 6his means that c+

Ke-rT

=p+ S0

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

rbitrage Opport#nities

Suppose thatc ) * S0 ) *1

T ) 0$+2 r) 10,

K )*0 D) 0

hat are the ar%itrage

possi%ilities #hen

p) +$+2 ( p) 1 (

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

Earl& E6ercise

;sually there is some chance that an

American option #ill %e e/ercised

earlyAn e/ception is an American call on a

non"dividend paying stock< #hich

should never %e e/ercised early

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n E6tre!e Sit#ation

=or an American call option:

S0= 100; T = 0.25;K= 60;D= 0

Should you e/ercise immediately(hat should you do if >ou #ant to hold the stock for the ne/t *

months( >ou do not feel that the stock is #orth holding

for the ne/t * months(

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

4easons 7or Not E6ercising a

$all Earl& (No -i"i+en+s)

?o income is sacrificed

>ou delay paying the strike price

@olding the call provides

insurance against stock price

falling %elo# strike price

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*o#n+s for E#ropean or !erican

$all Options (No -i"i+en+s)

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

So#l+ P#ts *e E6ercise+

Earl& '

Are there any advantages to

e/ercising an American put #hen

S0 ) 0B T) 0$+2Br)10,

K) 100BD) 0

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*o#n+s for E#ropean an+ !erican

P#t Options (No -i"i+en+s)

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S0 S0

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

Te 8!pact of -i"i+en+s on

oer *o#n+s to Option Prices(E#ations 10. an+ 10.9, pages 2/2/9)

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)0,max(0

rTKeDSc

)0,max( 0SKeDp rT

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 10, Copyright John C. ull !01"

E6tensions of P#t$all Parit&

American optionsBD) 0

S0-K C-P S0-Ke-rT

EDuation 10$ p$ +3*

European optionsBD 0

c+D+Ke -rT=p+ S0

EDuation 10$10 p$ +3F

American optionsBD 0

S0-D-K C-P S0-Ke-rT

EDuation 10$11 p$ +3F

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