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David Dubofskyand 16-1

Chaper 16!rbira"e #esri$ions on %pion &ri$es

' Calls( The upper boundis C ) *

( +f here are no dividend payous, he loer boundisC ma / 0, * - 213r4-T5 i.e., C ma / 0, * - &7245

C

*0 &724

C8*C8*-&724

C8*-

9oe ha C*- is a:eaker; loer boundhan C*-&724

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David Dubofskyand 16- S-PV(K)

( Wha if C ) *-&724=

( Then C ( * 3 &724 ) 0

( Then -C 3* - &724 0 permis arbira"e, be$ause $ash isre$eived oday, and here are no $ash ouflos a epiraion.

>>>>>>! ?piraion>>>>>>

( Today@ *T *T)

' Auy $all -C 32*T( 4 0' *ell so$k 3* - *T - *T' Bend -&724 3 3

0 0 -*T30

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David Dubofskyand 16-

&roof ha C Ma/0,*-&7245@! 9umeri$al ?ample

( Be@ C 8 , * 8 , 8 0, r 8 6E, T 8 1 mo., &724 8 F.G0

( Wha if ) - F.G0 8 .

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David Dubofskyand 16-

Ior AmericanCalls %nly

' The eaker loer bound is C * -

' 7iolaion of his bound permis insan arbira"eK.

' &roof@

( Wha if C ) *-= 2i.e., he $all is sellin" for less han is inrinsi$ valuee."., *8, 8 0 and C 8 .F04.

( Then,

Auy $all -C -.F0

Exercise$all - -0 2hereby a$Luirin" he so$k4

*ell so$k 3* 30 30.10

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David Dubofskyand 16-

Theorei$al +mpli$aions of hese Aounds

' Ae$ause he pri$e of an in-he-money $all mus e$eed*-&724, in he money $alls on non-dividend payin"so$ks ill alwayshave some ime value before

epiraion.' !n !meri$an $all on a non-dividend payin" so$k ill

neverbe eer$ised before epiraion. Why exercise forS-K, when yo can sell it for S-PV(K) or more!

' The value of an American$all on a non-dividend payin"so$k is he same as he value of a Ero"ean$all on hesame so$k, all else eLual.

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David Dubofskyand 16-6

Boer bound for Ero"ean$allson Dividend &ayin" *o$ks

' Cma /0, *- 213r4-1-213r4-T5

' is he hi"hes dividend possible paid a ime 1)T 2i is alsoassumed ha he e-dividend dae and he dividend paymen daeare he same4.

' This means ha deep in he money Ero"ean$alls on dividendpayin" so$ks cansell for less han heir inrinsi$ value.

( ?ample@ if *860, 8

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David Dubofskyand 16-H

Boer bound for!meri$an$allson Dividend &ayin" *o$ks

' &roposiion +7@

' Ae$ause of +7b, e $an sae ha @( An in the moneyAmericancall on a dividend paying stock will

always have some time value, except (possibly) on the day beforeit trades ex-dividend, and (always) on its expiration day.

( An in the moneyAmerican call will never be exercised early,except on the day before it trades ex-dividend (if Ib is binding,and t! is one day (!"#$% year)).

+++++

+

T-

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David Dubofskyand 16-G

When ill an American$all be ?er$ised?arly= The Bo"i$

' ?er$isin" an opion early desroys is ime value, so you ill onlyan o eer$ise early if he opion has no ime value.

'?er$isin" early also desroys he donside proe$ion provided bya $all 2i.e., if *T) 4, and reLuires spendin" O earlier 2hereby

losin" ineres ha $an be earned on O4.

' *o, he dividend ha ill be paid omorroK mus be suffi$ienly

"rea o $ompensae you for hese $ossK of early eer$ise.

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David Dubofskyand 16-F

When ill an AmericanCall be ?er$ised?arly= The !l"ebra

' *uppose ha oday, he day before a so$k rades e-dividend, a $all issellin" is sellin" for is inrinsi$ value@

C2ih-div4 8 *2ih-div4 (

' Tomorro, on he e-dividend day, he $all;s loer bound is@

C8 *2e-div4 ( &724

' !ssume ha ?PC2e-div4Q 8 *2e-div4-&7243?2 4

' Rou ill an o eer$ise he $all oday if@

C2ih-div4 ?PC2e-div4Q

*2ih-div4- ?P*2e-div4Q-&7243?2 4

!ssume ?2S4 8 0, and sin$e ?P*2e-div4Q 8 *2ih-div4 ( div,#iv > K $ PV(K)

' +.e., you ill an o eer$ise early if he dividend e$eeds he ineres ha $anbe earned by invesin" &724 unil he epiraion day.

z

~

z~

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David Dubofskyand 16-10

When ill an American$all be eer$isedearly= The Dia"ram

Boer bound, us prior o he e-dae, is *2ih-div4 ( 21 U 04

Boer bound, e-dividend,is *2e-div4 - 213r4-T

div

*2ih-div4*2e-div4&724

MinC2e-div4

C 2ih-div4

C

*

+ is possible ha he !meri$an $all ill fall in value from C2ih-div4 o aslo as C2e-div4, on he e-dividend day. !meri$an $all oners illeer$ise early, raher han a$h he $all de$line in value.

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David Dubofskyand 16-11

!rbira"e #esri$ions on &u &ri$es

' !ssume he so$k pays no dividends.

' Vpper bounds are( American@ & )

( Ero"ean@ & ) 213r4-T

' Boer bounds are( American@ & ma 20, -*4

( Ero"ean@ & ma 20, 213r4-T( *4

' Thus, an Americanpu $anno sell for less han isinrinsi$ value, bu a Ero"eanpu $an

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David Dubofskyand 16-1