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7/25/2019 DMCH16
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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
7/25/2019 DMCH16
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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
7/25/2019 DMCH16
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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 .
7/25/2019 DMCH16
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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$k 3* 30 30.10
7/25/2019 DMCH16
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David Dubofskyand 16-
Theorei$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$k, all else eLual.
7/25/2019 DMCH16
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David Dubofskyand 16-6
Boer bound for Ero"ean$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
7/25/2019 DMCH16
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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-
7/25/2019 DMCH16
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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.
7/25/2019 DMCH16
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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 $anbe earned by invesin" &724 unil he epiraion day.
z
~
z~
7/25/2019 DMCH16
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David Dubofskyand 16-10
When ill an American$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.
7/25/2019 DMCH16
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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
7/25/2019 DMCH16
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David Dubofskyand 16-1