Optio ns a nd the Bla c k-Sc ho le s Mo de l R GE JAE BY CHASE - - PDF document

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Optio ns a nd the Bla c k-Sc ho le s Mo de l R GE JAE BY CHASE - - PDF document

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Optio ns a nd the Bla c k-Sc ho le s Mo de l R GE JAE BY CHASE De fining Optio ns A put o ptio n (usua lly just c a lle d a "put") is a fina nc ia l c o ntra c t b e twe e n two pa rtie s, the write r (se lle r) a nd the

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SLIDE 1

Optio ns a nd the Bla c k-Sc ho le s Mo de l

BY CHASE JAE GE R

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SLIDE 2

De fining Optio ns

A put o ptio n (usua lly just c a lle d a "put") is a fina nc ia l c o ntra c t b e twe e n two pa rtie s, the write r (se lle r) a nd the b uye r o f the

  • ptio n. T

he b uye r a c q uire s a sho rt po sitio n with the rig ht, b ut no t the o b lig a tio n, to se ll the unde rlying instrume nt a t a n a g re e d-upo n pric e (the strike pric e ). I f the b uye r e xe rc ise s his rig ht to se ll the

  • ptio n, the se lle r is o b lig e d to b uy it a t the strike pric e . I

n e xc ha ng e fo r ha ving this o ptio n, the b uye r pa ys the write r a fe e (the o ptio n pre mium).

A Ca ll o ptio n g ive s the b uye r o f the o ptio n the rig ht, b ut no t the

  • b lig a tio n to b uy a n a g re e d q ua ntity o f a pa rtic ula r c o mmo dity o r

fina nc ia l instrume nt (the unde rlying instrume nt) fro m the se lle r o f the o ptio n a t a c e rta in time (the e xpira tio n da te ) fo r a c e rta in pric e (the strike pric e ). T he se lle r (o r "write r") is o b lig a te d to se ll the c o mmo dity o r fina nc ia l instrume nt sho uld the b uye r so de c ide . T he b uye r pa ys a fe e (c a lle d a pre mium) fo r this rig ht.

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SLIDE 3

Optio ns a nd I nsura nc e

I t is OK to ‘ think’ o f o ptio ns a s insura nc e b ut it is inc o rre c t to c a ll the m insura nc e .

A ke y diffe re nc e s is simply tha t fo r insura nc e a n inde mnity must b e tie d to a spe c ific a nd me a sure d lo ss

F ina nc ia l o ptio ns ha ve no re q uire me nt me a ning tha t the y ha ve spe c ula tive a nd tra da b le c ha ra c te ristic s

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SLIDE 4

Use s o f Optio ns

A money manager whose portfolio has reaped huge gains can safeguard them by buying index put options (portfolio insurance).

A meat processor can hedge input price from rising by buying a call option on pork belly futures.

An American manufacturer buying machines from Germany for which payment is due in three months can remove price risk from dollar/euro exchange rates by buying an option on a euro futures contract.

A speculator can make leveraged bets by trading options.

A sophisticated investor can alter portfolio’s risk-return tradeoff by trading

  • ptions.

An investor can avoid short selling restrictions on the New York Stock Exchange by taking a “sell” position in the options market.

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SLIDE 5

Histo ry o f Optio ns

T he a stro no me r T ha le s (624-547 BC), to o k o ptio ns o n

  • live o il pre sse s b y pa ying in a dva nc e fo r the rig ht

to hire the m. He b a se d his mo ve s o n a stro lo g y a nd whe n ha rve st wa s stro ng so ld his rig hts b y re nting the pre sse s.

Mo st fa mo us o ptio ns ma rke ts wa s the g re a t tulip b ub b le c ra ze o f the 1630’ s in Ho lla nd

Unre g ula te d o ptio ns sta rte d to tra de o n the L

  • ndo n

e xc ha ng e in the la te 1800s

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SLIDE 6

Ba c kg ro und to Optio ns Pric ing

T HE BL ACK

  • SCHOL

E S F ORMUL A

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SLIDE 7

I n the Be g inning ….

1840 Re ve re nd Bro wn a Sc o ttish b o ta nist o b se rve s po lle n in a fluid a nd o utline s the dyna mic mo tio n o f pa rtic le s in mo tio n

He nc e … Bro wnia n mo tio n

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SLIDE 8

F

  • llo we d b y…

1880 T .N. T hie le (Co pe nha g e n)

1900 L . Ba c he lie r (Pa ris)

L

  • o ke d a t ra ndo mne ss in Pa ris sto c k ma rke t b ut wa s

ig no re d b e c a use the a pplic a tio n o f pure ma the ma tic s to e c o no mic s wa s fro wne d upo n

1905 A. E inste in (Be rlin)

L a id o ut the b a sic fo rm fo r sto c ha stic diffe re ntia l e q ua tio n b ut ma the ma tic s re q uire d fo r g e ne ra l pro o f no t ye t inve nte d

1923 N. Wie ne r (Be rlin) wa s a b le to e sta b lish a pro o f o f E inste in’ s mo de l

T his is whe re the te rm Wie ne r Pro c e ss c o me s fro m

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SLIDE 9

I n the me a n time …

K

  • lmo g o ro v in Russia , Ma rko v in Russia a nd L

e vy in Pa ris we re a pplying ne w disc o ve rie s in pure ma the ma tic s to the study o f pro b a b ility.

 T

he ma the ma tic ia ns se e k o ut unive rsa l pro o fs tha t ho ld unde r a ll c o nditio ns.

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SLIDE 10

While in T

  • kyo …

K iyo si I to , a 24 ye a r o ld ma the ma tic ia n studie d Ma rko v, K

  • lmo g o ro v,

Wie ne r, a nd L e vy

L

  • o king fo r a n a ppro a c h

to unify the ir va rio us the o rie s.

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SLIDE 11

K iyo si I to

I n 1941 pub lishe d a mime o in Ja pa ne se de fining the first sto c ha stic inte g ra l fo r a Bro wnia n mo tio n.

I n 1951 this wa s pub lishe d in E ng lish

And b e c a me kno wn a s I to ’ s L e mma

But the L e mma sa w little use a nd ling e re d thro ug h the mid 1960’ s

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SLIDE 12

I to Go e s to Princ e to n

Whe n pub lishe d in E ng lish I to ’ s pa pe rs b e c o me no ta b le

1954 to o k le a ve to g o to Princ e to n’ s I nstitute fo r Adva nc e d Studie s whe re he me t up with the yo ung ma the ma tic ia n He nry Mc K e a n.

Mc K e a n wa s wo rking with the ma the ma tic ia ns Bo c hne r a nd F e lle r who we re a lso lo o king a t diffusio n pro c e sse s.

Mc K e a n tra ve le d to wo rk with I to in T

  • kyo fo r two ye a rs

in 1957/ 58 whe re the y sta rte d tra ining Ja pa ne se ma the ma tic ia ns in diffusio n pro c e sse s

I t wa s this g ro up tha t fine tune d the sto c ha stic c a lc ulus a nd c o ine d the te rm ‘ I to ’ s L e mma ’ in the la te 1960’ s

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SLIDE 13

And….

Ro b e rt Me rto n, Sa mue lso n’ s stude nt a t MI T sta rts e xa mining o ptio ns pric ing fro m the ra tio na l po int o f vie w de ve lo ping c e rta in b o unda ry c o nditio ns a nd is the first to a pply I to ’ s le mma in its c urre nt fo rm to fina nc ia l e c o no mic s

AND

Myro n Sc ho le s a lso a t MI T wa s ta king a no the r lo o k a t the pric ing o f o ptio ns a nd te a ms up with pra c titio ne r F isc he r Bla c k.

I t wa s Mc K e a n, Sa mue lso n, Me rto n a nd Sc ho le s a ll a t MI T a t the sa me time tha t c a me to g e the r to so lve the

  • ptio ns pric ing fo rmula .
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SLIDE 14

Bla c k a nd Sc ho le s

Applying I to ’ s L e mma the y c o me up with a sto c ha stic diffe re ntia l e q ua tio n fo r the dyna mic s o f the o ptio ns pric e b a se d o n the Bro wnia n mo tio n o f the unde rlying

                       

2 2 2 2 2 2 2 2 2 2

, , , 1 2 , , , 1 2 , , , 1 2 w p t w p t w p t dw dp dt dp p t p w p t w p t w p t dw pdt pdz dt pdt pdz p t p w p t w p t w p t dw pdt pdz p dt dt p p t                                     

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SLIDE 15

Bla c k a nd Sc ho le s

T he y e mplo y CAPM a nd risk ne utra l va lua tio ns a rg uing tha t b e c a use the he dg e po sitio n is riskle ss the va lue o f the po rtfo lio must e q ua l the risk fre e ra te

     

2 2 2 2

, , 1 1 , 2 w p t w p t dE p dt w p t p t p                

   

, , w p t dE p rdt w p t p                

                   

2 2 2 2 2 2 2 2

, , , , 1 1 , , 2 , , , 1 , 2 w p t p w p t w p t w p t p p dt rdt w p t w p t p t p p w p t w p t w p t rw p t rp p t p p                                           

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SLIDE 16

T he Bla c k Sc ho le s F

  • rmula fo r a

Ca ll & Put Optio n o n no n-divide nd pa ying sto c ks

B-S Ca ll:

     

1 2 2 1 2 2

, 1 ln 2 1 ln 2

rt

w p t pN d xe N d p r t x d t p r t x d t    

                               

B-S Put:

     

2 1 2 1 2 2

, 1 ln 2 1 ln 2

rt

w p t xe N d pN d p r t x d t p r t x d t    

                                 

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SLIDE 17

B-S Assumptio ns

 1: Pric e o f Unde rlying  2: Strike Pric e  3 T

ime to Ma turity

 4: I

nte re st Ra te s

 5: Vo la tility  6: Divide nds

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SLIDE 18

T ra ding Stra te g ie s

T HE BL ACK

  • SCHOL

E S F ORMUL A

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SLIDE 19

Va nilla Ca ll/ Put Optio n:

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SLIDE 20

Ca ll/ Put Spre a d

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SLIDE 21

Vo la tility T ra de s

Stra ddle :

Stra ng le :

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SLIDE 22

Synthe tic L

  • ng / Sho rt

Use d He a vily During F ina nc ia l Crisis

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SLIDE 23

T he Gre e ks

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SLIDE 24

De lta :

Me a sure s c ha ng e in the pric e o f a n o ptio n re la tive to a c ha ng e in the pric e o f the unde rlying se c urity

F

  • r a c a ll o ptio n: this will b e b e twe e n 0 a nd 1

F

  • r a put o ptio n: this will b e b e twe e n 0 a nd -1
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SLIDE 25

Ga mma :

Ga mma is the de riva tive o f De lta

Ga mma me a sure s the c ha ng e in de lta re la tive to a c ha ng e in the pric e o f the unde rlying se c urity

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SLIDE 26

T he ta

T he ta is the time de c a y o f the o ptio n

T he ta is a lwa ys ne g a tive

T he ta de c re a se s the c lo se r a n o ptio n g e ts to ma turity

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SLIDE 27

Ve g a

Me a sure s c ha ng e in the pric e o f a n o ptio n re la tive to a 1% c ha ng e in the vo la tility o f the unde rlying se c urity

T his will b e po sitive fo r b o th c a ll a nd put o ptio ns

T hus, whe n yo u o wn a n o ptio n… yo u a lwa ys wa nt vo la tility o f the unde rlying se c urity to inc re a se

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SLIDE 28

Rho

Me a sure s the c ha ng e in the pric e o f the pric e o f a n

  • ptio n re la tive to a c ha ng e in the risk fre e ra te

T his will b e po sitive fo r Ca ll Optio ns a nd ne g a tive fo r Put Optio ns

E a sie r to think o f why if yo u think o f the a lte rna tive to b uying a c a ll a nd put re spe c tive ly

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SLIDE 29

Be ne fits o f E xc ha ng e T ra de d Optio ns

a ) Or de r ly, e fficie nt and liquid mar ke ts with low tr ansactions costs- Sta nda rdize d o ptio ns tra de in

  • rde rly, e ffic ie nt, a nd liq uid ma rke ts.
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SLIDE 30

Be ne fits o f E xc ha ng e T ra de d Optio ns

b ) F le xibility- Optio ns a re a n e xtre me ly ve rsa tile inve stme nt to o l. Be c a use o f the ir uniq ue risk/ re wa rd struc ture , o ptio ns c a n b e use d in ma ny c o mb ina tio ns with o the r o ptio n c o ntra c ts a nd/ o r

  • the r fina nc ia l instrume nts to c re a te e ithe r a

he dg e d o r spe c ula tive po sitio n.

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SLIDE 31

Be ne fits o f E xc ha ng e T ra de d Optio ns

c ) L e ve r age - Options make it che ape r to spe culate . Allo ws yo u to fo rwa rd b uy o r se ll in multiple s o f wha t c o uld o the rwise b e purc ha se d in full.

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SLIDE 32

Be ne fits o f E xc ha ng e T ra de d Optio ns

d) L imite d r isk for buye r

  • Unlike o the r inve stme nts

whe re the risks ma y ha ve no limit, o ptio ns o ffe r a kno wn risk to b uye rs. T he ma ximum yo u c a n lo se is the a mo unt yo u pa id fo r the o ptio n. On the o the r ha nd, the na ture o f the g a me ma ke s c a ll write r fa c e unlimite d risk.

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SLIDE 33

Be ne fits o f E xc ha ng e T ra de d Optio ns

f) Guar ante e d contr act pe r for mance - E xc ha ng e - tra de d o ptio ns ha ve no c re dit risk (c o unte rpa rty risk) a s the ir pe rfo rma nc e s a re g ua ra nte e d b y the OCC (T he Optio ns Cle a ring Co rpo ra tio n).

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SLIDE 34

Be ne fits o f E xc ha ng e T ra de d Optio ns

g ) Ove r come stock mar ke t r e str ictions- suc h a s re stric tio ns o n sho rtse lling whe n the ma rke t is g o ing do wn. Optio ns do n’ t ha ve suc h re stric tio ns- in fa c t the y a re de sig ne d to g ive fle xib ility o f inve stme nt in a va rie ty o f ma rke t c o nditio ns.

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SLIDE 35

Optio ns ve rsus E q uitie s

Co mmo n with E q uitie s

Bo th o ptio ns a nd sto c ks a re liste d se c uritie s.

L ike sto c ks, o ptio ns tra de with b uye rs ma king b ids a nd se lle rs ma king o ffe rs.

Optio n inve sto rs, like sto c k inve sto rs, ha ve the a b ility to fo llo w pric e mo ve me nts, tra ding vo lume a nd o the r pe rtine nt info rma tio n

No t Co mmo n with E q uitie s

  • ptio n ha s a limite d life

T he re is no t a fixe d numb e r o f

  • ptio ns

Sto c ks ha ve c e rtific a te s e vide nc ing the ir o wne rship, o ptio ns a re c e rtific a te le ss

sto c k o wne rship pro vide s the ho lde r with a sha re o f the c o mpa ny, c e rta in vo ting rig hts a nd rig hts to divide nds (if a ny), o ptio n o wne rs pa rtic ipa te o nly in the po te ntia l b e ne fit o f the sto c k's pric e mo ve me nt

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SLIDE 36

Ho w do e s this Re la te to Our Co urse

 I

n o ur F ra g ile Ma c ro -E c o no mic E c o no my, the Sto c k Ma rke t is pa rtic ula rly F ra g ile

 Optio ns c a n a c t a s insura nc e a g a inst ta il-risk

e ve nts

 T

hro ug h pro pe r use o f o ptio ns, yo ur po rtfo lio c a n b e ro b ust a g a inst Ba nk Runs, infla tio n, pe rio ds o f hig h vo la tility, a nd Bla c k-Swa n e ve nts

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SLIDE 37

Wo rks Cite d

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*so me slide s ta ke n fro m le c ture b y Pro f. Ca lum T urve y (with pe rmissio n)