Fischer Black.pptx

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Financial Guru

Fisher Black

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Earlier Life Of Fischer Black

Born on jan 11, 1938 in in Georgetown,

Washington DC, USA

Grauate !ro" #ar$ar college in 19%9 &ecei$e 'hD in A((lie )athe"atics

!ro" #ar$ar Uni$ersit* in 19+

Black joine the consultanc* Bolt,Beranek an .ew"an

Black !oune his own consulting /r"

Associates in Finance in 19+9

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Black joine Arthur D 0ittle where he"et Black re*nor

Began work at Uni$ersit* o! Chicago21914

Black, along with )*ron Scholes(u5lishe the (a(er 6he 'ricing o!

7(tions an Cor(orate 0ia5ilities6 oine ) Sloan school o!

)anage"ent

oine Gol"an Sachs

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&:S:AC#:&)A.

.:&:S

:cono"ics

Social science that anal*;ethe (rouction ,istri5utionan consu"(tion o! goos

an ser$ices

)athe"atical

Financeis a /el o! a((lie

"athe"atics concernewith /nancial "arkets

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Publication F< Black, >.oise>, 2198+4< F< Black, :< Der"an, = W< o*, >A 7ne?

Factor )oel o! nterest &ates an its

A((lication to reasur* Bon7(tions>, 2199E4, 21994nterest &ates as7(tions>,Journal of Finance, $ol< %E,((< 13113+ 2199%4he'ricing o! 7(tionsan Cor(orate

0ia5ilities>hen !urthere$elo(e 5* &o5ert)erton >heor* o!&ational 7(tion'ricing>

Also known asthe Black-Scholes-Merton Model

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Option

Call2&ight to 5u*4 'ut2&ight to sell4

An Unerl*ing AssetAt a s(eci/c (rice 2Strike 'rice:Hercise'rice4Within or at a s(eci/c (erio o! ti"e

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A call o(tion is in the money if spot rate > strike price,

at the money if spot rate = strike price, out of the money if spot rate < strike price.

A (ut o(tion is in the money if spot rate < strike price,

at the money if spot rate = strike price, out of the money if spot rate > strike price

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Contingenc* Gra(hs !or Currenc* 7(tions

+$.02

+$.04

-$.02

-$.04

0$1.46 $1.50 $1.54

Net Profitper Unit

FutureSpotRate

For Buyer of Ca !ption

Stri"e pri#e $1.50Pre%iu% $ .02

+$.02

+$.04

-$.02

-$.04

0$1.46 $1.50 $1.54

Net Profitper Unit

FutureSpotRate

For Seer of Ca !ption

Stri"e pri#e $1.50Pre%iu% $ .02

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Contingenc* Gra(hs !or Currenc* 7(tions

+$.02

+$.04

-$.02

-$.04

0$1.46 $1.50 $1.54

Net Profitper Unit

FutureSpotRate

For Seer of Put !ption

Stri"e pri#e $1.50Pre%iu% $ .0&

+$.02

+$.04

-$.02

-$.04

0$1.46 $1.50 $1.54

Net Profitper Unit

FutureSpotRate

For Buyer of Put !ption

Stri"e pri#e $1.50Pre%iu% $ .0&

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The Model

Variable denitions:S = current stock price

K = option strike price

e = base of natural logarithmsR = riskless interest rate

= time until option e!piration

=standard de"iation #sigma$

of returns on the underl%ingsecurit%

ln= natural logarithm

d'$ and d($ = cumulati"e

standard normal distributionfunctions

Tdd

T

TRK

S

d

dNKedSNC RT

=

++=

=

12

2

1

21

and

2ln

where

)()(

)()( 12 dSNdNKeP RT

=

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ssu!ptions of the Black-ScholesModel

he stock pa%s no di"idendsduring the option)s life

*uropean e!ercise st%le +arkets are ecient &o transaction costs -nterest rates remain constant

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"eter!inants of the Option Pre!iu!

Strike price ime until e!piration Stock price Volatilit% i"idends Risk/free interest rate

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Proble!s #sing the Black-Scholes Model

Does not work well with o(tions that areee(?in?the?"one* or su5stantiall* out?o!?the?"one*

'rouces 5iase $alues !or $er* low or$er* high $olatilit* stocks ncreases as the ti"e until eH(iration increases

)a* *iel unreasona5le $alues when ano(tion has onl* a !ew a*s o! li!ere"aining

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Illness, death and Reward

n earl* 199, Black was iagnosewith throat cancer an Black ie inAugust 199%