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Finance: What is the Black Scholes Model? 11788 Views


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What is the Black Scholes Model? The Black Scholes Model is used to determine the price of call options. It looks at the change in stock price over time also using time value of money as well as the strike price and expiration date for the option.

Language:
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Transcript

00:00

Finance allah shmoop What is the black scholes model All

00:07

right people Yeah it sounds like something that has to

00:09

do with xu fashion right Black scholes are all the

00:12

rage in paris this year only instead of a bright

00:15

red soul there's is black and there isn't a doctor

00:19

in there as well right Somewhere Okay Okay The black

00:22

scholes stock option valuation model is actually a mathematical formula

00:26

and a whole system for coming up with stock option

00:29

prices for example disney's trading at a hundred bucks a

00:32

share today You see i owe our chief investment officer

00:36

of the milwaukee cardiologists investment club wanted by a call

00:41

option on disney with a strike price at one hundred

00:43

twenty bucks which won't expire for about four months Why

00:46

do you want to buy this Why do you want

00:47

to compete against goldman sachs Best and brightest people who

00:51

make twenty five million dollars a year Not really sure

00:53

about that But regardless you all believe disney is going

00:56

to spike in its stock price the next four months

00:59

And you want to take advantage of it Well how

01:00

much should that hundred twenty dollars Strike stock option cost

01:05

Expires in four months All right this call option is

01:08

notably an american style option that is in american cell

01:12

option You can sell the option any day until it

01:15

expires And traditional black scholes modeling is based on the

01:18

european style option which expires on lee on one day

01:22

at the very end of the period in which the

01:24

option is alive Got it So keep the approaching where

01:28

you gotta think about american sell options are worth more

01:30

because while you have more options in the option so

01:33

the valuations to be a little bit different paying on

01:35

which continent you're rolling the call option dice disney is

01:38

a global company right But here we just want to

01:40

give you the basic gist of how black scholes works

01:43

conceptually and save the math for a more advanced video

01:47

The key idea is that the more volatile the stock

01:50

the more volatile should be the call option underlying it

01:55

and a different strike price is relative to the existing

01:58

stock will have all come mine's a more volatility to

02:01

him as well if you think about it if they

02:03

were looking at one hundred dollars strike price option with

02:06

the stock at one hundred that'd be really volatile Where

02:09

as if they were looking at a one hundred fifty

02:12

dollars strike price option Well that'd be pretty cheap and

02:15

pretty much stay cheap Whether disney was one hundred box

02:17

one hundred five hundred ten ninety nine who wouldn't matter

02:21

Still be cheap because so far out of the money

02:23

right And yes there tons of mathematical errors in the

02:26

black scholes model not least of which is the fact

02:29

that past performance of stocks is not necessarily any indication

02:33

of future performance yet That's what black scholes uses teo

02:37

calculate its volatility here so we got all kinds of

02:40

problems going in Problem is we have nothing better No

02:43

other better option methodology to value things So we used

02:47

black scholes Alright so since we have no other ways

02:50

to navigate our future prognostications i've been driving a car

02:53

by looking in that rear view mirror Well then here's

02:55

what we do essentially the black scholes model takes an

02:58

average waiting of a stock price over a given duration

03:02

and multiplies it by some formula based on its volatility

03:07

So here's a stock with very low volatility last couple

03:11

of years Check out the line graph for a t

03:13

and t kind of a snoozer doesn't really grow in

03:16

only sits there pays a dividend and phone prices are

03:19

getting cheaper It's called skype Okay but here's another that

03:22

has been a hoot of a ride for the good

03:24

the bad the ugly in the form of quotient a

03:27

digital coupon and company Really volatile rocky mountains peaks valleys

03:31

all kinds of stuff Good bad ugly Well you can

03:34

imagine that a call option price with a strike price

03:37

twenty percent above it and tease price would not be

03:40

very expensive because given the low volatility of at and

03:44

t stocked the odds that that's stock itself suddenly breaks

03:48

out above that twenty percent line that was pretty low

03:51

It hadn't done it much in the past And when

03:53

it did it on lee did it by a very

03:55

small amount So if you were writing life insurance against

03:58

the financial death thing he broke out of that twenty

04:01

percent line Well pride wouldn't charge too much for it

04:04

right But then if you look at quotient well a

04:06

price twenty percent above well here or here here seems

04:09

highly likely because the stock trades in huge gaps up

04:13

and down of a few percentage is a day i

04:16

e the same volatility per day that a teen t

04:18

has per month So if you are the person writing

04:21

that call option or selling that call option to these

04:25

kind of loving people in milwaukee or people like him

04:28

and knowing that it would put you on the hook

04:30

to provide shares at a price roughly twenty percent above

04:32

where the stock is currently trading well of course you

04:35

would charge the call option buyer of quotient ah whole

04:38

lot more than you would charge the call option buyer

04:41

of a t and t for that twenty percent above

04:44

the stock price call option that expired at the same

04:47

time Well the question then that black scholes tries to

04:50

answer is just how much more you would charge for

04:53

the highly volatile or high beta quotient stock option versus

04:57

that of tea If you really care about the math

05:00

well then a We're sorry B you should probably take

05:03

a real investing course Not this one and go to

05:06

real business school and see you may need a hobby 00:05:09.79 --> [endTime] We suggest golf or or needle point I'm going

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