Black Scholes Model

Finance allah shmoop What is the black scholes model All

right people Yeah it sounds like something that has to

do with xu fashion right Black scholes are all the

rage in paris this year only instead of a bright

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

in there as well right Somewhere Okay Okay The black

scholes stock option valuation model is actually a mathematical formula

and a whole system for coming up with stock option

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

share today You see i owe our chief investment officer

of the milwaukee cardiologists investment club wanted by a call

option on disney with a strike price at one hundred

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

do you want to buy this Why do you want

to compete against goldman sachs Best and brightest people who

make twenty five million dollars a year Not really sure

about that But regardless you all believe disney is going

to spike in its stock price the next four months

And you want to take advantage of it Well how

much should that hundred twenty dollars Strike stock option cost

Expires in four months All right this call option is

notably an american style option that is in american cell

option You can sell the option any day until it

expires And traditional black scholes modeling is based on the

european style option which expires on lee on one day

at the very end of the period in which the

option is alive Got it So keep the approaching where

you gotta think about american sell options are worth more

because while you have more options in the option so

the valuations to be a little bit different paying on

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

a global company right But here we just want to

give you the basic gist of how black scholes works

conceptually and save the math for a more advanced video

The key idea is that the more volatile the stock

the more volatile should be the call option underlying it

and a different strike price is relative to the existing

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

him as well if you think about it if they

were looking at one hundred dollars strike price option with

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

as if they were looking at a one hundred fifty

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

pretty much stay cheap Whether disney was one hundred box

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

Still be cheap because so far out of the money

right And yes there tons of mathematical errors in the

black scholes model not least of which is the fact

that past performance of stocks is not necessarily any indication

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

calculate its volatility here so we got all kinds of

problems going in Problem is we have nothing better No

other better option methodology to value things So we used

black scholes Alright so since we have no other ways

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

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

what we do essentially the black scholes model takes an

average waiting of a stock price over a given duration

and multiplies it by some formula based on its volatility

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

of years Check out the line graph for a t

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

only sits there pays a dividend and phone prices are

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

has been a hoot of a ride for the good

the bad the ugly in the form of quotient a

digital coupon and company Really volatile rocky mountains peaks valleys

all kinds of stuff Good bad ugly Well you can

imagine that a call option price with a strike price

twenty percent above it and tease price would not be

very expensive because given the low volatility of at and

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

out above that twenty percent line that was pretty low

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

it did it on lee did it by a very

small amount So if you were writing life insurance against

the financial death thing he broke out of that twenty

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

right But then if you look at quotient well a

price twenty percent above well here or here here seems

highly likely because the stock trades in huge gaps up

and down of a few percentage is a day i

e the same volatility per day that a teen t

has per month So if you are the person writing

that call option or selling that call option to these

kind of loving people in milwaukee or people like him

and knowing that it would put you on the hook

to provide shares at a price roughly twenty percent above

where the stock is currently trading well of course you

would charge the call option buyer of quotient ah whole

lot more than you would charge the call option buyer

of a t and t for that twenty percent above

the stock price call option that expired at the same

time Well the question then that black scholes tries to

answer is just how much more you would charge for

the highly volatile or high beta quotient stock option versus

that of tea If you really care about the math

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

a real investing course Not this one and go to

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