Black Scholes Model

It sounds like something that has to do with shoe fashion. “Black Scholes are all the rage in Paris this year!" Only, instead of a bright red sole, theirs is black. And isn’t there a Doctor in there as well somewhere?

Okay, okay…the Black Scholes stock option valuation model is actually a mathematical formula, and a system for coming up with stock option prices.

Example.

Disney is trading at $100 a share today. You, the CIO of the Milwaukee Cardiologists Investment Club, want to buy a call option on Disney with strike price at $120, which won’t expire for about 4 months. How much should that call option cost?

Well, this call option is notably an American style option. Traditional Black Scholes modeling is based on the European style option, which expires only on one day at the end of the period in which the option is alive. So the valuations will be a little bit different depending on your continent. But here we just want to give you the basic gist. The key idea is that, the more volatile the stock, the more volatile should be the call option underlying it. And yes, there are tons of mathematical errors in this model, not the least of which is the fact that past performance of stocks is not necessarily any indication of future performance. But since we have no other way to navigate our future prognostications other than driving a car by looking in the rear-view mirror, then that’s what we have to do.

Essentially, the Black Scholes model takes an average weighting of a stock price over a given duration, and multiplies it by some formula of its volatility.

So...take AT&T. A stock with very low volatility the last several of years. Quotient (a digital coupon company), on the other hand, has been a hoot of a ride for the good, the bad, and the ugly.

You can imagine that a call option priced 20% above AT&T’s price would not be very expensive, because given the low volatility of AT&T stock, the odds that the stock itself breaks out above that 20% line is pretty low. But if you look at Quotient, a price 20% above it seems highly likely, because the stock trades in gaps up and down of a few percentages per day, i.e. the same volatility AT&T has per month.

So if you are the person writing that call option, or selling a call option, which put you on the hook to provide shares at a price roughly 20% above where the stock was currently trading, of course you would charge the call option buyer of Quotient a whole lot more than you would charge the call option buyer of AT&T.

The question that Black Scholes tries to answer is just how much more you would charge for the highly volatile or high-beta Quotient stock option v. that of AT&T.

If you really care about the math, then A) we’re sorry, B) You should probably take a real investing course and go to business school, and C) you may need a hobby. We suggest golf. Or needlepoint.

Related or Semi-related Video

Finance: What is the Black Scholes Model...11788 Views

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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

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scholes stock option valuation model is actually a mathematical formula

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and a whole system for coming up with stock option

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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

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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

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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

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at the very end of the period in which the

01:24

option is alive Got it So keep the approaching where

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you gotta think about american sell options are worth more

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because while you have more options in the option so

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the valuations to be a little bit different paying on

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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

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The key idea is that the more volatile the stock

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the more volatile should be the call option underlying it

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and a different strike price is relative to the existing

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

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him as well if you think about it if they

02:03

were looking at one hundred dollars strike price option with

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

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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

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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

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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

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and multiplies it by some formula based on its volatility

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

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of years Check out the line graph for a t

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

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only sits there pays a dividend and phone prices are

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

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has been a hoot of a ride for the good

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the bad the ugly in the form of quotient a

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digital coupon and company Really volatile rocky mountains peaks valleys

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all kinds of stuff Good bad ugly Well you can

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imagine that a call option price with a strike price

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twenty percent above it and tease price would not be

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very expensive because given the low volatility of at and

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

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out above that twenty percent line that was pretty low

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

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it did it on lee did it by a very

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small amount So if you were writing life insurance against

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the financial death thing he broke out of that twenty

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

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right But then if you look at quotient well a

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price twenty percent above well here or here here seems

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highly likely because the stock trades in huge gaps up

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and down of a few percentage is a day i

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e the same volatility per day that a teen t

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has per month So if you are the person writing

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that call option or selling that call option to these

04:25

kind of loving people in milwaukee or people like him

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and knowing that it would put you on the hook

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to provide shares at a price roughly twenty percent above

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where the stock is currently trading well of course you

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would charge the call option buyer of quotient ah whole

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lot more than you would charge the call option buyer

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of a t and t for that twenty percent above

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the stock price call option that expired at the same

04:47

time Well the question then that black scholes tries to

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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

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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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