Black's Model

Also called the “Black-76,” (no, not a cool car) Black’s Model is a revamped version of the Black-Scholes model, an options pricing model.

The Black-76 allowed for the valuing of future options, unlike the OG Black-Scholes model. Using Black’s model, financial institutions could find a price to buy or sell an option at any point in the future, without putting up any money in the present time (“what a great idea,” the financiers of the world said in 1976).

Like all models, Black’s model does have its assumptions, but these assumptions (like log-distributed prices) are pretty reasonable most of the time. You’ll find mutual funds, hedge funds, and global banks using some form of Black’s model to calculate interest rate derivatives, caps, and floors, among other things.

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

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right people Yeah it sounds like something that has to

00:09

do with xu fashion right Black scholes are all the

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rage in paris this year only instead of a bright

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

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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

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share today You see i owe our chief investment officer

00:36

of the milwaukee cardiologists investment club wanted by a call

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option on disney with a strike price at one hundred

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

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do you want to buy this Why do you want

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to compete against goldman sachs Best and brightest people who

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make twenty five million dollars a year Not really sure

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about that But regardless you all believe disney is going

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to spike in its stock price the next four months

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And you want to take advantage of it Well how

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much should that hundred twenty dollars Strike stock option cost

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Expires in four months All right this call option is

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notably an american style option that is in american cell

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option You can sell the option any day until it

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expires And traditional black scholes modeling is based on the

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european style option which expires on lee on one day

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at the very end of the period in which the

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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

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a global company right But here we just want to

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give you the basic gist of how black scholes works

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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

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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

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

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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

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Still be cheap because so far out of the money

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right And yes there tons of mathematical errors in the

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black scholes model not least of which is the fact

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that past performance of stocks is not necessarily any indication

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

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calculate its volatility here so we got all kinds of

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problems going in Problem is we have nothing better No

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other better option methodology to value things So we used

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black scholes Alright so since we have no other ways

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

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

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what we do essentially the black scholes model takes an

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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

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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

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time Well the question then that black scholes tries to

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answer is just how much more you would charge for

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the highly volatile or high beta quotient stock option versus

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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

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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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