When you buy an option, you can pick from a range of strike prices and a range of expiration dates. It's like picking the toppings on a pizza. You can mix 'n' match however you like.
Each option comes with a measurable amount of implied volatility. A volatility smile applies to options with the same expiration date but different strike prices. It relates to the shape made by graphing the implied volatility. The measure gets higher the further away the strike price gets from the current trading price for an asset. If a stock is trading at $20, implied volatility for the $20 strike price will be low. However, the further away from the current price you go (in either direction), the higher implied volatility gets.
So...with the stock trading at $20, the $15 strike price will have higher volatility than the $18 strike price. Meanwhile, the $25 strike price will have higher implied volatility than the $22 strike price. And $18 and $22 strike prices will have similar implied volatility.
The implied volatility here applies to the options themselves, rather than the underlying asset (like a stock). The prices for the options themselves are more likely to move around; that's because demand is higher for options further in-the-money or further out-of-the-money than it is for options closer to the at-the-money level.
Graph the IV for all strike prices for the same underlying asset and the same expiration date, and the graph will look like a smile. It's not true for all options, but it does hold for most. This situation comes as options show high levels of implied volatility for both extreme in-the-money options and extreme out-of-the-money ones. Meanwhile, IV is low for at-the-money options. The extremes are high...the middle is low. Like a smile. Ish.
Related or Semi-related Video
Finance: What is the Black Scholes Model...11788 Views
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
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