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Implied volatility | Finance & Capital Markets | Khan Academy - YouTube
Channel: Khan Academy
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Voiceover: In the last video,
we already got an overview
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that if you give me a stock price,
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and an exercise price,
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and a risk-free interest rate,
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and a time to expiration
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and the volatility or
the standard deviation
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of the log returns,
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if you give me these six things,
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I can put these into the
Black-Scholes Formula,
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so Black-Scholes Formula,
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and I will output for
you the appropriate price
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for this European call option.
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So it sounds all very straightforward,
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and some of this is straightforward.
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The stock price is easy to look up.
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The exercise price,
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well, that's part of the contract.
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You know that.
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The risk-free interest rate,
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there are good proxies for it,
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money market funds,
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there's government debt, things like that,
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so that's pretty easy to figure out,
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or at least approximate.
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The time to expiration,
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well you know that,
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you know what today's date is.
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You know when this
thing's going to expire,
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so that's pretty straightforward.
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Now let's think a little
bit about volatility,
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so how do you actually
measure the standard deviation
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of log returns.
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Now, one of the assumption
about Black-Scholes Formula
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is that this is a constant thing.
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This is just some intrinsic
propety of this security.
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Well, the only way that
you can at least attempt
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to estimate it is by
looking at the history
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of the standard deviation of log returns.
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The way that people
would normally do it is
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they'll say, "Okay, what
has historically been
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"the standard deviation of log
returns over some time period
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"where that security has not
changed in some dramatic way?"
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And then use that as the input,
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and then they would
come up with some price.
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Well, that's all interesting,
but it's very important to know
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that this is an estimate.
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This right over here is an estimate.
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There's no way of us actually
knowing the actual intrinsic
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and it's even up for
grabs whether there is,
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whether you can even as assume
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that there's some constant
intrinsic property
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as this volatility that's
going to be constant
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over the life of this option.
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So this is just an estimate.
It's important to know that.
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But what is interesting is that
these things are being traded.
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These call options are being
traded all of the time,
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and so you could actually look
up the price of this call option.
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You could look up a call
option with this stock price,
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this exercise price.
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You know what these two things are,
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and you could say, "Hey, look.
This traded for $3 just now."
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So you actually can
figure out what this is,
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which raises a very, very
interesting question.
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If you know exactly what this is
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because you know what the
market is pricing this at,
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so let me write this.
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You know what the market
believes this price should be,
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so the market belief,
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and it's based on their
actual transcations,
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so it's based on transactions.
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This is what the market is
saying the correct price is.
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You can figure that out,
you can just look that up.
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You can figure out all
of this other stuff.
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Can you then take this
output plus all of these
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to work backwards through
Black-Scholes to figure out
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what the market is guessing about this,
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or what the market is
estimating about that.
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The answer is yes.
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This is where this whole idea
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about when people talk
about what is the volatility
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in the market, or even where
are carton volatility rates,
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or even what does the market
expect volatility to be?
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How do we know what the market
expects volatility to be?
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Well, we can look at what
markets are trading options at.
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We could look at all of
this other information
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that would be inputted into
Black-Scholes equation,
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and we can say, "Hey,
look. Based on the fact
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"that the market is
paying $5 for this option,
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"and all of these other variables,
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"they must assume that the
standard deviation of log returns
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"for this security is now this."
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Now, let's say that
things get really scary.
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The market becomes a
lot dicier and choppier.
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Well then, people are gonna
pay more for this option.
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It's gonna drive the
implied volatility up.
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So when you hear people talk
about implied volatility,
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or implied vol, and there are even people
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who will actually trade
on implied volatility,
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This is what they're talking about.
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They're saying, "Look. Options
are trading all the time."
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Can we use that price, the market belief
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of what those prices should be,
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and then work backwards
through Black-Scholes
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to figure out, because we
know these are all facts.
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We can look these things up,
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but based on what the market
is trading these options at,
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can we figure out what
the implied volatility,
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what the implied market
belief about volatility
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for that security is,
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and then we can actually aggregate it
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across many, many securities,
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and come up with an implied volatility
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for given markets at a time.
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So it's a very, very,
very interesting idea,
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but in some levels, it's
kind of a basic one.
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You're just working backwards
through Black-Scholes.
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