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## Finance and capital markets

### Unit 9: Lesson 7

Black-Scholes formula

# Implied volatility

Created by Sal Khan.

## Want to join the conversation?

• •  A log return is another way of describing when interest is continuously compounded. It is a measure of exponential growth.

For example, if something grows at 5% continuously compounded, it will grow at an exponential rate because each additional 5% will be bigger than the previous 5%.
• I'm looking for information on the Newton / Raphson method. I entered those words into your search field and was led to this video. And although the video is interesting it seems to have little relation to my search string. • If the market is anticipating a possible crash, then Puts should be priced higher than Calls. The implied volatility from looking at Puts would therefore be higher than the implied volatility from looking at Calls. How are these 2 different volatility values reconciled, given that the volatility variable is a single scalar value, and is directionless? • The implied volatility is the level of ”sigma” replaced into the BS formula that will give you the lowest difference between the market price (that you already know) of the option and the price calculated in the BS model. The thing is, that the implied volatility shoud be calculated with the newton-raphson algoritm, in a more difficult way. If you go backwards in the BSF, you will only get the real volatility from the market (of that moment you calculated it). So, the point is, the implied volatility is a theoretical level of the volatility that, replaced into the BSF will give you the most reality-like price. Please, tell me if I am wrong. Sorry for my bad english.
• so is sal saying here that the B.S.F isn't the only way options are priced? I went into this thinking it was a formula for pricing options, based on using historical volatility. But now he's saying you can figure out volatility based on options prices! So which came first...the price of the option (using this formula) or the volatility?
Are options originally priced using this formula, and then subjected to market forces? • Sal,

First of all, thank you... you provide great instruction. My question comes into play around . If we know S(o), X, r, T, AND C(o), then we can obviously determine sigma, as you indicated. My question is this: if the value of the option C(o) is constantly changing based on market transactions, then why is sigma, which is an estimate, even included in the formula? Why does it matter? Sure, we can determine an implied volatility and apply it across various markets, but why does that matter when we already know the market value of all securities?
(1 vote) • The option formula is trying to use a statistical approach to figure out the likelihood that the market price will go above the exercise price. Imagine a call option that is out of the money, Let's say the stock is at 15 and the strike price is 20. If the stock normally moves up and down from day to day by 1, then you are not going to be very excited about the chance that the option will finish in the money (ie with the stock above 20). But let's suppose that the stock price is very volatile. It still averages 15, but some days it's 25 and some days it's 5. Isn't the option worth more in that second situation? A lot more, right?
• Is there a formula that can be used to determine the implied volatility, or can it only be estimated using an iterative approach?
(1 vote) • options use days to expiry rather than years, so how would time be enter in these conditions.
(1 vote) • secondly can you use 10 yr treasury as the risk free rate..
(1 vote) • Will there be more videos on the Black-Scholes Formula coming soon?
(1 vote) • Something's not quite making sense to me.

I've been trying to look for a good explanation of implied vol but still can't find it.

The Call REQUIRES five parameters: S(0), X, T, R and Sigma. (ASSUMPTION)

Of these five, Sigma is hard to find, so we get the value of C and "reverse engineer" to fnd Sigma.

Hold on!

In the line I wrote above, labelled ASSUMPTION, to find C, we REQUIRE all 5 parameters, INCLUDING Sigma.

So if we use C to "reverse engineer" to find Sigma, that must mean we already had Sigma in the first place (or else, how did we manage to find C)?

Furthermore, we also said we need all 5 parameters to find C but if we somehow have found C, why do we care about "reverse engineering" to find Sigma?
(1 vote) 