looking for ... Volatility Smiles

I was talking to my brother-in-law about Call options and he said: "Even volatilty can be volatile".
That got me thinking, so ...

>That was a mistake.
Pay attention!
Remember when we talked about selling a Call?
We used the magic Black Scholes formula to estimate the premium: C.
That formula requires the Strike price, the Stock price, the Time to expiry, some Risk-free rate
... and some Volatility.

In fact, you don't use the standard, garden variety volatility that you'd calculate from historical returns.
You use whatever value allows the magic BS formula to accurately predict the Call price.

>And that's the "Implied Volatility", right?
Right! So if you look up IBM, for example, you'd find this:
The price of IBM stock (at that time) was $82.
See the Volatility values needed so that BS would generate a Call price equal to the Actual selling price of the option?
>They vary with the Strike price, eh?
Exactly ... and that's where the Volatility Smile comes in.
I thought it'd be interesting if I could find examples of this "smile" and ...

>Just vary the Strike price in the BS formula.
No. We have to look at actual, real-live Strike prices and, for each, vary the Volatility in BS so we get the actual, real-live Option price.

>Don't tell me! You have a spreadsheet.
What else? It looks like this:

>Huh? That's a volatility smile? It looks more like a ...
A volatility grimace. I know! I know!
What I'm looking for is some Call option that ... uh ... that ...

>That smiles?
You got it.

Here are some examples of Implied Volatility versus Strike Price.:

>Have you ever found volatilities that have a nice smile?
Yes. The charts above are for options that expire in (about) three months.

Here's one that expires in (about) one month:

>So I click on the picture of the spreadsheet, to download it?

>And will I know what to do?
There's an Explain sheet, like so:

>Okay, so why would one expect to see a Volatility "smile"?
I have no idea. It's a characteristic of people who buy & sell options.
Normally, to match a larger Strike price, the implied Volatility should go down.
If it goes up, it suggests that option traders are willing to pay more for the option.
In a sense, then, "bumps" in the curve indicate that such an option is in demand, so the actual trading price of the option is larger than "normal", so ...

>So there's a bump in the chart.
Yeah ... I guess.