## 05 May 2008

### Implied Volatility

We have now gone through the six inputs into the Black Scholes Option Pricing Model (as proxy for any model in use). The sixth input, volatility, is problematic as a forward guestimation of volatility is used, it is equivocal; different traders will have different ideas of what this input should be.

For instance, I may believe a particular option’s fair value is \$2.65 using my own volatility projection, but when I go into the market it may be \$3.75, for the sake of example. What is going on?

What is happening here is that the “market” believes that the future volatility of the underlier is going to be a lot more volatile than you do. How does the market do that? Simply by the bids and asks in the market depth and by arbitrage. Depending on your data supplier or broker, there may be a figure supplied called “Implied Volatility”.

This is worked out by algebra, using the first five unequivocal inputs into the option pricing model and the tradable price, which is also unequivocal at that point in time, to derive a volatility figure. So what we are saying here, is that the volatility “implied” by the option’s price is x; Hence “Implied Volatility”.

Let’s look at an example:

* The underlier (XYZ) is trading at 52.75 with no dividend payable.
* I’m looking the XYZ \$55.00 call option, which expires in 63 days, which I can buy for \$2.45.
* Risk free interest rates are 5%

By plugging those known values into our option pricing model, (in this case I’m using the Cox, Ross & Rubinstein Binomial Model) we can calculate an implied volatility of 36.7%.

So how does that help us?

Quite simply, it is from this figure that you can determine whether the option is fair value or not.

Often in various textbooks and spots around the Internet, the suggestion is to compare Implied Volatility (IV) to Historical Volatility (HV) to determine whether an option is over, or under priced. This is a gross oversimplification. Historical volatility should be studied to get an idea of the volatility characteristics of the underlier, but says very little about what volatility will be going forward.

Remember Implied Volatility looks forward, while Historical Volatility looks backward. For instance, IV can rise before an earnings announcement, sometimes quite dramatically, even though the underlying stock has become very non-volatile as the market waits for the announcement. The market is therefore making a judgment on the volatility once earnings are released. IV invariable drops equally dramatically once the earnings are actually released, as the market discounts the move from the announcement.

The history of Implied Volatility can be plotted on a chart, just like Historical Volatility, again to see the characteristics of IV and how it changes under various circumstances. There are various vendors of IV data, but there is a free source from www. cboe.com from where I sourced the following chart:

The IV plotted in the above is an average of near expiry, implied volatilities across several strikes, so the IV of the particular option you’re interested in may vary somewhat from what is represented here. It does however give the trader an idea of the ebb and flow of volatility over time. You can use this information to make volatility projections and to bet on future volatility fluctuations with a suitable strategy.

The standard wisdom is to buy low volatility and sell high volatility. While this may make sense on the face of it, it isn’t always the wisest thing to do, but more on that later.

Next - More On Volatility

so we cannot compare the implied volatility with historical volatility.

Wayne said...

Yes you can, it just doesn't necessarily tell you whether an option is expensive or cheap at any point in time.

It is most certainly one thing that should be taken into consideration, I use HV as a tool to make volatility projections as it tells me the underlier's volatility characteristics.

But a direct comparison? No.

I can only reiterate that HV looks backward, while IV looks forward.

Maybe I should do a post specifically on this topic.

Cheers

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