So far in this series, we've discussed what volatility is and walked through the basic math behind implied volatility. There are many option calculators that will provide these calculations with much more accuracy then the "quick and dirty" math used in my previous post. Now let's try TradeKing's probability calculators and apply it to a practical trading example. 

Everybody wishes they'd bought Google at 85 when it first went public. The question now is: what is the next Google stopping point? If you're like me and practically all my trading friends, you have an opinion on the downside and the upside for Google. Let's use the options market place to try to answer what are the highest and lowest points the market expects by the June expiration date.

Using TradeKing's probability calculator input the underlying stock symbol for Google (GOOG) and then select the expiration, June. Automatically the price of the underlying (427.55), the ATM implied volatility for the June expiration (45.64%), the risk free interested rate (4.6859%) and dividend information for the stock appear. On the right hand side you will see the target prices, in this example based on a one standard deviation move (555.15 and 312.30). If you look at the bottom of the screen, you will see that based on our inputs, there's a 68.26% chance of Google finishing between the two prices (555.15 and 312.30), a 16.18% of it finishing above the highest target price (555.15), and a 15.56% chance of it finishing below the lowest target price (312.30).

 

(The reason there's a slight better percentage chance of reaching the upside target is because this model correctly uses a log normal distribution, as opposed to the basic normal distribution described in previous posts.)

There is also some bonus information. See the "Probability of Touching'" fields on the right hand side of the screen, below the target prices? TradeKing's calculator shows you not only the probability at expiration of the stock finishing above, between or below targets -- it also calculates the chances of Google actually touching the target points at any point before the expiration date.  So there is a 36.54% chance of Google touching 555.15 and a 27.64% chance of it touching 312.30. Notice that the probability of it touching the target points is about double the probability of it expiring.

To summarize, with Google trading at 427.55 on January 23, 2006 and the June options trading at an implied volatility of 45.64%, the options marketplace as a whole says there is reasonable chance for the stock to touch 555.15 on the upside and 312.30 on the downside. This is based on a one standard deviation move of the stock.

Next week's post will tackle another, slightly less volatile example. It'll also offer some hard facts on using volatility to manage risk -- there are more ways to trade smart with volatility than you may realize. See you soon!

Regards,
Brian (OG)

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options.

While implied volatility represents the consensus of the marketplace as to the future level of stock price volatility there is no guarantee that this forecast will be correct.

Hi,

I've often heard about stocks getting ''pinned'' to options strike price on expiration day. Is this a fact? I've observed this a few times, but may be those were just coincidences.

For example, from this page: http://finance.yahoo.com/q/op?s=GOOG, since the highest open interest and volume occurred at $360, does it mean there's a high probability that the stock will close very near $360 this Friday?

Thanks for your information.

john

There a little of “What comes first - the chicken or the Egg”, in that, the bulk of the open interest, in general, follows where the stock is at in the near term expiration. So is the stock going to where the open interest is or is the open interest centering around where the current stock price is? Bottom line, there is some truth to your statement, but I would not bet the farm on it.

Regards,
Brian

Excellent question and one I get asked quite often. Yes, it is sometimes true that a stock will expire close to or right on a strike price and there is a logical reason for it. Each expiration as market makers roll options and start to re-hedge their positions (or Deltas) the stock will tend to gravitate to the closest strike. This move is usually small and only happens when the stock is near a strike. The roll of market makers positions might move a stock a few nickels or dimes, but not usually full points. I have seen big movements in Google though, mainly because a few points in a $400 stock is not as big a move on a percentage basis. (continued below)

Thanks, Brian.

john

What do we input as risk free interest rate? T-note, T-bill, what term, etc... Thanks for sharing your knowledge! I love your blog,

Ivolatility.com powers our calculators and they are very good with interest rates. Specifically, they use the LIBOR rates for terms up to one year, and ISDA interest rate swaps rates for longer terms. They take interest rates to the extreme; bottom line is a change in interest rates and dividends have a small effect on short term options prices. I am going to have a posting soon about Rho (Greek on interest) and it will explain this further.
Regards,
Brian (OG)