Options Volatility: Projected or Implied Volatility
By John Summa, CTA, PhD, Founder of OptionsNerd.com
Most traders generally think of the strike price in relation to the underlying price and how much time remains on the option as the key fundamentals of pricing. This approach, however, often leads to some negative surprises due to unnoticed changes in implied volatility (IV). In this part of the tutorial, we'll learn how IV impacts option prices and how IV differs from historical volatility (covered in the previous chapter).
Options volatility is one of the least understood variables behind the movement of daily price changes of an option, but the role volatility plays is quite easy to understand. When an option is quoted throughout the market day, the prices in the form of bids and asks don't tell you much about its valuation in terms of fundamentals. Like any asset with a market price, such prices may actually deviate from the fundamentals due to expected or projected events not captured by asset pricing models  and that difference largely can be attributed to implied volatility (IV).
A Common IV Pitfall
Let's say that an option trader is interested in buying high beta tech stock call options because he or she is bullish on the stock. Because high beta stocks have the potential to make big moves, the trader thinks that the potential for profit is higher when buying call options. However, options on these stocks, especially around pending news, can experience a change in the price even without movement of the underlying. Prices may move higher (again even without a stock price move) simply because there is a big move expected. And this will typically occur on the puts and calls. In this case, IV is going to be high. (To learn more, read Beta: Gauging Price Fluctuations.)
When the news comes out and the stock moves higher as expected by the trader, the results are often disappointing in terms of changes in the option price and what Delta implies the price should actually be. The reason is that the reverse movement in IV occurs, IV falls after the news (like letting the air out of a balloon) and the IV (and with it lots of extrinsic value) deflates quickly. With this drop in IV, the call buyer is often left miffed as to why he or she did not make much, if anything, on his or her speculative purchase of calls. (For related reading, see Getting To Know The "Greeks" and Price Plunging? Buy A Put!)
Now, when it comes to put buying, there can be both good and bad surprises. The same process outlined above will operate when buying puts, especially if puts are purchased during bearish cycles in the stock (IV typically for most large cap stocks will be pumped up at this point). If the puts are purchased when they are "cheap" in terms of IV levels (this occurs when you buy the puts when the trend has been upward and price action relatively uniform (and assuming no big pending news outcome), then it is possible for IV to rise if the stock enters a bearish cycle. This can lead to a positive surprise in the change of the option price, provided you purchased the option when the IV was low near the market top. Here, the price would increase more than that which is suggested by Delta (leaving any significant changes due to Theta or the rate of time value decay aside for now).
How does IV get calculated?
IV is best understood by reference to an option pricing model, such as the BlackScholes model. As you can see in Figure 5, there are five main ingredients or inputs (rightfacing arrows). These are:
 Stock price
 Strike price
 Historical volatility
 Days to expiration
 Riskfree rate of interest.
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Figure 5: BlackScholes options pricing model inputs 
Figure 6 helps to explain the fact that option prices in the marketplace tend to deviate from theoretical prices. This fact is captured in the reverse flow model in Figure 6, which shows that the price output is now an input and the volatility input is now an output. The model is solved for volatility when market price is used as an input, and this essentially is how IV gets calculated. Therefore, if market price is greater than it was the day before (all other things remaining the same), the explanation for that difference is attributed to implied volatility.
Copyright © 2007 Investopedia.com 
Figure 6: BlackScholes options pricing model reversed 
The exact derivation of IV we can leave to mathematicians. Practically speaking, if market price is above theoretical prices, this is simply the premium placed on an option's market price by market participants. They are expecting greater volatility than SV currently is signaling, and therefore the imputed volatility, or IV, is telling us what the best guess of the marketplace is for the future volatility of the underlying stock.
Conclusion
Implied volatility (IV) measures the market's expected best guess of future volatility of the underlying. It is calculated using the market price of an option, along with other inputs used in price models, and then solving for volatility, in effect by working backwards to solve the price equation (it is actually an iterative process). While this may oversimplify the math somewhat, what is important to remember is that IV captures the degree of excess or deficit value on an option in terms of its theoretical price. Many broker trading platforms provide an IV value for each strike (and usually an average IV for all the stock's options), so you don't need to do the calculation. What should be done, instead, is an analysis of how high or low IV is in relation to previous levels so you can avoid one of the common mistakes made by traders: buying high IV and selling low IV.
Options Volatility: Valuation

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