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# Implied Volatility

Implied volatility (IV) is generally a topic beginners tend to struggle with and yet it is one of the most important concepts for options traders.  It is called « implied » volatility because it is derived from a pricing model like Black & Scholes.  As B&S and its numerous variants are closed equations, it is implied in the sense that theory has to meet reality, i.e. the pricing model is compared with actual options prices to determine IV.  The result is that IV represents an estimate of future volatility.  In that sense, it is radically different from historical volatility calculated from standard deviation.  Also IV can help the trader calculate non-directional probability.  This is thus a critical component of options trading which may be helpful when trying to determine the likelihood of the underlying reaching a specific price by a certain time.  One should keep in mind these 2 pieces of information:

• IV does not provide any information on direction and
• It remains probabilistic i.e. it cannot be directly associated with the Greeks although it is closely linked to Vega.

Basically IV predicts the size of market swings either way.

IV is determined from actual prices, so understanding IV means you can enter an options trade knowing the market’s opinion each time, yet one should nonetheless oversimplify it to the extent that low IV literally means cheap (low premium) or conversely that high IV is expensive (high premium).   While certain trading strategies are more suitable in either low IV or high IV environments, one should always look at it in probabilistic terms.

IV, or its index proxy (RVX for the RUT, VIX for SPX) is often analysed via IVR (IV Ranking) or IVP (IV Percentile).

## Volatility

There are many different types of volatility including average true range (ATR), but options traders tend to focus more on historical and implied volatilities.  Historical volatility is the annualised standard deviation of past price movements of the underlying.  Many options calculators exist, and one can also use a simple Excel formula for that matter.

In contrast, let’s repeat it: IV is derived from an option’s price and shows what the market “implies” about the underlying’s volatility in the future.  Implied volatility is one of six inputs used in an options pricing model (e.g. B&S), but it’s the only one that is not directly observable in the market itself.  IV can only be determined by knowing the other five variables and solving for it using a given model (and none of them are perfect…).  Again, there are good calculators available, starting with the excellent Hoadley’s package for Excel.  Implied volatility acts as a critical surrogate for option value – the higher the IV, the higher the option premium, but also higher the risk of larger movements.

## Volatility from another angle

CBOE publishes a number of volatility related indices, starting with RVX based on the RUT and the well known VIX based on SPX.  It is an average of implied volatilities across available strikes over a period of 30 days.  Another important source of information is VIXCentral which calculates and displays the term structure of volatility over time.  Although a little advanced, these tools are essential in effective options trading.

## Volatility Skew

Since most option trading volume usually occurs in at-the-money (ATM) options, these are the contracts generally used to calculate IV.  Once we know the price of the ATM options, we can use an options pricing model and a little algebra to solve for the implied volatility.  That being said, life is not always that simple… In reality, IV often varies according to strikes (hence newer variants of B&S model where it was assumed constant).  Curves can be drawn, there showing a volatility skew, e.g. a volatility « smile ».  This is a more advanced topic.  Do not get frightened :-), OM wants to keep the required theoretical knowledge to the absolute minimum.  Please feel free to contact us about OM’s prerequisites to trade options (in our view).

Lastly, a few references to educational resources.  Options brokers obviously want your business and often do a fairly good job at getting the novice trader acquainted, yet beginners should not rely too much on those tutorials without the assistance of a coach.