## History of the Volatility World: Part I

### A refresher on volatility's two forms

by 1/14/2013 7:52 AM

We get a little technical here at times -- it's often 'VIX this and VIX that' -- so how about we take a day or so each week to get back to basics? Call this "Understanding Volatility," Part 1.

Volatility, in an options-related context, refers to the rate and range of motion of an underlying instrument. It is a standard deviation converted to a user-friendly format. It comes in two forms.

One is called historical (or realized) volatility (HV or RV for short). Here's the definition from Investopedia:

The realized volatility of a financial instrument over a given time period. Generally, this measure is calculated by determining the average deviation from the average price of a financial instrument in the given time period. Standard deviation is the most common but not the only way to calculate historical volatility.

Not sure how you calculate HV without using a formula to calculate standard deviation, but not sure that's crucial as far as basic knowledge is concerned.

Typically, we'll say something like "The 10-day HV of the SPX is 15." In plain English, that tells you that the historical volatility of the S&P 500 Index (SPX) was 15 over the last 10 trading days.

Implied volatility (IV) is the other volatility we refer to. The price of every option on every board you see is determined by a series of fixed variables and one moving variable. The fixed variables are the absolute price of the underlying instrument, the strike price of the option, time remaining until expiration, and the cost of carry until expiration (interest less dividends). The moving variable is the implied volatility.

Since we know the end result of the formula (the price of the option you see on the board) we can calculate for implied volatility of every option.

The IV you see associated with each series shows you the market's estimation of historical volatility going forward from now until when the option expires.

You may notice some oddities. Calls and puts of the same strike and class should trade at the same implied volatility. If they don't, an arbitrage trader could theoretically trade both sides (buy calls and sell puts, or sell calls/buy puts) -- creating a synthetic version of the stock -- and could then trade the actual stock against it and lock in profits. But sometimes your trading screen will suggest this trade (called a reversal or conversion) lines up. Specifically, it will likely tell you the puts trade at a higher implied volatility than the calls.

Rest assured, there's no free money there. The stock is probably hard to borrow, meaning anyone going short the stock will have to pay interest on the short. Any extra money you receive for selling puts goes out the window on the borrow. No trading system I've ever seen adjusts for this. When you see this happen, simply average the IV on the call and corresponding put to get the real IV of that strike.

You may also notice not all strike prices trade at the same volatility. Out-of-the-money (OTM) puts virtually always trade at a higher IV than at-the-money puts. This is called skew, and it's a function of the natural tendencies of investors as far as options usage is concerned. The world at large is net long the market and uses out-of-the-money puts to effectively insure their portfolios, whereas they generally write OTM calls to earn income versus said portfolios. There are obviously exceptions to this -- for example a stock with takeover rumors may see skew towards dollar-cheap OTM calls -- but the majority of individual names and essentially all index products trade at what we call negative skew.

How does HV relate to IV, and where does the CBOE Market Volatility Index (VIX) figure into all this? We'll answer these questions and more in future episodes.

Disclaimer: The views represented on this blog are those of the individual author's only, and do not necessarily represent the views of Schaeffer's Investment Research.