Implied volatility is the volatility that is implied from the market price of an option. It differs from historical volatility as the latter is estimated by already existing prices, whereas implied volatility is estimated indirectly via a theoretical valuation model.

As we have learnt, if we insert certain parameter values in the Black & Scholes model we can estimate the theoretical price of an option. In order to find the implied volatility we can place in the equations the real market price of an option and leave the input *σ* as the unknown parameter. All the other factors that are incorporated in the model are already known (*S, X, T, r*). By using mathematical methods for solving complex equations, we can find the corresponding *σ* for an option real market price instead of entering the historical volatility to find its theoretical price. In other words we estimate the expected volatility of the underline security that is implied by the real market price of an option.

A practical consequence of the above estimation is that every different call and put has different implied volatility. To estimate only one value of implied volatility for all the options of the underline security, we must take an average of the implied volatilities of different strike prices and expirations of calls and puts. There are many approaches as to which particular strikes and expirations someone can use.

The notion of implied volatility is very important in options trading because if it has a high value then the option might be overvalued. Also implied volatility is mean reverting. When it is on the highs of its historical diagram range then the chances are that it will decline to revert to its average in the future and when it is on the lows then the chances are it will rise in order to revert to the average. Below, is the historical and implied volatility diagram of a stock.

Notice that when historical volatility at point 2 is very low, implied volatility at point 1 is very high. Options traders are anticipating high price movement of the stock and to benefit or protect already existing positions (hedging), they buy calls and puts (depending on their bias). The high demand raises their price and this is mirrored in the high implied volatility. In this particular case it seems that they were right because from point 2 the historical volatility of returns is rising rapidly from about 23% to almost 35%, irrelevantly of the direction of the underline security.

Notice also that points 3 and 5 define the lows of the implied volatility curve, whereas 1 and 4 define the highs of the range. In that sense, we can infer with high degree of accuracy (but not 100%), that these are the boundaries that define if the volatility is high or low, in order to make a decision if it is better for us to sell or buy options.

High implied volatility most of the times means overvalued options prices. Practically this happens because traders and hedgers, for their own reasons and according to their expectations, are buying calls & puts. So, the economical low of demand and supply raises their price. Calls and puts are mostly overvalued before the announcement of important news about a company because speculators and hedgers buy them in an attempt to speculate or hedged against an undesirable movement on the underline security. Also, when the implied volatility of calls is higher than that of puts, in most cases, the market is biased for an upward move in the underline security and vice versa.

When the implied volatility is high relatively to its average traders are generally trying to apply an options strategy that has to do with writing of options in order to benefit from their price decline due to the deflation of volatility (reversion to the mean). When implied volatility is low then traders attempt to apply a buying options strategy in order to benefit from the upward reversion of volatility to the average. These are general rules and the strategy that someone will employ is not depending solely on the value of implied volatility but also on other factors.

In a sense, we can say that implied volatility captures all the psychological and subjective factors that can’t be quantified.