Definition of implied volatility

An option pricing term that describes the use of the observed market price of a derivative security to infer more fundamental information.

This is best understood by recognising that an option contract increases in value as the volatility of the underlying asset increases.  This seems counterintuitive as we typically think of volatility as detrimental.

Economists have developed mathematical models to value such options.  The formula produces an estimate of an option’s price if the terms of the option (exercise price, time until expiration), relevant market conditions (current price of the underlying asset, interest rates), and an estimate of the volatility are plugged in. Furthermore, if the market price for an option can be observed, we can use the model to work backwards and infer the level of volatility that market participants appear to be plugging into the formula to price the option.

This is the implied volatility, a measure of the market’s best estimate of the volatility of the price of the underlying asset. It is a useful gauge of the market’s perception of risk, and it can experience very large, rapid changes in, for example, a financial crisis or market downturn.

Example

Suppose two pieces of land are each worth exactly $1m.  Piece A is a vast tract of dozens of square miles of inaccessible land in the interior of Alaska. Piece B is a few hundred square yards just outside the entrance to the Dallas Fort Worth airport.

Consider two derivative contracts, each relating to one of these properties. Call Option A allows you to buy the Alaskan tract for $1m at any time in the next five years. Call Option B allows you to buy the Dallas Fort Worth tract for $1 at any time in the next five years.

Little is likely to happen to the Alaskan land’s value so that you offer only a very small price for Option A.  However, the value of the DFW land can shoot up or crash dramatically depending on the fortunes of the airport.  If the value shoots up within the next five years, you can exercise the option, buy the land for a million dollars, and sell it at a large profit. If the value of the land drops below a million dollars, you do not care whether it drops ten dollars or half a million dollars as you will not exercise your purchase option in either case. Thus, the value of an option benefits from volatility or dispersion: the option holder gains any upside and can walk away from any downside. Therefore, Option B sells for much more than Option A. [1]

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