Implied volatility

In order to estimate volatilities, one approach is to use purely historical data. The alternative is to use the volatility implied by current securities prices.

To see how this works, consider the Black-Scholes equation. In order to price an option one would simply plug in the time till expiry, the exercise price, the price of the underlying security, the volatility of the underlying, etc. into the equation and calculate a price.

However, as there will usually be a market price for a publicly traded option we can take the price as known, take the volatility as the unknown and then solve the equation for the volatility.

The result is the implied volatility.

This is an estimate based on market prices and is therefore the volatility expected by the market. If the security is correctly priced, as implied by the efficient markets hypothesis, this should be a good estimate. The problem is that, because implied volatility varies with strike price, so different options will give different volatility numbers for the same underlying over the same period.

As with other market price derived data, there are periods during which market prices may be badly wrong (for example, during investment bubbles).

If you are not convinced that markets are efficient, or that one of the available option pricing models (such as Black-Scholes) is correct, then it may be preferable to use realised volatility. Realised volatility is also more appropriate when dealing with purely historical concerns, as when risk-adjusting portfolio performance.

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