Implied Volatility
The implied volatility of an option is the volatility, or standard deviation, required so that the theoretical price of the option calculated using an options pricing formula — the Black Scholes pricing formula for European options, for example — is equal to the market price. While the implied volatility for options tends to be correlated with the expected standard deviation of the option’s underlying, the two quantities are not necessarily equal. For one thing, options on the same underlying with the same expiry, but different strike prices, typically do not have the same implied volatility. Options for most securities display what is known as a volatility smile, with implied volatility lower for strike prices near the current market price, and higher for out-of-the-money (OTM) options. While volatility smiles for fx options tend to be symmetric, smiles for equity options are typically asymmetric — more of a smirk than a smile. For equities the implied volatility for options with strikes that are far below the current market price of the underlying tend to have much higher implied volatility than those with strikes far above the current underlying price.