Implied volatility as an option-premium construction gauge

Inverting a pricing model for implied volatility

Implied volatility is the volatility output obtained when an options pricing model is given an option’s current market price and solved for volatility rather than for a theoretical price.

The Black-Scholes model is presented as a standard pricing model that can compute a theoretical fair value for a call or put from strike, underlying price, time remaining to expiration, an interest rate, expected dividends if any, and a volatility input. The same model can be inverted on the live quote so that the unknown is volatility instead of price.

When that model is inverted on the live quote, a higher observed option price produces a higher implied volatility and a lower observed option price produces a lower implied volatility.

Time premium inside the quoted price

An option’s market price is described as intrinsic value plus extrinsic value. Intrinsic value is the in-the-money amount, equal to how far the underlying already sits beyond the strike. The extrinsic component is also called time premium, the compensation demanded for taking the risk of selling the option.

Larger embedded time premium corresponds to higher implied volatility, and smaller embedded time premium corresponds to lower implied volatility. High implied volatility is treated as evidence that a large amount of time premium is built into option prices, while low implied volatility is treated as evidence that much less time premium is built in.

Cheap or expensive against its own history

Each listed option has its own implied volatility, while practitioners often average implied volatility across the options on one underlying. Comparing a security’s current average implied volatility with that same series’ historical range is presented as an objective way to judge whether its options are relatively cheap or expensive.

A historically low implied-volatility reading, illustrated by 90-day at-the-money implied volatility on a gold-miners exchange-traded fund making a new four-year low, is framed as a cheap-premium regime in which constructions that buy time premium are typically preferred.