Historical and implied volatility

In simple terms

Volatility describes how much a price swings. For options it matters enormously, because an option pays off only if the price moves far enough. The more a price is expected to swing, the more an option is worth.

There are two kinds to keep apart:

• Historical volatility: how much the price has moved.
• Implied volatility: how much the market expects it to move, as implied by option prices.

Historical volatility

Historical volatility is the standard deviation of past returns, as the averages and volatility lesson explains, usually converted to a yearly figure.

Implied volatility

Option prices depend on the share price, strike, time to expiry, interest rates and volatility. All but volatility can be observed. So traders work backwards: implied volatility (IV) is the volatility that, put into a pricing model, produces the option's current market price.

IV is therefore a price, expressed as a volatility. High IV means options are expensive; low IV means they are cheap, relative to the expected size of moves.

Reading IV as a range

A rough rule converts IV into an expected range over a period, assuming a typical spread of outcomes:

Roughly two times in three, the price might end within that distance of today's price, if the assumption holds. Real price moves have more extreme days than this simple picture suggests, as the volatility and drawdowns lesson explains.

Volatility indices

Exchanges publish volatility indices calculated from index option prices. In India, NSE publishes India VIX. A rising volatility index means index options are becoming more expensive because larger moves are expected. It is a measure of expected movement, not a forecast of direction.

Why IV behaves as it does

• Falling markets: IV usually rises when markets fall, because investors rush to buy protection, such as puts, and sharp falls tend to come with large daily moves.
• Scheduled events: before results, policy decisions or elections, IV often rises because a big move is possible. Afterwards, the uncertainty is resolved and IV often drops sharply, sometimes called a volatility crush. Option buyers can lose money even when the price moves in their favour, as the time decay and vega lesson explains.
• Supply and demand: heavy buying or selling of particular options moves their IV.

Why it matters

Implied volatility explains why option prices change when the share price does not, why options are expensive before events and cheap afterwards, and why direction alone does not make an option trade profitable. It is the most important input that beginners overlook.

Limitations

The square-root-of-time rule and pricing models rest on simplifying assumptions that real markets break, especially in crises. IV differs across strikes and expiries, and a single figure is a summary. Volatility indices measure index options, not individual shares.

Common mistakes

• Reading high IV as a signal that prices will rise.
• Buying options before events without allowing for the IV drop afterwards.
• Confusing historical and implied volatility.
• Treating the one-standard-deviation range as a limit.

Try it yourself

1. Take ten days of closing prices for a share, calculate daily returns, their standard deviation, and the yearly volatility.
2. Find the implied volatility of an at-the-money option on the same share and compare it with your figure.
3. Use the rough rule to estimate the share's one-standard-deviation range over 30 days.