Volatility is one of the most important and most misunderstood concepts in financial markets. At its core, volatility measures how much prices move — it is a statistical measure of price dispersion over time. But in financial markets, volatility has two distinct forms with different implications for pricing, risk management, and trading.

Historical vs implied volatility

*Historical (realised) volatility* is calculated from past price data. It tells you how much an asset actually moved over a specific period, expressed as an annualised standard deviation. If the FTSE 100 moved an average of 1% per day over the past month, annualised volatility is approximately 16% (1% × √252 trading days).

*Implied volatility* is derived from current option prices — it tells you how much the market expects an asset to move in the future, based on what options traders are willing to pay. If a 3-month at-the-money FTSE call option is trading at a price consistent with 20% annualised volatility when plugged into the Black-Scholes formula, then implied vol is 20%.

Implied volatility is the option market's consensus forecast of future realised volatility. It is also the 'common language' in which options are quoted — traders say 'I bought the 3-month ATM at 18 vol' rather than stating a price in pounds.

The volatility surface

Implied volatility is not a single number — it varies by strike and by expiry date, creating a three-dimensional 'volatility surface'. For any given underlying, the surface shows the implied volatility for every combination of strike and maturity.

*Volatility smile*: Out-of-the-money options often have higher implied vol than at-the-money options, creating a 'smile' shape when plotted against strike.

*Volatility skew*: For equity indices, the smile is actually asymmetric — downside puts (protection against falls) are more expensive than upside calls, creating a 'skew'. This reflects the market's fear of sharp downward moves (the 'crash risk') and the demand for protection from institutional investors.

VIX: the fear index

The VIX (CBOE Volatility Index) measures the implied volatility of S&P 500 options at a 30-day horizon. It rises sharply when markets are stressed — during the 2020 COVID crash, VIX exceeded 80. Below 15 signals market complacency; above 30 indicates significant anxiety.

Why the difference between implied and realised volatility matters

If implied vol is 20% and realised vol turns out to be 15%, the option seller has earned a positive return — they received more premium than their hedging cost. This 'long volatility carry' has been one of the most profitable systematic strategies in options markets over the long run, precisely because implied vol tends to exceed realised vol (investors overpay for options as insurance).

Conversely, if realised vol is higher than implied (as in market crises), option buyers profit. The 2020 COVID crash was a period where realised vol dramatically exceeded even elevated implied vol levels.

Vol regime changes

Volatility is mean-reverting but exhibits 'regime' behaviour — extended periods of low volatility (the post-2012 'volatility compression') can be followed by sharp spikes (2020) that persist before mean-reverting. Risk management systems must account for both normal and stressed vol regimes.