Volatility (Implied vs. Realised)

Realised volatility is arithmetic on history: the standard deviation of a series of returns, annualised by the square root of the number of periods in a year. A share whose daily returns have a standard deviation of 1.5% has an annualised realised volatility of 1.5% times the square root of 252, or 23.8%. The number is meaningless without the window and the scaling attached to it, because the same share can print very different figures over twenty days and over a year.

Implied volatility runs a pricing model backwards. The observable inputs are the share price, the strike, the time to expiry and the risk-free rate; the observable output is the traded price of the option. The volatility figure is the only unknown, so it is solved for. A three-month call struck at £55 on a £50 share, trading at £2.00 with a 4% risk-free rate, implies about 36.7% a year. Nothing measured 36.7%. It is what has to be assumed to explain the £2.00.

Setting the two side by side is most of what an options desk talks about. In the example above the option is priced for 36.7% and the share may go on to realise 24%, or 45%, and only the passage of time settles it. That gap is why market makers quote and hedge in volatility terms rather than in cash prices: the price of the option changes constantly as the share moves, while the volatility number is the part of the quote that carries the actual view.

The gap has a documented sign. Across most liquid markets and long samples, implied volatility has on average exceeded the volatility subsequently realised, a pattern usually explained as compensation for bearing the risk of a large adverse move. It is an average over long periods and not a rule that holds in any given month, which is why a desk treats it as context rather than as a conclusion, and why the same statement is worth stating carefully in an interview rather than as a slogan.