# Risk glossary

## Volatility

A measure of the variability of a market factor, most often the price of the underlying instrument. Volatility is defined mathematically as the annualised standard deviation of the natural log of the ratio of two successive prices. The actual volatility realised over a period of time (the historical volatility) can be calculated from recorded data.

Volatility is one of the variables that must be specified in the Black-Scholes model of option pricing: a vanilla option will cost more when volatility is high than when it is low. However, volatility is the only one of these variables whose value must be estimated.

The estimate used (known as the implied volatility) can be derived from the prices of options in the market and the known input variables. However, the Black-Scholes model also assumes that volatility is constant, which is not true. New techniques have been developed to cope with volatility’s variability, including mean-reverting models (such as Garch) and stochastic volatility models.