The degree of variability of any financial or other variable over time.
For example an asset price, a foreign exchange rate, or a periodic rate of return. It can be quantified on a simplified basis as the annualised standard deviation of the variable.
In relation to bond price sensitivity (to changes in market yields) volatility means the same as modified duration.
In relation to options, volatility refers to the expected variability of the returns from investing in the underlying asset at its prevailing market price, over the remaining maturity of the option.
This is sometimes known as the underlying volatility or the underlying asset volatility.
In this context volatility is most commonly - though not always - quoted on an annualised basis.
By convention, volatility in the context of market prices is most often quantified as the annualised standard deviation of the natural logs of [1 + periodic return] for the number of periods for which the return is considered.
In relation to options, volatility of the underlying asset price can be estimated:
(i) From historical underlying asset price data, or
(ii) As implied volatility in the current market price of the option, if all of the other drivers of the current market price of the option (including the risk-free rate of return) are known.
Any other form of instability.
For example, volatile bank deposits or other liabilities are more likely to be withdrawn under stress.