The magnitude of the instantaneous fluctuation of a dynamic process, e.g., the log of an underlying asset price/ underlying rate at a given point in time (presently or in the past, or even in the future- future instantaneous volatility). Instantaneous volatility is measured under multiple methodologies including one involving high frequency data (where the latent price of an asset follows a continuous time process, and hence instantaneous volatility is perceived as the coefficient of the diffusion component, which is defined as the (conditional) variance of the (logarithmic) price).
Instantaneous volatility is a key consideration in option pricing (and also in areas such as risk management and portfolio selection, etc.) In addition to its practical uses, spot has other specific theoretical applications in statistical inference for stochastic processes.
It is also known as spot volatility.
