It reflects the magnitude of the instantaneous fluctuation of a dynamic process, e.g., the log of an underlying asset price/ underlying rate (in an option or a derivative) at a given point in time in the future. In a one-factor options pricing model, valuation reflects expectations about the future instantaneous volatility of a defined index (along with implied volatilities derived therefrom), where future index volatilities are assumed to conversely correlate with the index.
The uncertainty associated with the future instantaneous volatility is estimated under multiple models for the uncertainty, such as the stochastic volatility model. Other models allow the level of volatility to change over time, and also for the observed skew to vary stochastically over time.
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