# Stochastic Volatility - SV

## DEFINITION of 'Stochastic Volatility - SV'

A statistical method in mathematical finance in which volatility and codependence between variables is allowed to fluctuate over time rather than remain constant. "Stochastic" in this sense refers to successive values of a random variable that are not independent. Stochastic volatility is typically analyzed through sophisticated models, which became increasingly useful and accurate as computer technology improved.

Examples of stochastic volatility models include the Heston model, the SABR model, the Chen model and the GARCH model.

## BREAKING DOWN 'Stochastic Volatility - SV'

Stochastic volatility models for options were developed out of a need to modify the Black Scholes model for option pricing, which failed to effectively take the volatility in the price of the underlying security into account. The Black Scholes model assumed that the volatility of the underlying security was constant, while stochastic volatility models categorized the price of the underlying security as a random variable. Allowing the price to vary in the stochastic volatility models improved the accuracy of calculations and forecasts.