Stochastic Volatility (SV)

Stochastic volatility refers to the fact that the volatility of asset prices is not constant, as assumed in the Black Scholes options pricing model. Stochastic volatility modeling attempts to correct for this problem with Black Scholes by allowing volatility to vary over time.

The word "stochastic" refers to something that is randomly determined and may not be predicted precisely. In the context of stochastic modeling, it refers to successive values of a random variable that are not independent. Examples of stochastic volatility models include the Heston model, the SABR model, and the GARCH model.

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 take into account the fact that price volatility of the underlying security fluctuates. Stochastic volatility modeling treats price volatility as a random variable. Allowing the price to vary in the stochastic volatility models improved the accuracy of calculations and forecasts.