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Stochastic volatility is volatility that varies over time at random. Stochastic volatility is used in the pricing of derivatives, mostly options. Such pricing models assume that the volatility of the underlying asset’s price fluctuates at random, with the random process driving the volatility sometimes correlated with the random process driving the asset price. Stochastic volatility models are more accurate than local volatility models but also more computationally intensive. They include the Heston model, published in 1993, and the stochastic alpha beta rho (SABR) model, introduced in 2002.
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