The name derives from the models'treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others.
2.
Where \ omega is the mean long-term volatility, \ theta is the rate at which the volatility reverts toward its long-term mean, \ xi is the volatility of the volatility process, and dB _ t is, like dW _ t, a gaussian with zero mean and \ sqrt { \ nu _ t } standard deviation.
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