We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility...

The empirically observed asymmetry of sharp peaks and flat troughs in stock market fluctuations is recovered by a feedback mechanism in the Cont–Bouchaud model, changing the trader activity proportionally to the price change.