observed in the dynamics of some financial variables, such as volatilities, stock volumes or interest rates, is their tendency to permanently relax, towards a reference level $\theta$, a property known as mean reversion. Another feature is the multiplicative market processing of random news, whose strength becomes modulated by a function of the stochastic variable itself. These two properties are modeled by means of a nonlinear mean-reverting force and nonlinear multiplicative noise. They are discussed in detail in Sect. \[Sec:props\].

In Sect. \[Sec:mean\_rev\], we discuss the shapes of the PDFs that such family of models yields. Despite being of a general form, they give rise to PDFs that, decay exponentially fast, either above the mode, below it, or both, in disagreement with empirical observations. For instance, log-normal behavior has been reported for volatility computed from global data of S&P500[@liu], at intermediate values. However, at high values, a power-law behavior, with exponent outside the stable Lévy range, was observed. The same analysis performed for individual companies[@liu] yields also power-law tails. But in that case, the results show a variation slower than log-normal below the mode, suggesting a power-law also in the limit of small values. The volatility of capitalized stocks traded in 