Stationarity tests are used to detect mean reversion in a certain dataset. Mean Reversion processes suggest a non-random behavior in a time series (Lo and MacKinley, 1988). Previous research has focused on studying mean reversion at stock price level (Debondt and Thaler, 1985; Lindemann et al.,...

The standard hypothesis concerning the behavior of asset returns states that they follow a random walk in discrete time or a Brownian motion in continuous time. The Brownian motion process is characterized by a quantity, called the Hurst exponent, which is related to some fractal aspects of the...

Let (X1, Y1), . . ., (Xn, Yn) be i.i.d. rvs and let l(x) be the unknown p-quantile regression curve of Y on X. A quantile-smoother ln(x) is a localised, nonlinear estimator of l(x). The strong uniform consistency rate is established under general conditions. In many applications it is necessary...

We propose a new framework for studying the evolution of heterogeneous beliefs in a dynamic feedback setting. Beliefs distributions are defined on a beliefs space representing a continuum of possible strategies agents can choose from. Agents base their choices on past performances, re-evaluating...

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the...

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as auxiliary model a time-varying generalization of the HAR model...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...

We use stochastic volatility models to describe the evolution of the asset price, its instantaneous volatility, and its realized volatility. In particular, we concentrate on the Stein-Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic...

We introduce the beta stochastic volatility model and discuss empirical features of this model and its calibration. This model is appealing because, first, its parameters can be easily understood and calibrated and, second, it produces steeper forward skews, compared to traditional stochastic...