In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a non-stationary gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval, are very close to continuous cascade models. These...

We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the...

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as...

We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square...

Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review of their main properties and show that most of these...

In the context of statistics for random processes, we prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0,T] when T→∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the...

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes....

Multifractal models and random cascades have been successfully used to model asset returns. In particular, the log-normal continuous cascade is a parsimonious model that has proven to reproduce most observed stylized facts. In this paper, several statistical issues related to this model are...

In this paper we briefly review the recently inrtroduced Multifractal Random Walk (MRW) that is able to reproduce most of recent empirical findings concerning financial time-series : no correlation between price variations, long-range volatility correlations and multifractal statistics. We then...