Modeling stylized features in default rates.

We propose a stochastic model for the probability of default based on diffusions with given marginal distribution and autocorrelation function. The model tries to capture stylized features observed in historical default rates and is analytically tractable. Estimation procedures and expressions for analysis and prediction are provided.

Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes.

Continuous non-Gaussian stationary processes of the OU-type are becoming increasingly popular given their flexibility in modelling stylized features of financial series such as asymmetry, heavy tails and jumps. The use of non-Gaussian marginal distributions makes likelihood analysis of these processes unfeasible for virtually all cases of interest. This paper exploits the self-decomposability of the marginal laws of OU processes to provide explicit expressions of the characteristic function which can be applied to several models as well as to develop e±cient estimation techniques based on the empirical characteristic function. Extensions to OU-based stochastic volatility models are provided.Ornstein-Uhlenbeck process; Lévy process; self-decomposable distribution; characteristic function; estimation

The use of Mean Residual Life in testing departures from Esxponentiality.

vita media residua; test di esponenzialità; processo di wiener; processo di quantili

Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models.

Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. In this paper we propose a characteristic function-based estimation method for non-Gaussian Ornstein-Uhlenbeck-based stochastic volatility models. After deriving explicit expressions of the characteristic functions for various cases of interest we analyze the asymptotic properties of the estimators and evaluate their performance by means of a simulation experiment. Finally, a real-data application shows that the superposition of two Ornstein-Uhlenbeck processes gives a good approximation to the dependence structure of the process.ornstein-uhlenbeck process; lévy process; stochastic volatility; characteristic function estimation

Asymptotic Properties of the Partition Function and Applications in Tail Index Inference of Heavy-Tailed Data

The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution underlying the data either in i.i.d. and weakly dependent cases. These results will be exploited to develop graphical and estimation methods for the tail index of a distribution. The performance of the tools proposed is analyzed and compared with other methods by means of simulations and examples.Comment: 31 pages, 5 figure

Outlier detection through mixtures with an improper component

The  paper  investigates the use of a finite  mixture model with an additional uniform density for outlier detection and robust estimation.  The main contribution of this paper lies in the  analysis of the properties of the improper component and the introduction of a modified EM algorithm  which, beyond providing the maximum likelihood estimates of the mixture parameters, endogenously provides a numerical value for the density of the uniform distribution used for the improper component. The mixing proportion of outliers may be known or unknown.  Applications to robust estimation and outlier detection will be discussed with particular attention to the normal mixture case