Pascale Valéry

On a Simple Two-Stage Closed-form Estimator for a Stochastic Volatility in a General Linear Regression

In this paper, we consider the estimation of volatility parameters in the context of a linear regression where the disturbances follow a stochastic volatility (SV) model of order one with Gaussian log-volatility. The linear regression represents the conditional mean of the process and may have a fairly general form, including for example finite-order autoregressions. We provide a computationally simple two-step estimator available in closed form. Under general regularity conditions, we show that this two-step estimator is asymptotically normal. We study its statistical properties by simulation, compare it with alternative generalized method-of-moments (GMM) estimators, and present an application to the S&P composite index.

Diffusion Processes with Polynomial Eigenfunctions

The aim of this paper is to characterize the one-dimensional stochastic differential equations, for which the eigenfunctions of the infinitesimal generator are polynomials in y. Affine transformations of the Ornstein-Uhlenbeck process, the Cox-Ingersoll-Ross process and the Jacobi process belong to the solutions of this stochastic differential equation family. Such processes exhibit specific patterns of the drift and volatility functions and can be represented by means of a basis of polynomial transforms which can be used to approximate the likelihood function. We also discuss the constraints on parameters to ensure the nonnegativity of the volatility function and the stationarity of the process. The possibility to fully characterize the dynamic properties of these processes explain why they are benchmark models for unconstrained variables such as asset returns (Ornstein-Uhlenbeck), for nonnegative variables as volatilities or interest rates (Cox, Ingersoll, Ross), or for variables which can be interpreted as probabilities (Jacobi).

Credible reforms and stock return volatility: Evidence from privatization☆

In this paper we investigate how privatization affects stock return volatility. A credible privatization builds investors’ confidence through a reduction in political risk. In particular, a privatization program that is maintained over time signals credibility, which reduces political risk and in turn volatility. We further show that privatization is associated with lower idiosyncratic volatility mainly among developed markets, while it is associated with lower systematic volatility in developing markets. Additional tests suggest that the reduction in volatility is greater when privatization sales are carried out through the stock market than through asset sales.