Shortcomings of a Parametric VaR Approach and Nonparametric Improvements Based on a Non-stationary Return Series Model

In this paper we first investigate the validity of a general Value at Risk approach, which iswidely used for risk management in banking and insurance companies. We discuss and widely rejectthe conventional assumptions, e.g. independent identically distributed normal returns, and as consequencedevelop an improved model for non-stationary returns. Therein volatility dynamics are modelledboth exogenously and deterministic, captured by a nonparametric regression-type approach.Consistency and asymptotic normality of a symmetric and of a one-sided kernel estimator of volatilityare outlined with remarks on the bandwidth decision. We pay further..