Abstract. In this paper we first investigate the validity of a general Value at Risk approach, which is widely used for risk management in banking and insurance companies. We discuss and widely reject the conventional assumptions, e.g. independent identically distributed normal returns, and as consequence develop an improved model for non-stationary returns. Therein volatility dynamics are modelled both 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 volatility are outlined with remarks on the bandwidth decision. We pay further attention to asymmetry and heavy tails of the return distribution, implemented by the framework for innovations. On a multitude of financial time series for equity indices, exchange rates, interest rates and credit spreads it is shown that the univariate approach is practically manageable and outperforms the standard tools.

Abstract.A non-stationary regression model for financial returns is examined theoretically in this paper. Volatility dynamics are modelled both exogenously and deterministic, captured by a nonparametric curve estimation on equidistant centered returns. We prove consistency and asymptotic normality of a symmetric variance estimator and of a one-sided variance estimator analytically, and derive remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, implemented by an asymmetric version of the Pearson type VII distribution for random innovations. By providing a method of moments for its parameter estimation and a connection to the Student-t distribution we offer the framework for a factor-based VaR approach. The approximation quality of the non-stationary model is supported by simulation studies.

In this paper we analyze an econometric model for non-stationary asset returns. Volatility dynamics are modelled by nonparametric regression; consistency and asymptotic normality of a symmetric and of a one-sided kernel estimator are outlined with remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, involved by the framework for innovations. We survey the practicability and automatization of the implementation. For simulated price processes and a multitude of financial time series we observe a satisfying model approximation and good short-term forecasting abilities of the univariate approach. The non-stationary regression model outperforms parametric risk models and famous ARCH-type implementations.JEL classification: C14, C5

In an extensive study we estimate the linear dependence of a broad portfolio of equities and fixed income securities (including credit and currency risks) and fit the whole approach to provide distributional forecasts. Our evaluations verify a reasonable approximation and a satisfactory forecasting quality with an outperformance against a traditional risk model. JEL classification: C14, C5