Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments

This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterizations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges with such models is to perform robust estimation for the loss model parameters that will be amenable to practitioners when fitting such models. In this paper we develop a novel, efficient and robust estimation procedure for estimation of model parameters in this family Tukey transform models, based on L-moments. It is shown to be more robust and efficient than current state of the art methods of estimation for such families of loss models and is simple to implement for practical purposes.Comment: 42 page

Bayesian Semi-parametric Realized-CARE Models for Tail Risk Forecasting Incorporating Range and Realized Measures

A new framework named Realized Conditional Autoregressive Expectile (Realized- CARE) is proposed, through incorporating a measurement equation into the conventional CARE model, in a framework analogous to Realized-GARCH. The Range and realized measures (Realized Variance and Realized Range) are employed as the dependent variables of the measurement equation, since they have proven more efficient than return for volatility estimation. The dependence between Range & realized measures and expectile can be modelled with this measurement equation. The grid search accuracy of the expectile level will be potentially improved with introducing this measurement equation. In addition, through employing a quadratic fitting target search, the speed of grid search is significantly improved. Bayesian adaptive Markov Chain Monte Carlo is used for estimation, and demonstrates its superiority compared to maximum likelihood in a simulation study. Furthermore, we propose an innovative sub-sampled Realized Range and also adopt an existing scaling scheme, in order to deal with the micro-structure noise of the high frequency volatility measures. Compared to the CARE, the parametric GARCH and the Realized-GARCH models, Value-at-Risk and Expected Shortfall forecasting results of 6 indices and 3 assets series favor the proposed Realized-CARE model, especially the Realized-CARE model with Realized Range and sub-sampled Realized Range

The Two-sided Weibull Distribution and Forecasting Financial Tail Risk

A two-sided Weibull is developed to model the conditional financial return distribution, for the purpose of forecasting Value at Risk (VaR) and conditional VaR. A range of conditional return distributions are combined with four volatility specifications to forecast tail risk in four international markets, two exchange rates and one individual asset series, over a four year forecast period that includes the recent global financial crisis. The two-sided Weibull performs at least as well as other distributions for VaR forecasting, but performs most favourably for conditional Value at Risk forecasting, prior to as well as during and after the recent crisis

Forecasting risk via realized GARCH, incorporating the realized range

The realized GARCH framework is extended to incorporate the realized range, and the intra-day range, as potentially more efficient series of information than re- alized variance or daily returns, for the purpose of volatility and tail risk forecasting in a financial time series. A Bayesian adaptive Markov chain Monte Carlo method is employed for estimation and forecasting. Compared to a range of well known parametric GARCH models, predictive log-likelihood results across six market in- dex return series favor the realized GARCH models incorporating the realized range. Further, these same models also compare favourably for tail risk forecasting, both during and after the global financial crisis