Joseph H.T. Kim

Estimating extreme tail risk measures with generalized Pareto distribution

The generalized Pareto distribution (GPD) has been widely used in modelling heavy tail phenomena in many applications. The standard practice is to fit the tail region of the dataset to the GPD separately, a framework known as the peaks-over-threshold (POT) in the extreme value literature. In this paper we propose a new GPD parameter estimator, under the POT framework, to estimate common tail risk measures, the Value-at-Risk (VaR) and Conditional Tail Expectation (also known as Tail-VaR) for heavy-tailed losses. The proposed estimator is based on a nonlinear weighted least squares method that minimizes the sum of squared deviations between the empirical distribution function and the theoretical GPD for the data exceeding the tail threshold. The proposed method properly addresses a caveat of a similar estimator previously advocated, and further improves the performance by introducing appropriate weights in the optimization procedure. Using various simulation studies and a realistic heavy-tailed model, we compare alternative estimators and show that the new estimator is highly competitive, especially when the tail risk measures are concerned with extreme confidence levels. A new GPD parameter estimator is proposed.It is based on a nonlinear weighted least squares method.Under the POT framework, we estimate tail risk measures. Extensive simulation studies show the new method works well.

Designing an Alternative Public Pension Scheme: A Korean Case Study

Abstract The trends of ageing population and slow economic growth have become a major concern for public pension schemes with the defined benefit (DB) type. To mitigate the impact of this trend and secure long-term financial sustainability, several countries have recently adopted notional defined contribution (NDC) schemes. In this paper, we show how to apply an NDC scheme to the public pension system of Korea, arguably the fastest ageing country. In particular, we create a new pension system by combining the current Korean pension scheme and an NDC. Through simulations it is shown that the proposed scheme can reduce the financial instability caused by the changes in demographic and economic factors, while retaining the income redistribution component. We further consider applying a German-type automatic balancing mechanism to the proposed scheme, by using the average income to determine the return rate of the fund, to make it sustainable in the long term.

Exponentiated generalized Pareto distribution: Properties and applications towards extreme value theory

ABSTRACT The GPD is a central distribution in modelling heavy tails in many applications. Applying the GPD to actual datasets however is not trivial. In this paper we propose the Exponentiated GPD (exGPD), created via log-transform of the GPD variable, which has less sample variability. Various distributional quantities of the exGPD are derived analytically. As an application we also propose a new plot based on the exGPD as an alternative to the Hill plot to identify the tail index of heavy tailed datasets, and carry out simulation studies to compare the two.