CONFIDENCE INTERVALS OF THE ADJUSTED TAIL CONDITIONAL EXPECTATION RISK MEASURE FOR A STATIONARY SERIE

In this paper we present a semi-parametric estimator of the adjusted tail conditional expectation risk measure based on the theory of extreme values for a stationary serie. We prove its asymptotic normality and we construct the confidence intervals. The accuracy of these intervals is evaluated through a simulation study.

Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks

The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.

TAIL CONDITIONAL EXPECTATIONS FOR GENERALIZED SKEW-ELLIPTICAL DISTRIBUTIONS

This paper deals with the multivariate tail conditional expectation (MTCE) for generalized skew-elliptical distributions. We present tail conditional expectation for univariate generalized skew-elliptical distributions and MTCE for generalized skew-elliptical distributions. There are many special cases for generalized skew-elliptical distributions, such as generalized skew-normal, generalized skew Student-t, generalized skew-logistic and generalized skew-Laplace distributions.

A review on Poisson, Cox, Hawkes, shot-noise Poisson and dynamic contagion process and their compound processes

The Poisson process is an essential building block to move up to complicated counting processes, such as the Cox (“doubly stochastic Poisson”) process, the Hawkes (“self-exciting”) process, exponentially decaying shot-noise Poisson (simply “shot-noise Poisson”) process and the dynamic contagion process. The Cox process provides flexibility by letting the intensity not only depending on time but also allowing it to be a stochastic process. The Hawkes process has self-exciting property and clustering effects. Shot-noise Poisson process is an extension of the Poisson process, where it is capable of displaying the frequency, magnitude and time period needed to determine the effect of points. The dynamic contagion process is a point process, where its intensity generalises the Hawkes process and Cox process with exponentially decaying shot-noise intensity. To facilitate the usage of these processes in practice, we revisit the distributional properties of the Poisson, Cox, Hawkes, shot-noise Poisson and dynamic contagion process and their compound processes. We provide simulation algorithms for these processes, which would be useful to statistical analysis, further business applications and research. As an application of the compound processes, numerical comparisons of value-at-risk and tail conditional expectation are made.

Innovation of impairment loss allowance model of Indonesian financial accounting standards 71

PurposeThis study aims to develop a high-quality impairment loss allowance model in conformity with Indonesian Financial Accounting Standards 71 (PSAK 71) that has significant contribution to national interests and the banking industry.Design/methodology/approachThe determination of the impairment loss allowance model is settled through 7 stages, using integration of some statistical methods such as Markov chain, exponential smoothing, time series analysis of behavioral inherent trends of probability of default, tail conditional expectation and Monte Carlo simulation.FindingsThe model which is developed by the authors is proven to be a high-quality and reliable model. By using the model, it can be shown that the implementation of the expected credit losses model on Indonesian Financial Accounting Standards 71 is more prudent than the implementation of the incurred loss model on Indonesian Financial Accounting Standards 55.Research limitations/implicationsDetermination of defaults was based on days past due, and the analysis in this study did not touch the aspects of hedge accounting in general.Practical implicationsThis developed model will contribute significantly to national interests as a source of reference for other banks operating in Indonesia in calculating impairment loss allowance (CKPN) and can be used by the Financial Services Authority of Indonesia (OJK) as a guideline in assessing the formation of impairment loss allowance for banks operating in Indonesia.Originality/valueAs so far there is not yet an available standardized model for calculating impairment loss allowance on the basis of Indonesian Financial Accounting Standards 71, the model developed by the authors will be a new breakthrough in Indonesia.

An evaluation and comparison of Value at Risk and Expected Shortfall

As a risk measure, Value at Risk (VaR) is neither sub-additive nor coherent. These drawbacks have coerced regulatory authorities to introduce and mandate Expected Shortfall (ES) as a mainstream regulatory risk management metric. VaR is, however, still needed to estimate the tail conditional expectation (the ES): the average of losses that are greater than the VaR at a significance level These two risk measures behave quite differently during growth and recession periods in developed and emerging economies. Using equity portfolios assembled from securities of the banking and retail sectors in the UK and South Africa, historical, variance-covariance and Monte Carlo approaches are used to determine VaR (and hence ES). The results are back-tested and compared, and normality assumptions are tested. Key findings are that the results of the variance covariance and the Monte Carlo approach are more consistent in all environments in comparison to the historical outcomes regardless of the equity portfolio regarded. The industries and periods analysed influenced the accuracy of the risk measures; the different economies did not.