The impact of multiple structural changes on mortality predictions

Most mortality models proposed in recent literature rely on the standard ARIMA framework (in particular: a random walk with drift) to project mortality rates. As a result the projections are highly sensitive to the calibration period. We therefore analyse the impact of allowing for multiple structural changes on a large collection of mortality models. We find that this may lead to more robust projections for the period effect but that there is only a limited effect on the ranking of the models based on backtesting criteria, since there is often not yet sufficient statistical evidence for structural changes. However, there are cases for which we do find improvements in estimates and we therefore conclude that one should not exclude on beforehand that structural changes may have occurred.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Tail risk in emerging markets of Southeastern Europe

This article examines the left-tail behaviour of returns on stocks in Southeastern Europe (SEE). We apply conditional extreme value theory (EVT) approach on daily returns of six stock market indices from SEE between 2004 and 2013. Predictive performance of value-at-risk (VaR) and expected shortfall (ES) based on EVT is compared against several alternatives, such as historical simulation and analytical approach based on GARCH with a single conditional distribution. Model backtesting with daily returns shows that EVT-based models provide more reliable VaR and ES forecasts than the alternative models in all six markets. Unlike the alternatives, the EVT-based models cannot be rejected as VaR confidence level is increased. This emphasizes the importance of extreme events in SEE markets and indicates that the ability of a model to capture volatility clustering accurately is not sufficient for a correct assessment of risk in these markets.     

Expected shortfall assessment in commodity (L)ETF portfolios with semi-nonparametric specifications

ABSTRACT

This paper studies the risk assessment of semi-nonparametric (SNP) distributions for leveraged exchange trade funds, (L)ETFs. We applied the SNP model with dynamic conditional correlations (DCC) and EGARCH innovations, and implement recent techniques to backtest Expected Shortfall (ES) to portfolios formed by bivariate combinations of major (L)ETFs on metal (Gold and Silver) and energy (Oil and Gas) commodities. Results support that multivariate SNP-DCC model outperforms the Gaussian-DCC and provides accurate risk measures for commodity (L)ETFs.     

Forecasting value at risk with intra-day return curves

Methods for incorporating high resolution intra-day asset price data into risk forecasts are being developed at an increasing pace. Existing methods such as those based on realized volatility depend primarily on reducing the observed intra-day price fluctuations to simple scalar summaries. In this study, we propose several methods that incorporate full intra-day price information as functional data objects in order to forecast value at risk (VaR). Our methods are based on the recently proposed functional generalized autoregressive conditionally heteroscedastic (GARCH) models and a new functional linear quantile regression model. In addition to providing daily VaR forecasts, these methods can be used to forecast intra-day VaR curves, which we considered and studied with companion backtests to evaluate the quality of these intra-day risk measures. Using high-frequency trading data from equity and foreign exchange markets, we forecast the one-day-ahead daily and intra-day VaR with the proposed methods and various benchmark models. The empirical results suggested that the functional GARCH models estimated based on the overnight cumulative intra-day return curves exhibited competitive performance with benchmark models for daily risk management, and they produced valid intra-day VaR curves.     

IMPLEMENTING A ROBUST RISK MODEL FOR SOUTH AFRICAN EQUITY MARKETS: A PEAK‐OVER‐THRESHOLD APPROACH

This paper implements a market risk model for the South African equity market using daily returns of the Johannesburg Stock Exchange All Share Index. Firstly, we separate positive returns from negative returns and model them using the peak‐over‐threshold (POT) method in order to compute the downside as well as upside risk measures separately. We thereafter compute the value‐at‐risk (VAR) and the expected shortfall (ES) estimates corresponding to upside and downside risks. We bootstrap these risk measures and compute their standard errors and confidence intervals (CIs) to see whether they fall inside these CIs. Secondly, we compute out‐sample forecasts of VAR estimates using the POT method and the generalised autogressive conditional heteroscedasticity process. Three backtesting methodologies are employed: the unconditional and conditional coverage tests and the counting of number of exceptions according to Basel II green zone. We find that all our VAR and ES estimates are well inside their CIs and that at lower quantiles, parametric ES estimates are equal to POT‐ES estimates, although the difference between the two is more pronounced at higher quantiles (99% or higher). Furthermore, our market risk model falls into the Basel II green zone, as it produces fewer exceptions in out‐sample space.     

Backtesting expected shortfall: evidence from European securitized real estate

Events such as the European sovereign debt crisis, terrorism and Brexit cause more uncertainty and volatility in capital markets. This encourages us to use both conditional and unconditional forecasts (backtests) for expected shortfall (ES) in 8 indices of listed European real estate securities and Real estate investment trusts (REITs). Using the method proposed by Du and Escanciano, we find that ES is generally superior to Value-at-Risk in describing and capturing risk during extreme events such as the financial crisis. Our results are important to regulators, risk managers and investors.     

Forecasting market risk of portfolios: copula-Markov switching multifractal approach

This paper proposes a new methodology for modeling and forecasting market risks of portfolios. It is based on a combination of copula functions and Markov switching multifractal (MSM) processes. We assess the performance of the copula-MSM model by computing the value at risk of a portfolio composed of the NASDAQ composite index and the S&P 500. Using the likelihood ratio (LR) test by Christoffersen [1998. “Evaluating Interval Forecasts.” International Economic Review 39: 841–862], the GMM duration-based test by Candelon et al. [2011. “Backtesting Value at Risk: A GMM Duration-based Test.” Journal of Financial Econometrics 9: 314–343] and the superior predictive ability (SPA) test by Hansen [2005. “A Test for Superior Predictive Ability.” Journal of Business and Economic Statistics 23, 365–380] we evaluate the predictive ability of the copula-MSM model and compare it to other common approaches such as historical simulation, variance–covariance, RiskMetrics, copula-GARCH and constant conditional correlation GARCH (CCC-GARCH) models. We find that the copula-MSM model is more robust, provides the best fit and outperforms the other models in terms of forecasting accuracy and VaR prediction.