A comparison of extreme value theory approaches for determining value at risk

This paper compares a number of different extreme value models for determining the value at risk (VaR) of three LIFFE futures contracts. A semi-nonparametric approach is also proposed, where the tail events are modeled using the generalised Pareto distribution, and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that, for a holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models.

A note on estimating market–based minimum capital risk requirements: a multivariate GARCH approach

Internal risk management models of the kind popularized by J. P. Morgan are now used widely by the world’s most sophisticated financial institutions as a means of measuring risk. Using the returns on three of the most popular futures contracts on the London International Financial Futures Exchange, in this paper we investigate the possibility of using multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models for the calculation of minimum capital risk requirements (MCRRs). We propose a method for the estimation of the value at risk of a portfolio based on a multivariate GARCH model. We find that the consideration of the correlation between the contracts can lead to more accurate, and therefore more appropriate, MCRRs compared with the values obtained from a univariate approach to the problem.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

The impact of real estate on the terminal wealth of the UK mixed-asset portfolio

The argument for the inclusion of real estate in the mixed-asset portfolio has concentrated on examining its effect in reducing the portfolio risk - the time series standard deviation (TSSD), mainly using ex-post time series data. However, the past as such is not really relevant to the long-term institutional investors, such as the insurance companies and pension funds, who are more concerned the terminal wealth (TW) of their investments and the variability of this wealth, the terminal wealth standard deviation (TWSD), since it is from the TW of their investment portfolio that policyholders and pensioners will derive their benefits. These kinds of investors with particular holding period requirements will be less concerned about the within period volatility of their portfolios and more by the possibility that their portfolio returns will fail to finance their liabilities. This variability in TW will be closely linked to the risk of shortfall in the quantity of assets needed to match the institution’s liabilities. The question remains therefore can real estate enhance the TW of the mixed-asset portfolio and/or reduce the variability of the TW. This paper uses annual data from the United Kingdom (UK) for the period 1972-2001 to test whether real estate is an asset class that not only reduces ex-post portfolio risk but also enhances portfolio TW and/or reduces the variability of TW.

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts

Customer retention management in the recession

The purpose of this article is to explore customer retention strategies and tactics implemented by firms in recession. Our investigations show just how big a challenge many organizations face in their ability to manage customer retention effectively. While leading organizations have embedded real-time customer life cycle management, developed accurate early warning systems, price elasticity models and ‘deal calculators’, the organizations we spoke to have only gone as far as calculating the value at risk and building simple predictive models.

Time-variations in commodity price jumps

In this paper, we study jumps in commodity prices. Unlike assumed in existing models of commodity price dynamics, a simple analysis of the data reveals that the probability of tail events is not constant but depends on the time of the year, i.e. exhibits seasonality. We propose a stochastic volatility jump–diffusion model to capture this seasonal variation. Applying the Markov Chain Monte Carlo (MCMC) methodology, we estimate our model using 20 years of futures data from four different commodity markets. We find strong statistical evidence to suggest that our model with seasonal jump intensity outperforms models featuring a constant jump intensity. To demonstrate the practical relevance of our findings, we show that our model typically improves Value-at-Risk (VaR) forecasts.

A value chain approach to animal diseases risk management: technical foundations and practical framework for field application

Classical risk assessment approaches for animal diseases are influenced by the probability of release, exposure and consequences of a hazard affecting a livestock population. Once a pathogen enters into domestic livestock, potential risks of exposure and infection both to animals and people extend through a chain of economic activities related to producing, buying and selling of animals and products. Therefore, in order to understand economic drivers of animal diseases in different ecosystems and to come up with effective and efficient measures to manage disease risks from a country or region, the entire value chain and related markets for animal and product needs to be analysed to come out with practical and cost effective risk management options agreed by actors and players on those value chains. Value chain analysis enriches disease risk assessment providing a framework for interdisciplinary collaboration, which seems to be in increasing demand for problems concerning infectious livestock diseases. The best way to achieve this is to ensure that veterinary epidemiologists and social scientists work together throughout the process at all levels.