Computing the finite-time expected discounted penalty function for a family of Lévy risk processes

Ever since the first introduction of the expected discounted penalty function (EDPF), it has been widely acknowledged that it contains information that is relevant from a risk management perspective. Expressions for the EDPF are now available for a wide range of models, in particular for a general class of Lévy risk processes. Yet, in order to capitalize on this potential for applications, these expressions must be computationally tractable enough as to allow for the evaluation of associated risk measures such as Value at Risk (VaR) or Conditional Value at Risk (CVaR). Most of the models studied so far offer few interesting examples for which computation of the associated EDPF can be carried out to the last instances where evaluation of risk measures is possible. Another drawback of existing examples is that the expressions are available for an infinite-time horizon EDPF only. Yet, realistic applications would require the computation of an EDPF over a finite-time horizon. In this paper we address these two issues by studying examples of risk processes for which numerical evaluation of the EDPF can be readily implemented. These examples are based on the recently introduced meromorphic processes, including the beta and theta families of Lévy processes, whose construction is tailor-made for computational ease. We provide expressions for the EDPF associated with these processes and we discuss in detail how a finite-time horizon EDPF can be computed for these families. We also provide numerical examples for different choices of parameters in order to illustrate how ruin-based risk measures can be computed for these families of Lévy risk processes.     

Selecting copulas for risk management

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper, we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student’s t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student’s t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.     

Inflation risk and international asset returns

We show that inflation risk is priced in international asset returns. We analyze inflation risk in a framework that encompasses the International Capital Asset Pricing Model (ICAPM) of Adler and Dumas (1983). In contrast to the extant empirical literature on the ICAPM, we relax the assumption that inflation rates are constant. We estimate and test a conditional version of the model for the G5 countries (France, Germany, Japan, the UK, and the US) over the period 1975–1998 and find evidence of statistically and economically significant prices of inflation risk (in addition to priced nominal exchange rate risk). Our results imply a rejection of the restrictions imposed by the ICAPM. In an extension of our analysis to 2003, we show that even after the termination of nominal exchange rate fluctuations in the euro area in 1999, differences in inflation rates across countries entail non-trivial real exchange rate risk premia.     

Corporate credit risk modeling and the macroeconomy

Despite a surge in the research efforts put into modeling credit and default risk during the past decade, few studies have incorporated the impact that macroeconomic conditions have on business defaults. In this paper, we estimate a duration model to explain the survival time to default for borrowers in the business loan portfolio of a major Swedish bank over the period 1994–2000. The model takes both firm-specific characteristics, such as accounting ratios and payment behaviour, loan-related information, and the prevailing macroeconomic conditions into account. The output gap, the yield curve and consumers’ expectations of future economic development have significant explanatory power for the default risk of firms. We also compare our model with a frequently used model of firm default risk that conditions only on firm-specific information. The comparison shows that while the latter model can make a reasonably accurate ranking of firms’ according to default risk, our model, by taking macro conditions into account, is also able to account for the absolute level of risk.     

Stock market bubbles, inflation and investment risk

This paper proposes an autoregressive regime-switching model of stock price dynamics in which the process creates pricing bubbles in one regime while error-correction prevails in the other. In the bubble regime the stock price depends negatively on inflation. In the error-correction regime it depends on the price-dividend ratio. We find that the probability of regime-switch depends on exogenous inflation and lagged price. The model is consistent with Shleifer and Vishny's theoretical noise trader and arbitrageur model and Modigliani's inflation illusion phenomenon. The results emphasize the importance of inflation and the price-dividend ratio when assessing investment risk.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.     

Discrete hedging of American-type options using local risk minimization

Local risk minimization and total risk minimization discrete hedging have been extensively studied for European options [e.g., Schweizer, M., 1995. Variance-optimal hedging in discrete time. Mathematics of Operation Research 20, 1–32; Schweizer, M., 2001. A guided tour through quadratic hedging approaches. In: Jouini, E., Cvitanic, J., Musiela, M., Option pricing, interest rates and risk management, Cambridge University Press, pp. 538–574]. In practice, hedging of options with American features is more relevant. For example, equity linked variable annuities provide surrender benefits which are essentially embedded American options. In this paper we generalize both quadratic and piecewise linear local risk minimization hedging frameworks to American options. We illustrate that local risk minimization methods outperform delta hedging when the market is highly incomplete. In addition, compared to European options, distributions of the hedging costs are typically more skewed and heavy-tailed. Moreover, in contrast to quadratic local risk minimization, piecewise linear risk minimization hedging strategies can be significantly different, resulting in larger probabilities of small costs but also larger extreme cost.     

Ruin probabilities in multivariate risk models with periodic common shock

We propose a multidimensional risk model where the common shock affecting all classes of insurance business is arriving according to a non-homogeneous periodic Poisson process. In this multivariate setting, we derive upper bounds of Lundberg-type for the probability that ruin occurs in all classes simultaneously using the martingale approach via piecewise deterministic Markov processes theory. These results are numerically illustrated in a bivariate risk model, where the beta-shape periodic claim intensity function is considered. Under the assumption of dependent heavy-tailed claims, asymptotic bounds for the finite-time ruin probabilities associated to three types of ruin in this multivariate framework are investigated.     

Fuzzy logic and financial risk. A proposed classification of financial risk to the cooperative sector

Applying fuzzy logic to financial indicators is not a well disseminated proposal in the accounting field. This methodology allows observing the results of financial ratios with a broader perspective, showing neither completely true nor completely false results, since they can take an undetermined truthfulness value within a set of values, applying the fuzzy logic theory. The objective of this work is to introduce the reader to the application of fuzzy logic on financial risk indicators, using the ratios of one of the sector one cooperatives of Ecuador, and thus validate the level of relevance of this indicator when compared to the standardized objective of the CAMEL model and its risk rating. To apply this theory, linguistic variables were used, the ranges of which were evaluated in 0–1 scales. It was determined that the fuzzy methodology, applied to financial risks, presents a greater level of relevance toward a good credit rating, ensuring a low level of risk and a very good solvency. However, in periods of low economic activity it would stagnate in this level due to the increased risk.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Measuring portfolio credit risk correctly: Why parameter uncertainty matters

Why should risk management systems account for parameter uncertainty? In addressing this question, the paper lets an investor in a credit portfolio face non-diversifiable uncertainty about two risk parameters – probability of default and asset-return correlation – and calibrates this uncertainty to a lower bound on estimation noise. In this context, a Bayesian inference procedure is essential for deriving and analyzing the main result, i.e. that parameter uncertainty raises substantially the tail risk perceived by the investor. Since a measure of tail risk that incorporates parameter uncertainty is computationally demanding, the paper also derives a closed-form approximation to such a measure.     

World market risk,country-specific risk and expected returns in international stock markets

This paper determines whether the world market risk, country-specific total risk, and country-specific idiosyncratic risk are priced in an international capital asset pricing model (ICAPM). Portfolio-level analyses, country-level cross-sectional regressions, stacked time-series, and pooled panel regressions indicate that the world market risk is not, but country-specific total and idiosyncratic risks are significantly priced in an ICAPM framework with partial integration. This result is robust to different methods for estimating risk measures, different investment horizons, and after controlling for the countries’ aggregate dividend yield, earnings-to-price ratios, inflation risk, exchange rate uncertainties, aggregate volatility risk, and past return characteristics. The main findings turn out to be insensitive to the choice of one-factor vs. multifactor models used to estimate systematic and idiosyncratic risk measures.     

Methods for evaluating mortality risk

An important aspect of decisions related to the long-range planning of large-scale systems, eg world energy supplies, is their possible environmental side-effects. These decisions, which potentially affect the public's health and safety, increasingly require a formal consideration of mortality risk. Several methods have been proposed for the evaluation of public programmes which probabilistically alter human mortality. This article reviews the relevant literature and the practical applications of these proposed methods. Particular emphasis is placed upon the explicit identification of the social objectives implied by their use.     

Incorporating risk input into the analysis of bank productivity: Application to the Taiwanese banking industry

This study reappraises banks’ productivity by using 42 Taiwanese banks during 1999–2007 as observations. It introduces an input-oriented generalized metafrontier Malmquist productivity index (I-gMMPI), while considering the latent effect of risk-taking behavior in the analytic framework. We learn that public and private banks should face separate short-term technological frontiers, while the econometric model considering risk input can portray banks’ operating frontiers better. Moreover, neglecting the influence of risk input would bring about distortions of efficiency, technology and TFP dynamic estimations for banks; meanwhile, the degree of scale economies would also be overestimated. The paper concludes that neglecting the risk-taking essence in bank performance evaluation is equal to allowing banks to barter risk-bearing as the term for further output growth. Consequently, the potential cost is that banks may excessively aggrandize their scales of business, implying the possibility of another financial crisis.     

Risk factor contributions in portfolio credit risk models

Determining contributions to overall portfolio risk is an important topic in risk management. For positions (instruments and sub-portfolios), this problem has been well studied, and a significant theory built, around the calculation of marginal contributions. We consider the problem of determining the contributions to portfolio risk of risk factors. This cannot be addressed through an immediate extension of techniques for position contributions, since the portfolio loss is a nonlinear function of the risk factors. We employ the Hoeffding decomposition of the portfolio loss into a sum of terms depending on the factors. This decomposition restores linearity, but includes terms arising from joint effects of groups of factors. These cross-factor terms provide information to risk managers, since they can be viewed as best hedges of the portfolio loss involving instruments of increasing complexity. We illustrate the technique on multi-factor portfolio credit risk models, where systematic factors represent industries, geographical sectors, etc.     

Systemic risk in the European sovereign and banking system

We investigate the systemic risk of the European sovereign and banking system during 2008–2013. We utilize a conditional measure of systemic risk that reflects market perceptions and can be intuitively interpreted as an entity’s conditional joint probability of default, given the hypothetical default of other entities. The measure of systemic risk is applicable to high dimensions and not only incorporates individual default risk characteristics but also captures the underlying interdependent relations between sovereigns and banks in a multivariate setting. In empirical applications, our results reveal significant time variation in systemic risk spillover effects for the sovereign and banking system. We find that systemic risk is mainly driven by risk premiums coupled with a steady increase in physical default risk.     

Translational benchmark risk analysis

Translational development – in the sense of translating a mature methodology from one area of application to another, evolving area – is discussed for the use of benchmark doses in quantitative risk assessment. Illustrations are presented with traditional applications of the benchmark paradigm in biology and toxicology, and also with risk endpoints that differ from traditional toxicological archetypes. It is seen that the benchmark approach can apply to a diverse spectrum of risk management settings. This suggests a promising future for this important risk‐analytic tool. Extensions of the method to a wider variety of applications represent a significant opportunity for enhancing environmental, biomedical, industrial, and socio‐economic risk assessments.     

Accounting,risk, and revolution

In response to the position of Steve Toms, this article argues that risk must be understood not as it has been posited by capital but rather as it might be taken up by labour. It uses Marx's socialization thesis to maintain that risk is a symptom of possibility for labour. Drawing on the work of Randy Martin the argument culminates in a consideration of the interanimation of capital in labour occasioned by the second helping of risk produced by its commoditisation. It concludes that far from being just what Michel Aglietta calls a social evaluation of private economic activity, risk offers the opportunity to develop an accounting not just to provoke capital's contradictions with its own tools but to develop an immanent accounting of socialized labour in revolution, an accounting to come.     

Co-dependence of extreme events in high frequency FX returns

In this paper, we investigate extreme events in high frequency, multivariate FX returns within a purposely built framework. We generalize univariate tests and concepts to multidimensional settings and employ these novel techniques for parametric and nonparametric analysis. In particular, we investigate and quantify the co-dependence of cross-sectional and intertemporal extreme events. We find evidence of the cubic law of extreme returns, their increasing and asymmetric dependence and of the scaling property of extreme risk in joint symmetric tails.     

Translational benchmark risk analysis

Translational development - in the sense of translating a mature methodology from one area of application to another, evolving area - is discussed for the use of benchmark doses in quantitative risk assessment. Illustrations are presented with traditional applications of the benchmark paradigm in biology and toxicology, and also with risk endpoints that differ from traditional toxicological archetypes. It is seen that the benchmark approach can apply to a diverse spectrum of risk management settings. This suggests a promising future for this important risk-analytic tool. Extensions of the method to a wider variety of applications represent a significant opportunity for enhancing environmental, biomedical, industrial, and socio-economic risk assessments.