This issue of The Journal of Risk covers topics that have been around for a long time, such as the valuation of risky cashflows and the estimation of errors in the computation of commonly used risk measures. It also addresses issues that became particularly prominent following the financial crisis of 2007–9, especially with regard to regulatory capital requirements.
The standard valuation of risky cashflows rests firmly on the expected values of payoffs – which can often be replicated via different portfolios – or of their utility values. In our first paper, “Valuing streams of risky cashflows with risk-value models”, Gregor Dorfleitner and Werner Gleißner present an alternative method that accounts for risk management considerations. Specifically, it relies on identifying a portfolio of a risky and a risk-free asset with a risk that matches that of the cashflow, where the risk can be assessed via any risk measure satisfying only a subset of the axioms for coherence. One advantage of this approach is that it no longer requires market completeness or the reliance of hard-to-obtain utility functions.
Errors in the estimation of the most prevalent risk measures – value-at-risk and expected shortfall – are generally difficult to assess. Using the standard approach of directly comparing an exact value, when known, of either of these risk measures and their estimates may be misleading. In “Estimation risk for value-at-risk and expected shortfall”, the second paper in this issue, Paul Kabaila and Rheanna Mainzer propose a regression-based model that sheds light on some important features regarding this estimation exercise. For example, an estimate may be found to be unbiased across a large number of possible scenarios but could very significantly differ from the exact value with a substantial probability.
The financial crisis of 2007–9 highlighted the contagious effect of overlapping counterparty credit risks in bilateral over-the-counter (OTC) contracts. As a consequence of the regulatory reforms that ensued, central clearing parties are now involved as buffers, requesting collateral assets. Among these, initial margin addresses the riskiness of other collateral assets posted in relation to the OTC contracts. In the issue’s third paper, “Initial margin with risky collateral”, Ming Shi, Xinxin Yu and Ke Zhang introduce a framework to determine such margins and to contrast the effect of the collateral of reference in this evaluation.
The financial crisis also led to more stringent capital requirements for solvency. In “Optimal equity protection of Solvency II regulated portfolios”, the fourth paper of this issue, Benoit Vaucher appeals to the risk-mitigation aspect of put contracts to help reduce these capital requirements. In particular, he shows how one can optimally select strike values in order to get the best reduction in capital charges, that is, the opportunity costs that result from holding capital for regulatory reasons. He also highlights instances where the best put option choice reduces capital requirements without affecting the budget allocated to risk reduction.
The previous two papers focus on strategies in anticipation of potential losses within the context of risk management, without paying particular attention to their causes. Following the 2007–9 financial crisis, a concerted effort to stress test risk models began to emerge, supported by both firms and regulators. In particular, the so-called reverse stress test involves the identification of specific events that result in particular outcomes with critical damage. In the fifth and final paper of this issue, “The quickest way to lose the money you cannot afford to lose: reverse stress testing with maximum entropy”, Riccardo Rebonato presents a general method, assuming a linear relation between risk factors and portfolio loss, that is capable of identifying the most likely combination of factor values leading to specific portfolio losses. This method relies on principal component analysis and is particularly appealing in high-dimensional settings involving a variety of micro- and macrolevel factors.
Warrington College of Business,
University of Florida
Based on risk-value models this paper introduces a multi-period approach to the valuation of streams of risky cash flows.
This paper provides a detailed analysis of the relationship between approximate VaR (ES) and exact VaR (ES) by finding a linear regression model in which the response variable is the approximate VaR (ES) and the explanatory variable is the exact VaR (ES)…
This paper explores the complication of calculating the IM amount requirement when collateral comprises risky assets in a parametric VaR framework. The authors show that the required IM amount can be calculated by solving a quadratic inequality.
In the context of equity investments, this paper examines the relationship between the cost of acquiring protection (in the form of put option) and the reduction of capital charges that it entails. The paper develops the idea that Solvency II regulations…
The quickest way to lose the money you cannot afford to lose: reverse stress testing with maximum entropy
This paper extends a technique devised by Saroka and Rebonato to “optimally” deform a yield curve in order to deal with a common and practically relevant class of optimization problems subject to linear constraints.