This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Quantitative Risk Management: Concepts, Techniques, and Tools

Foundations Of Statistics

Few areas of monetary economics have been studied as extensively as the transmission mechanism. The literature on this topic has evolved substantially over the years, following the waxing and waning of conceptual frameworks and the changing characteristics of the financial system. In this paper, taking as a starting point a brief overview of the extant work on the interaction between capital regulation, the business cycle and the transmission mechanism, we offer some broader reflections on the characteristics of the transmission mechanism in light of the evolution of the financial system. We argue that insufficient attention has so far been paid to the link between monetary policy and the perception and pricing of risk by economic agents - what might be termed the "risk-taking channel" of monetary policy. We develop the concept, compare it with current views of the transmission mechanism, explore its mutually reinforcing link with "liquidity" and analyse its interaction with monetary policy reaction functions. We argue that changes in the financial system and prudential regulation may have increased the importance of the risk-taking channel and that prevailing macroeconomic paradigms and associated models are not well suited to capturing it, thereby also reducing their effectiveness as guides to monetary policy.

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Capital Regulation, Risk-Taking and Monetary Policy: A Missing Link in the Transmission Mechanism?

Today's financial regulatory systems assume that regulations which make individual banks safe also make the financial system safe. The eleventh Geneva Report on the World Economy shows that this thinking is flawed. Actions that banks take to make themselves safer can - in times of crisis - undermine the system's stability. The Report argues for a different approach. What is needed is micro-prudential (i.e. bank-level) regulation, macro-prudential (i.e. system-wide) regulation, and careful coordination of the two. Macro-prudential regulation in particular needs reform to ensure it countervails the natural decline in measured risk during booms and its rise in subsequent collapses. "Counter-cyclical capital charges" are the way forward; regulators should adjust capital adequacy requirements over the cycle by two multiples - the first related to above-average growth of credit expansion and leverage, the second related to the mismatch in the maturity of assets and liabilities. Changes to mark-to-market procedures are also needed. Macro- and micro-prudential regulation should be carried out by separate institutions since they differ in focus and expertise required. Central Banks should be tasked with macro-prudential regulation, Financial Services Authorities with micro-prudential regulation. Improved international coordination is also important. Since financial and asset-price cycles differ from country to country, counter-cyclical regulatory policy needs to be implemented mainly by the "host" rather than the "home" country.

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The fundamental principles of financial regulation

The recent financial crisis has highlighted the need to go beyond a purely micro approach to financial regulation and supervision. As a consequence, the number of policy speeches, research papers and conferences that discuss a macro perspective on financial regulation has grown considerably. The policy debate is focusing in particular on macroprudential tools and their usage, their relationship with monetary policy, their implementation and their effectiveness. Macroprudential policy has recently also attracted considerable attention among researchers. This paper provides an overview of research on this topic. We also identify important future research questions that emerge from both the literature and the current policy debate.

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Macroprudential policy – a literature review

Recent crises in the financial industry have shown weaknesses in the modeling of Risk-Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes in the RWA numbers. Similar problems are encountered in the Value-at-Risk (VaR)-aggregation of risks. In this article, we highlight some of the underlying issues, both methodologically, as well as through examples. In particular, we frame this discussion in the context of two recent regulatory documents we refer to as Basel 3.5.

https://sas.uwaterloo.ca/~wang/papers/2014Embrechts-Puccetti-Ruschendorf-Wang-Beleraj-Risks.pdf

An Academic Response to Basel 3.5

Despite well-known shortcomings as a risk measure, Value-at-Risk (VaR) is still the industry and regulatory standard for the calculation of risk capital in banking and insurance. This paper is concerned with the numerical estimation of the VaR for a portfolio position as a function of different dependence scenarios on the factors of the portfolio. Besides summarizing the most relevant analytical bounds, including a discussion of their sharpness, we introduce a numerical algorithm which allows for the computation of reliable (sharp) bounds for the VaR of high-dimensional portfolios with dimensions d possibly in the several hundreds. We show that additional positive dependence information will typically not improve the upper bound substantially. In contrast higher order marginal information on the model, when available, may lead to strongly improved bounds. Several examples of practical relevance show how explicit VaR bounds can be obtained. These bounds can be interpreted as a measure of model uncertainty induced by possible dependence scenarios.

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Model uncertainty and VaR aggregation

Model Uncertainty and VaR Aggregation

http://www.archiv.stochastik.uni-freiburg.de/homepages/rueschendorf/papers/PR12af-20110701.pdf

Computation of sharp bounds on the distribution of a function of dependent risks

The problem of finding the best-possible lower bound on the distribution of a non-decreasing function of n dependent risks is solved when n=2 and a lower bound on the copula of the portfolio is provided. The problem gets much more complicated in arbitrary dimensions. When no information on the structure of dependence of the random vector is available, we provide a bound on the dis- tribution function of the sum of risks which we prove to be better than the one generally used in the literature.

Giovanni Puccetti

Papers

An Academic Response to Basel 3.5

Model uncertainty and VaR aggregation

Model Uncertainty and VaR Aggregation

Computation of sharp bounds on the distribution of a function of dependent risks

Bounds for Functions of Dependent Risks