Market risk, quantitative analysis, market risk measurement, value at risk, VaR - variance/covariance, VaR - simulation approaches, probability, simulation, risk factors, loss distributions, risk measurement approaches, notional-amount approach, factor-sensitivity approach, risk measures based on loss distributions, scenario-based risk measures, coherent risk measures, generalized inverse and quantile function, variance, semi-variance, expected shortfall, multi-period measures, scaling, backtesting, comparison of VaR approaches
From the Authors - In this chapter we discuss essential concepts in quantitative risk management. We begin by introducing a probabilistic framework for modelling financial risk and we give formal definitions for notions such as risk, profit and loss, risk factors and mapping. Moreover, we discuss a number of examples from the areas of market and credit risk, illustrating how typical risk-management problems fit into the general framework. In Section 2.2 we give an overview of the existing approaches to measuring risk and discuss their strengths and weaknesses. Particular attention will be given to Value-at-Risk and the related notion of expected shortfall. In Section 2.3 we present some standard methods used in the financial industry for measuring market risk over a short horizon, such as the variance–covariance method, the historical-simulation method and methods based on Monte Carlo simulation. We consider the use of scaling rules for transforming one-period risk-measure estimates into estimates for longer time horizons and give a short discussion of backtesting approaches for monitoring the performance of risk-measurement systems. We conclude with an example of the application of standard methodology.
2.1 Risk Factors and Loss Distributions
2.1.1 General Definitions
2.1.2 Conditional and Unconditional Loss Distribution
2.1.3 Mapping of Risks: Some Examples
2.2 Risk Measurement
2.2.1 Approaches to Risk Measurement
2.2.3 Further Comments on VaR
2.2.4 Other Risk Measures Based on Loss Distributions
2.3 Standard Methods for Market Risks
2.3.1 Variance–Covariance Method
2.3.2 Historical Simulation
2.3.3 Monte Carlo
2.3.4 Losses over Several Periods and Scaling
2.3.6 An Illustrative Example
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*** From the publisher ***
The implementation of sound quantitative risk models is a vital concern for all financial institutions, and this trend has accelerated in recent years with regulatory processes such as Basel II. This book provides a comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management and equips readers--whether financial risk analysts, actuaries, regulators, or students of quantitative finance--with practical tools to solve real-world problems. The authors cover methods for market, credit, and operational risk modelling; place standard industry approaches on a more formal footing; and describe recent developments that go beyond, and address main deficiencies of, current practice.
The book`s methodology draws on diverse quantitative disciplines, from mathematical finance through statistics and econometrics to actuarial mathematics. Main concepts discussed include loss distributions, risk measures, and risk aggregation and allocation principles. A main theme is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. The techniques required derive from multivariate statistical analysis, financial time series modelling, copulas, and extreme value theory. A more technical chapter addresses credit derivatives. Based on courses taught to masters students and professionals, this book is a unique and fundamental reference that is set to become a standard in the field.