prm handbook introduction and contents
TRANSCRIPT
PRM Handbook Introduction and Contents
Updated May 2011
The Professional Risk Managers’ Handbook A Comprehensive Guide to Current Theory and Best Practices
___________________________________________________
Edited by Carol Alexander and Elizabeth Sheedy
The Official Handbook for the PRM Certification
PRM Handbook Introduction and Contents
2010 © The Professional Risk Managers’ International Association ii
Contents Author Biographies
Section I – for PRM Exam I FINANCE THEORY, FINANCIAL INSTRUMENTS AND MARKETS
Section I, Part A From PRM Handbook Volume I: Book 1 – GUIDE TO FINANCIAL THEORY APPLICATION
I.A.0 INTEREST RATES AND TIME VALUE I.A.0.1 COMPOUNDING METHODS I.A.0.2 INTEREST RATES: NOMINAL, PERIODIC, CONTINUOUS OR EFFECTIVE
I.A.1 RISK AND RISK AVERSION
I.A.1.1 INTRODUCTION I.A.1.2 MATHEMATICAL EXPECTATIONS: PRICES OR UTILITIES? I.A.1.3 THE AXIOM OF INDEPENDENCE OF CHOICE I.A.1.4 MAXIMISING EXPECTED UTILITY I.A.1.5 ENCODING A UTILITY FUNCTION I.A.1.6 THE MEAN–VARIANCE CRITERION I.A.1.7 RISK-ADJUSTED PERFORMANCE MEASURES
I.A.2 PORTFOLIO MATHEMATICS
I.A.2.1 MEANS AND VARIANCES OF PAST RETURNS I.A.2.2 MEAN AND VARIANCE OF FUTURE RETURNS I.A.2.3 MEAN–VARIANCE TRADEOFFS I.A.2.4 MULTIPLE ASSETS I.A.2.5 A HEDGING EXAMPLE I.A.2.6 SERIAL CORRELATION I.A.2.7 NORMALLY DISTRIBUTED RETURNS
I.A.3 CAPITAL ALLOCATION
I.A.3.1 AN OVERVIEW I.A.3.2 MEAN–VARIANCE CRITERION I.A.3.3 EFFICIENT FRONTIER: TWO RISKY ASSETS I.A.3.4 ASSET ALLOCATION I.A.3.5 COMBINING THE RISK-FREE ASSET WITH RISKY ASSETS I.A.3.6 THE MARKET PORTFOLIO AND THE CML I.A.3.7 THE MARKET PRICE OF RISK AND THE SHARPE RATIO I.A.3.8 SEPARATION PRINCIPLE
I.A.4 THE CAPM AND MULTIFACTOR MODELS
I.A.4.1 OVERVIEW I.A.4.2 CAPITAL ASSET PRICING MODEL I.A.4.3 SECURITY MARKET LINE I.A.4.4 PERFORMANCE MEASURES I.A.4.5 THE SINGLE-INDEX MODEL I.A.4.6 MULTIFACTOR MODELS AND THE APT
I.A.5 BASICS OF CAPITAL STRUCTURE
I.A.5.1 INTRODUCTION I.A.5.2 MAXIMISING SHAREHOLDER VALUE, INCENTIVES AND AGENCY COSTS I.A.5.3 CHARACTERISTICS OF DEBT AND EQUITY I.A.5.4 CHOICE OF CAPITAL STRUCTURE I.A.5.5 MAKING THE CAPITAL STRUCTURE DECISION
PRM Handbook Introduction and Contents
2010 © The Professional Risk Managers’ International Association iii
I.A.6 THE TERM STRUCTURE OF INTEREST RATES
I.A.6.1 INTRODUCTION TO THE TERM STRUCTURE OF INTEREST RATES I.A.6.2 THEORIES OF THE TERM STRUCTURE I.A.6.3 TERM STRUCTURE MODELS I.A.6.4 USING TERM STRUCTURE MODELS TO EVALUATE BONDS
I.A.7 VALUING FORWARD CONTRACTS
I.A.7.1 THE DIFFERENCE BETWEEN PRICING AND VALUATION FOR FORWARD CONTRACTS I.A.7.2 PRINCIPLES OF PRICING AND VALUATION FOR FORWARD CONTRACTS ON ASSETS I.A.7.3 PRINCIPLES OF PRICING AND VALUATION FOR FORWARD CONTRACTS ON INTEREST RATES I.A.7.4 THE RELATIONSHIP BETWEEN FORWARD AND FUTURES PRICES
I.A.8 BASIC PRINCIPLES OF OPTION PRICING
I.A.8.1 FACTORS AFFECTING OPTION PRICES I.A.8.2 PUT–CALL PARITY I.A.8.3 ONE-STEP BINOMIAL MODEL AND THE RISKLESS PORTFOLIO I.A.8.4 DELTA NEUTRALITY AND SIMPLE DELTA HEDGING I.A.8.5 RISK-NEUTRAL VALUATION I.A.8.6 REAL VERSUS RISK-NEUTRAL I.A.8.7 THE BLACK–SCHOLES–MERTON PRICING FORMULA I.A.8.8 THE GREEKS I.A.8.9 IMPLIED VOLATILITY I.A.8.10 INTRINSIC VERSUS TIME VALUE
Section I, Part B From PRM Handbook - Volume I: Book 2 – GUIDE TO FINANCIAL INSTRUMENTS
I.B.1 GENERAL CHARACTERISTICS OF BONDS
I.B.1.1 DEFINITION OF A BULLET BOND I.B.1.2 TERMINOLOGY AND CONVENTION I.B.1.3 MARKET QUOTES I.B.1.4 NON-BULLET BONDS
I.B.2 THE ANALYSIS OF BONDS
I.B.2.1 FEATURES OF BONDS I.B.2.2 NON-CONVENTIONAL BONDS I.B.2.3 PRICING A CONVENTIONAL BOND I.B.2.4 MARKET YIELD I.B.2.5 RELATIONSHIP BETWEEN BOND YIELD AND BOND PRICE I.B.2.6 DURATION I.B.2.7 HEDGING BOND POSITIONS I.B.2.8 CONVEXITY I.B.2.9 SUMMARY OF MARKET RISK ASSOCIATED WITH BONDS
I.B.3 FUTURES AND FORWARDS
I.B.3.1 INTRODUCTION I.B.3.2. STOCK INDEX FUTURES I.B.3.3 CURRENCY FORWARDS AND FUTURES I.B.3.4 COMMODITY FUTURES I.B.3.5 FORWARD RATE AGREEMENTS I.B.3.6 SHORT-TERM INTEREST-RATE FUTURES I.B.3.7 T-BOND FUTURES I.B.3.8 STACK AND STRIP HEDGES
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I.B.4 SWAPS
I.B.4.1 WHAT IS A SWAP? I.B.4.2 TYPES OF SWAPS I.B.4.3 ENGINEERING INTEREST RATE SWAPS I.B.4.4 RISKS OF SWAPS I.B.4.5 OTHER SWAPS I.B.4.6 USES OF SWAPS I.B.4.7 SWAP CONVENTIONS
I.B.5 VANILLA OPTIONS
I.B.5.1 STOCK OPTIONS – CHARACTERISTICS AND PAYOFF DIAGRAMS I.B.5.2 AMERICAN VERSUS EUROPEAN OPTIONS I.B.5.3 STRATEGIES INVOLVING A SINGLE OPTION AND A STOCK I.B.5.4 SPREAD STRATEGIES I.B.5.5 OTHER STRATEGIES
I.B.6 CREDIT DERIVATIVES
I.B.6.1 INTRODUCTION I.B.6.2 CREDIT DEFAULT SWAPS I.B.6.3 CREDIT-LINKED NOTES I.B.6.4 TOTAL RETURN SWAPS I.B.6.5 CREDIT OPTIONS AND NEW INVESTMENT INSTRUMENTS I.B.6.6 SYNTHETIC COLLATERALISED DEBT OBLIGATIONS I.B.6.7 GENERAL APPLICATIONS OF CREDIT DERIVATIVES I.B.6.8 UNINTENDED RISKS IN CREDIT DERIVATIVES
I.B.7 CAPS, FLOORS AND SWAPTIONS
I.B.7.1 CAPS, FLOORS AND COLLARS: DEFINITION AND TERMINOLOGY I.B.7.2 PRICING CAPS, FLOORS AND COLLARS I.B.7.3 USES OF CAPS, FLOORS AND COLLARS I.B.7.4 SWAPTIONS: DEFINITION AND TERMINOLOGY I.B.7.5 PRICING SWAPTIONS I.B.7.6 USES OF SWAPTIONS
I.B.8 CONVERTIBLE BONDS
I.B.8.1 INTRODUCTION I.B.8.2 CHARACTERISTICS OF CONVERTIBLES I.B.8.3 CAPITAL STRUCTURE IMPLICATIONS FOR BANKS I.B.8.4 MANDATORY CONVERTIBLES I.B.8.5 VALUATION AND RISK ASSESSMENT
I.B.9 SIMPLE EXOTICS
I.B.9.1 INTRODUCTION I.B.9.2 A SHORT HISTORY I.B.9.3 CLASSIFYING EXOTICS I.B.9.4 NOTATION I.B.9.5 DIGITAL OPTIONS I.B.9.6 TWO ASSET OPTIONS I.B.9.7 QUANTOS I.B.9.8 SECOND-ORDER CONTRACTS I.B.9.9 DECISION OPTIONS I.B.9.10 AVERAGE OPTIONS I.B.9.11 OPTIONS ON BASKETS OF ASSETS I.B.9.12 BARRIER AND RELATED OPTIONS I.B.9.13 OTHER PATH-DEPENDENT OPTIONS I.B.9.14 RESOLUTION METHODS
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Section 1, Part C From PRM Handbook Volume I: Book 3 – GUIDE TO FINANCIAL MARKETS
I.C.1 THE STRUCTURE OF FINANCIAL MARKETS
I.C.1.1 INTRODUCTION I.C.1.2 GLOBAL MARKETS AND THEIR TERMINOLOGY I.C.1.3 DRIVERS OF LIQUIDITY I.C.1.4 LIQUIDITY AND FINANCIAL RISK MANAGEMENT I.C.1.5 EXCHANGES VERSUS OTC MARKETS I.C.1.6 TECHNOLOGICAL CHANGE I.C.1.7 POST-TRADE PROCESSING I.C.1.8 RETAIL AND WHOLESALE BROKERAGE I.C.1.9 NEW FINANCIAL MARKETS
I.C.2 THE MONEY MARKETS
I.C.2.1 INTRODUCTION I.C.2.2 CHARACTERISTICS OF MONEY MARKET INSTRUMENTS I.C.2.3 DEPOSITS AND LOANS I.C.2.4 MONEY MARKET SECURITIES
I.C.3 BOND MARKETS
I.C.3.1 INTRODUCTION I.C.3.2 THE PLAYERS I.C.3.3 BONDS BY ISSUERS I.C.3.4 THE MARKETS I.C.3.5 CREDIT RISK
I.C.4 THE FOREIGN EXCHANGE MARKET
I.C.4.1 INTRODUCTION I.C.4.2 THE INTERBANK MARKET I.C.4.3 EXCHANGE-RATE QUOTATIONS I.C.4.4 DETERMINANTS OF FOREIGN EXCHANGE RATES I.C.4.5 SPOT AND FORWARD MARKETS I.C.4.6 STRUCTURE OF A FOREIGN EXCHANGE OPERATION
I.C.5 THE STOCK MARKET
I.C.5.1 INTRODUCTION I.C.5.2 THE CHARACTERISTICS OF COMMON STOCK I.C.5.3 STOCK MARKETS AND THEIR PARTICIPANTS I.C.5.4 THE PRIMARY MARKET – IPOS AND PRIVATE PLACEMENTS I.C.5.5 THE SECONDARY MARKET – THE EXCHANGE VERSUS OTC MARKET I.C.5.6 TRADING COSTS I.C.5.7 BUYING ON MARGIN I.C.5.8 SHORT SALES AND STOCK BORROWING COSTS I.C.5.9 EXCHANGE-TRADED DERIVATIVES ON STOCKS
I.C.6 THE FUTURES MARKETS
I.C.6.1 INTRODUCTION I.C.6.2 HISTORY OF FORWARD-BASED DERIVATIVES AND FUTURES MARKETS I.C.6.3 FUTURES CONTRACTS AND MARKETS I.C.6.4 OPTIONS ON FUTURES I.C.6.5 FUTURES EXCHANGES AND CLEARING HOUSES I.C.6.6 MARKET PARTICIPANTS – HEDGERS I.C.6.7 MARKET PARTICIPANTS – SPECULATORS I.C.6.8 MARKET PARTICIPANTS – MANAGED FUTURES INVESTORS
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I.C.7. THE STRUCTURE OF COMMODITIES MARKETS
I.C.7.1 INTRODUCTION I.C.7.2 THE COMMODITY UNIVERSE AND ANATOMY OF MARKETS I.C.7.3 SPOT–FORWARD PRICING RELATIONSHIPS I.C.7.4 SHORT SQUEEZES, CORNERS AND REGULATION I.C.7.5 RISK MANAGEMENT AT THE COMMODITY TRADING DESK I.C.7.6 THE DISTRIBUTION OF COMMODITY RETURNS
I.C.8 THE ENERGY MARKETS
I.C.8.1 INTRODUCTION I.C.8.2 MARKET OVERVIEW I.C.8.3 ENERGY FUTURES MARKETS I.C.8.4 OTC ENERGY DERIVATIVE MARKETS I.C.8.5 EMERGING ENERGY MARKETS I.C.8.6 THE FUTURE OF ENERGY TRADING
Section II – for PRM Exam II
MATHEMATICAL FOUNDATIONS OF RISK MEASUREMENTS
From PRM Handbook Volume II: Mathematical Foundations of Risk Measurements
II.A FOUNDATIONS
II.A.1 SYMBOLS AND RULES II.A.2 SEQUENCES AND SERIES II.A.3 EXPONENTS AND LOGARITHMS II.A.4 EQUATIONS AND INEQUALITIES II.A.5 FUNCTIONS AND GRAPHS II.A.6 CASE STUDY − CONTINUOUS COMPOUNDING
II.B DESCRIPTIVE STATISTICS
II.B.1 INTRODUCTION II.B.2 DATA II.B.3 THE MOMENTS OF A DISTRIBUTION II.B.4 MEASURES OF LOCATION OR CENTRAL TENDENCY – AVERAGES II.B.5 MEASURES OF DISPERSION II.B.6 BIVARIATE DATA
II.C CALCULUS
II.C.1 DIFFERENTIAL CALCULUS II.C.2 CASE STUDY: MODIFIED DURATION OF A BOND II.C.3 HIGHER-ORDER DERIVATIVES II.C.4 FINANCIAL APPLICATIONS OF SECOND DERIVATIVES II.C.5 DIFFERENTIATING A FUNCTION OF MORE THAN ONE VARIABLE II.C.6 INTEGRAL CALCULUS II.C.7 OPTIMISATION
II.D LINEAR MATHEMATICS AND MATRIX ALGEBRA
II.D.1 MATRIX ALGEBRA II.D.2 APPLICATION – MATRIX ALGEBRA AND SIMULTANEOUS LINEAR EQUATIONS II.D.3 QUADRATIC FORMS II.D.4 CHOLESKY DECOMPOSITION II.D.5 EIGENVALUES AND EIGENVECTORS
II.E PROBABILITY THEORY IN FINANCE
II.E.1 DEFINITIONS AND RULES
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II.E.2 PROBABILITY DISTRIBUTIONS II.E.3 JOINT DISTRIBUTIONS II.E.4 SPECIFIC PROBABILITY DISTRIBUTIONS
II.F REGRESSION ANALYSIS IN FINANCE
II.F.1 SIMPLE LINEAR REGRESSION II.F.2 MULTIPLE LINEAR REGRESSION II.F.3 EVALUATING THE REGRESSION MODEL II.F.4 CONFIDENCE INTERVALS II.F.5 HYPOTHESIS TESTING II.F.6 PREDICTION II.F.7 BREAKDOWN OF THE OLS ASSUMPTIONS II.F.8 RANDOM WALKS AND MEAN REVERSION II.F.9 MAXIMUM LIKELIHOOD ESTIMATION
II.G NUMERICAL METHODS
II.G.1 SOLVING (NON-DIFFERENTIAL) EQUATIONS II.G.2 NUMERICAL OPTIMISATION II.G.3 NUMERICAL METHODS FOR VALUING OPTIONS
Section III – for PRM Exam III RISK MANAGEMENT PRACTICES
From PRM Handbook Volume III: Risk Management Practices Additionally, three publically available readings for Exam III can be found on the PRMIA website at http://prmia.org/index.php?page=exam&option=trainingWebBasedResource and, for those who have purchased PRM Handbook Volume III: Risk Management Practices, four supplemental papers can be found in your PRMIA "My Library".
III.0 CAPITAL ALLOCATION AND RAPM
III.0.1 INTRODUCTION III.0.2 ECONOMIC CAPITAL III.0.3 REGULATORY CAPITAL III.0.4 CAPITAL ALLOCATION AND RISK CONTRIBUTIONS III.0.5 RAROC AND RISK-ADJUSTED PERFORMANCE
III.A.1 MARKET RISK MANAGEMENT
III.A.1.1 INTRODUCTION III.A.1.2 MARKET RISK III.A.1.3 MARKET RISK MANAGEMENT TASKS III.A.1.4 THE ORGANISATION OF MARKET RISK MANAGEMENT III.A.1.5 MARKET RISK MANAGEMENT IN FUND MANAGEMENT III.A.1.6 MARKET RISK MANAGEMENT IN BANKING III.A.1.7 MARKET RISK MANAGEMENT IN NON-FINANCIAL FIRMS
III.A.2 INTRODUCTION TO VALUE AT RISK MODELS
III.A.2.1 INTRODUCTION III.A.2.2 DEFINITION OF VAR III.A.2.3 INTERNAL MODELS FOR MARKET RISK CAPITAL III.A.2.4 ANALYTICAL VAR MODELS III.A.2.5 MONTE CARLO SIMULATION VAR III.A.2.6 HISTORICAL SIMULATION VAR III.A.2.7 MAPPING POSITIONS TO RISK FACTORS III.A.2.8 BACKTESTING VAR MODELS
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III.A.2.9 WHY FINANCIAL MARKETS ARE NOT ‘NORMAL’
III.A.3: ADVANCED VALUE AT RISK MODELS
III.A.3.1 INTRODUCTION III.A.3.2 STANDARD DISTRIBUTIONAL ASSUMPTIONS III.A.3.3 MODELS OF VOLATILITY CLUSTERING III.A.3.4 VOLATILITY CLUSTERING AND VAR III.A.3.5 ALTERNATIVE SOLUTIONS TO NON-NORMALITY III.A.3.6 DECOMPOSITION OF VAR III.A.3.7 PRINCIPAL COMPONENT ANALYSIS
III.A.4 STRESS TESTING
III.A.4.1 INTRODUCTION III.A.4.2 HISTORICAL CONTEXT III.A.4.3 CONCEPTUAL CONTEXT III.A.4.4 STRESS TESTING IN PRACTICE III.A.4.5 APPROACHES TO STRESS TESTING: AN OVERVIEW III.A.4.6 HISTORICAL SCENARIOS III.A.4.7 HYPOTHETICAL SCENARIOS III.A.4.8 ALGORITHMIC APPROACHES TO STRESS TESTING III.A.4.9 EXTREME-VALUE THEORY AS A STRESS-TESTING METHOD III.A.4.10 SUMMARY AND CONCLUSIONS
III LIQUIDITY RISK MANAGEMENT
FUNDING LIQUIDITY: RISK ANALYSIS AND MANAGEMENT (SEE “MY LIBRARY”) by Selwyn Blair-Ford and Ioannis Akkizidis
III STRESS AND SCENARIO TESTING
This section is focused on 3 papers from financial authorities and regulators. These papers are publically available on the PRMIA website at http://prmia.org/index.php?page=exam&option=trainingWebBasedResource
Principles for sound stress testing practices and supervision Basel Committee on Banking Supervision (BCBS)
Stress and Scenario Testing Financial Services Authority (FSA)
The Supervisory Capital Assessment Program: Overview of Results Board of Governors of the Federal Reserve System.
III.B.1 CREDIT RISK MANAGEMENT
III.B.1.1 INTRODUCTION III.B.1.2 A CREDIT TO-DO LIST III.B.1.3 OTHER TASKS
III.B.2 FOUNDATIONS OF CREDIT RISK MODELLING
III.B.2.1 INTRODUCTION III.B.2.2 WHAT IS DEFAULT RISK? III.B.2.3 EXPOSURE, DEFAULT AND RECOVERY PROCESSES III.B.2.4 THE CREDIT LOSS DISTRIBUTION III.B.2.5 EXPECTED AND UNEXPECTED LOSS III.B.2.6 RECOVERY RATES
III.B.3 CREDIT EXPOSURE
III.B.3.1 INTRODUCTION III.B.3.2 PRE-SETTLEMENT VERSUS SETTLEMENT RISK III.B.3.3 EXPOSURE PROFILES III.B.3.4 MITIGATION OF EXPOSURES
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III.B.4 DEFAULT AND CREDIT MIGRATION
III.B.4.1 DEFAULT PROBABILITIES AND TERM STRUCTURES OF DEFAULT RATES III.B.4.2 CREDIT RATINGS III.B.4.3 AGENCY RATINGS III.B.4.4 CREDIT SCORING AND INTERNAL RATING MODELS III.B.4.5 MARKET-IMPLIED DEFAULT PROBABILITIES III.B.4.6 CREDIT RATING AND CREDIT SPREADS
III.B.5 PORTFOLIO MODELS OF CREDIT LOSS
III.B.5.1 INTRODUCTION III.B.5.2 WHAT ACTUALLY DRIVES CREDIT RISK AT THE PORTFOLIO LEVEL? III.B.5.3 CREDIT MIGRATION FRAMEWORK III.B.5.4 CONDITIONAL TRANSITION PROBABILITIES– CREDITPORTFOLIOVIEW III.B.5.5 THE CONTINGENT CLAIM APPROACH TO MEASURING CREDIT RISK III.B.5.6 THE KMV APPROACH III.B.5.7 THE ACTUARIAL APPROACH
III.B.6 CREDIT RISK CAPITAL CALCULATION
III.B.6.1 INTRODUCTION III.B.6.2 ECONOMIC CREDIT CAPITAL CALCULATION III.B.6.3 REGULATORY CREDIT CAPITAL: BASEL I III.B.6.4 REGULATORY CREDIT CAPITAL: BASEL II III.B.6.5 BASEL II: CREDIT MODEL ESTIMATION AND VALIDATION III.B.6.6 BASEL II: SECURITISATION III.B.6.7 ADVANCED TOPICS ON ECONOMIC CREDIT CAPITAL
III.C.1 THE OPERATIONAL RISK MANAGEMENT FRAMEWORK
III.C.1.1 INTRODUCTION III.C.1.2 EVIDENCE OF OPERATIONAL FAILURES III.C.1.3 DEFINING OPERATIONAL RISK III.C.1.4 TYPES OF OPERATIONAL RISK III.C.1.5 AIMS AND SCOPE OF OPERATIONAL RISK MANAGEMENT III.C.1.6 KEY COMPONENTS OF OPERATIONAL RISK III.C.1.7 SUPERVISORY GUIDANCE ON OPERATIONAL RISK III.C.1.8 IDENTIFYING OPERATIONAL RISK – THE RISK CATALOGUE III.C.1.9 THE OPERATIONAL RISK ASSESSMENT PROCESS III.C.1.10 THE OPERATIONAL RISK CONTROL PROCESS III.C.1.11 SOME FINAL THOUGHTS
III.C.2 OPERATIONAL RISK PROCESS MODELS
III.C.2.1 INTRODUCTION III.C.2.2 THE OVERALL PROCESS III.C.2.3 SPECIFIC TOOLS III.C.2.4 ADVANCED MODELS III.C.2.5 KEY ATTRIBUTES OF THE ORM FRAMEWORK III.C.2.6 INTEGRATED ECONOMIC CAPITAL MODEL III.C.2.7 MANAGEMENT ACTIONS III.C.2.8 RISK TRANSFER III.C.2.9 IT OUTSOURCING
III.C.3 OPERATIONAL VALUE-AT-RISK
III.C.3.1 THE ‘LOSS MODEL’ APPROACH III.C.3.2 THE FREQUENCY DISTRIBUTION III.C.3.3 THE SEVERITY DISTRIBUTION III.C.3.4 THE INTERNAL MEASUREMENT APPROACH III.C.3.5 THE LOSS DISTRIBUTION APPROACH III.C.3.6 AGGREGATING ORC
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III ENTERPRISE INFORMATION RISK
ENTERPRISE RISK INFORMATION MANAGEMENT (SEE “MY LIBRARY” ON THE PRMIA WEBSITE) by Dilip Krishna and Robert Mark
III SYSTEMIC RISK
WHY BANKS FAILED THE STRESS TESTS (SEE “MY LIBRARY” ON THE PRMIA WEBSITE) by Andrew G. Haldane
VIEWING THE FINANCIAL CRISIS FROM 20,000 FEET UP (SEE “MY LIBRARY” ON THE PRMIA WEBSITE) by Stephen Figlewski
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Introduction If you're reading this, you are seeking to attain a higher standard. Congratulations!
Those who have been a part of financial risk management for the past twenty years, have seen it
change from an on-the-fly profession, with improvisation as a rule, to one with substantially
higher standards, many of which are now documented and expected to be followed. It’s no
longer enough to say you know. Now, you and your team need to prove it.
As its title implies, this book is the Handbook for the Professional Risk Manager. It is for those
professionals who seek to demonstrate their skills through certification as a Professional Risk
Manager (PRM) in the field of financial risk management. And it is for those looking simply to
develop their skills through an excellent reference source.
With contributions from nearly 40 leading authors, the Handbook is designed to provide you
with the materials needed to gain the knowledge and understanding of the building blocks of
professional financial risk management. Financial risk management is not about avoiding risk.
Rather, it is about understanding and communicating risk, so that risk can be taken more
confidently and in a better way. Whether your specialism is in insurance, banking, energy, asset
management, weather, or one of myriad other industries, this Handbook is your guide.
In Volume II, we take you through the mathematical foundations of risk assessment. While there
are many nuances to the practice of risk management that go beyond the quantitative, it is
essential today for every risk manager to be able to assess risks. The chapters in this section are
accessible to all PRM members, including those without any quantitative skills. The Excel
spreadsheets that accompany the examples are an invaluable aid to understanding the
mathematical and statistical concepts that form the basis of risk assessment. After studying all
these chapters, you will have read the materials necessary for passage of Exam II of the PRM
Certification program.
Those preparing for the PRM certification will also be preparing for Exam I on Finance Theory,
Financial Instruments and Markets, covered in Volume I of the PRM Handbook, Exam III on
Risk Management Practices, covered in Volume III of the PRM Handbook and Exam IV - Case
Studies, Standards of Best Practice Conduct and Ethics and PRMIA Governance. Exam IV is
where we study some failed practices, standards for the performance of the duties of a
Professional Risk Manager, and the governance structure of our association, the Professional
Risk Managers’ International Association. The materials for Exam IV are freely available on our
website (see http://prmia.org/index.php?page=exam&option=trainingWebBasedResource ) and
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2010 © The Professional Risk Managers’ International Association xii
are thus outside of the Handbook. For Exam IV Learning Outcomes, see PRM Study Guide for
Exam IV or go to PRMIA webpage for link: http://prmia.org/index.php?page=exam.
At the end of your progression through these materials, you will find that you have broadened
your knowledge and skills in ways that you might not have imagined. You will have challenged
yourself as well. And, you will be a better risk manager. It is for this reason that we have created
the Professional Risk Managers’ Handbook.
Our deepest appreciation is extended to Prof. Carol Alexander and Prof. Elizabeth Sheedy,
dedicated PRMIA Leaders, for their editorial work on this document. The commitment they
have shown to ensuring the highest level of quality and relevance is beyond description.
Our thanks also go to the authors who have shared their insights with us. The demands for
sharing of their expertise are frequent. Yet, they have each taken special time for this project and
have dedicated themselves to making the Handbook and you a success. We are very proud to
bring you such a fine assembly.
Much like PRMIA, the Handbook is a place where the best ideas of the risk profession meet. We
hope that you will take these ideas, put them into practice and certify your knowledge by
attaining the PRM designation. Among our membership are several hundred Chief Risk Officers
/ Heads of Risk and tens of thousands of other risk professionals who will note your
achievements. They too know the importance of setting high standards and the trust that capital
providers and stakeholders have put in them. Now they put their trust in you and you can prove
your commitment and distinction to them.
We wish you much success during your studies and for your performance in the PRM exams!
PRMIA
PRM Handbook Introduction and Contents
2010 © The Professional Risk Managers’ International Association xiii
Section I Finance Theory, Financial Instruments and Markets
Preface to Section I: Finance Theory, Financial Instruments and Markets
For Exam I Learning Outcomes, see PRM Study Guide for Exam I. See PRMIA webpage for link: http://prmia.org/index.php?page=exam
Section I of this Handbook has been written by a group of leading scholars and practitioners and
represents a broad overview of the theory, instruments and markets of finance. This section
corresponds to Exam I in the Professional Risk Manager (PRM) certification programme.
The modern theory of finance is the solid basis of risk management and thus it naturally
represents the basis of the PRM certification programme. All major areas of finance are involved
in the process of risk management: from the expected utility approach and risk aversion, which
were the forerunners of the capital asset pricing model (CAPM), to portfolio theory and the risk-
neutral approach to pricing derivatives. All of these great financial theories and their interactions
are presented in Part I.A (Finance Theory). Many examples demonstrate how the concepts are
applied in practical situations.
Part I.B (Financial Instruments) describes a wide variety of financial products and connects them
to the theoretical development in Part I.A. The ability to value all the instruments/assets within
a trading or asset portfolio is fundamental to risk management. This part examines the valuation
of financial instruments and also explains how many of them can be used for risk management.
The designers of the PRM curriculum have correctly determined that financial risk managers
should have a sound knowledge of financial markets. Market liquidity, the role of intermediaries
and the role of exchanges are all features that vary considerably from one market to the next and
over time. It is crucial that professional risk managers understand how these features vary and
their consequences for the practice of risk management. Part I.C (Financial Markets) describes
where and how instruments are traded, the features of each type of financial asset or commodity
and the various conventions and rules governing their trade.
This background is absolutely necessary for professional risk management, and Exam I therefore
represents a significant portion of the whole PRM certification programme. For a practitioner
who left academic studies several years ago, this part of the Handbook will provide efficient
revision of finance theory, financial instruments and markets, with emphasis on practical
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2010 © The Professional Risk Managers’ International Association xiv
application to risk management. Such a person will find the chapters related to his/her work
easy reading and will have to study other topics more deeply.
The coverage of financial topics included in Section I of the Handbook is typically deeper and
broader than that of a standard MBA syllabus. But the concepts are well explained and
appropriately linked together. For example, Chapter I.B.6 on credit derivatives covers many
examples (such as credit-linked notes and credit default swaps) that are not always included in a
standard MBA-level elective course on fixed income. Chapter I.B.9 on simple exotics also
provides examples of path-dependent derivatives beyond the scope of a standard course on
options. All chapters are written for professionals and assume a basic understanding of markets
and their participants.
Finance Theory
Chapter I.A.1 provides a general overview of risk and risk aversion, introduces the utility
function and mean–variance criteria. Various risk-adjusted performance measures are described.
A summary of several widely used utility functions is presented in the appendix.
Chapter I.A.2 provides an introduction to portfolio mathematics, from means and variances of
returns to correlation and portfolio variance. This leads the reader to the efficient frontier,
portfolio theory and the concept of portfolio diversification. Eventually this chapter discusses
normally distributed returns and basic applications for value-at-risk, as well as the probability of
reaching a target or beating a benchmark. This chapter is very useful for anybody with little
experience in applying basic mathematical models in finance.
The concept of capital allocation is another fundamental notion for risk managers. Chapter I.A.3
describes how capital is allocated between portfolios of risky and riskless assets, depending on
risk preference. Then the efficient frontier, the capital markets line, the Sharpe ratio and the
separation principle are introduced. These concepts lead naturally to a discussion of the CAPM
model and the idea that marginal risk (rather than absolute risk) is the key issue when pricing
risky assets. Chapter I.A.4 provides a rigorous description of the CAPM model, including betas,
systematic risk, alphas and performance measures. Arbitrage pricing theory and multifactor
models are also introduced in this chapter.
Capital structure is an important theoretical concept for risk managers since capital is viewed as
the last defence against extreme, unexpected outcomes. Chapter I.A.5 introduces capital
structure, advantages and costs related to debt financing, various agency costs, various types of
debt and equity, return on equity decomposition, examples of attractive and unattractive debt,
bankruptcy and financial distress costs.
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Most valuation problems involve discounting future cash flows, a process that requires
knowledge of the term structure of interest rates. Chapter I.A.6 describes various types of
interest rates and discounting, defines the term structure of interest rates, introduces forward
rates and explains the three main economic term structure theories.
These days all risk managers must be well versed in the use and valuation of derivatives. The two
basic types of derivatives are forwards (having a linear payoff) and options (having a non-linear
payoff). All other derivatives can be decomposed to these underlying payoffs or alternatively
they are variations on these basic ideas. Chapter I.A.7 describes valuation methods used for
forward contracts. Discounting is used to value forward contracts with and without intermediate
cash flow. Chapter I.A.8 introduces the principles of option pricing. It starts with definitions of
basic put and call options, put–call parity, binomial models, risk-neutral methods and simple delta
hedging. Then the Black–Scholes–Merton formula is introduced. Finally, implied volatility and
smile effects are briefly described.
Financial Instruments
Having firmly established the theoretical basis for valuation in Part I.A, Part I.B applies these
theories to the most commonly used financial instruments.
Chapter I.B.1 introduces bonds, defines the main types of bonds and describes the market
conventions for major types of treasuries, strips, floaters (floating-rate notes) and inflation-
protected bonds in different countries. Bloomberg screens are used to show how the market
information is presented. Chapter I.B.2 analyses the main types of bonds, describes typical cash
flows and other features of bonds and also gives a brief description of non-conventional
instruments. Examples of discounting, day conventions and accrued interest are provided, as
well as yield calculations. The connection between yield and price is described, thus naturally
leading the reader to duration, convexity and hedging interest-rate risk.
While Chapter I.A.7 explained the principles of forward valuation, Chapter I.B.3 examines and
compares futures and forward contracts. Usage of these contracts for hedging and speculation is
discussed. Examples of currency, commodity, bonds and interest-rate contracts are used to
explain the concept and its applications. Mark-to-market, quotation, settlements and other
specifications are described here as well. The principles of forward valuation are next applied to
swap contracts, which may be considered to be bundles of forward contracts. Chapter I.B.4
analyses some of the most popular swap varieties, explaining how they may be priced and used
for managing risk.
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The remaining chapters in Part I.B all apply the principles of option valuation as introduced in
Chapter I.A.8. The power of the option concept is obvious when we see its applications to so
many instruments and risk management problems. Chapter I.B.5 begins with an analysis of
vanilla options. Chapter I.B.6 covers one of the newer applications of options: the use of credit
risk derivatives to manage credit risk. Chapter I.B.7 addresses caps, floors and swaptions, which
are the main option strategies used in interest-rate markets. Yet another application of the
option principle is found in Chapter I.B.8 – convertible bonds. These give investors the right to
convert a debt security into equity. Finally, Chapter I.B.9 examines exotic option payoffs. In
every case the author defines the instrument, discusses its pricing and illustrates its use for risk
management purposes.
Financial Markets
Financial risk management takes place in the context of markets and varies depending on the
nature of the market. Chapter I.C.1 is a general introduction to world financial markets. They
can be variously classified – geographically, by type of exchange, by issuers, liquidity and type of
instruments – all are provided here. The importance of liquidity, the distinction between
exchange and over-the-counter markets and the role of intermediaries in their various forms are
explained in more detail.
Money markets are the subject of Chapter I.C.2. These markets are of vital importance to the
risk manager as the closest thing to a ‘risk-free’ asset is found here. This chapter covers all short-
term debt securities, whether issued by governments or corporations. It also explains the repo
markets – markets for borrowing/lending on a secured basis. The market for longer-term debt
securities is discussed in Chapter I.C.3, which classifies bonds by issuer: government, agencies,
corporate and municipal. There is a comparison of bond markets in major countries and a
description of the main intermediaries and their roles. International bond markets are introduced
as well.
Chapter I.C.4 turns to the foreign exchange market – the market with the biggest volume of
trade. Various aspects of this market are explained, such as quotation conventions, types of
brokers, and examples of cross rates. Economic theories of exchange rates are briefly presented
here along with central banks’ policies. Forward rates are introduced together with currency
swaps. Interest-rate parity is explained with several useful examples.
Chapter I.C.5 provides a broad introduction to stock markets. This includes the description and
characteristics of several types of stocks, stock market indices and priorities in the case of
liquidation. Dividends and dividend-based stock valuation methods are described in this
chapter. Primary and secondary markets are distinguished. Market mechanics, including types of
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orders, market participants, margin and short trades, are explained here with various examples
clarifying these transactions. Some exchange-traded options on stocks are introduced as well.
Chapter I.C.6 introduces the futures markets; this includes a comparison of the main exchange-
traded markets, options on futures, specifications of the most popular contracts, the use of
futures for hedging, trade orders for futures contracts, mark-to-market procedures, and various
expiration conventions. A very interesting description of the main market participants concludes
this chapter.
Chapter I.C.7 introduces the structure of the commodities market. It starts with the spot market
and then moves to commodity forwards and futures. Specific features, such as delivery and
settlement methods, are described. The spot–forward pricing relationship is used to decompose
the forward price into spot and carry. Various types of price term structure (such as
backwardation and contango) are described, together with some economic theory. The chapter
also describes short squeezes and regulations. Risk management at the commodity trading desk
is given at a good intuitive level. The chapter concludes with some interesting facts on
distribution of commodity returns.
Finally, Chapter I.C.8 examines one of the most rapidly developing markets for risk – the energy
markets. These markets allow participants to manage the price risks of oil and gas, electricity,
coal and so forth. Some other markets closely linked with energy are also briefly discussed here,
including markets for greenhouse gas emissions, weather derivatives and freight. Energy markets
create enormous challenges and opportunities for risk managers – in part because of the extreme
volatility of prices that can occur.
As a whole, Section I gives an overview of the theoretical and practical aspects of finance that are
used in the management of financial risks. Many concepts, some quite complex, are explained in
a relatively simple language and are demonstrated with numerous examples. Studying this part of
the Handbook should refresh your knowledge of financial models, products and markets and
provide the background for risk management applications.
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Section II
Mathematical Foundations of Risk Measurement
Preface to Section II: Mathematical Foundations of Risk Measurement
For Exam II Learning Outcomes, see PRM Study Guide for Exam II. See PRMIA webpage for link: http://prmia.org/index.php?page=exam
The role of risk management in financial firms has evolved far beyond the simple insurance of
identified risks. Today it is recognised that risks cannot be properly managed unless they are
quantified. And the assessment of risk requires mathematics. Take, for instance, a large portfolio
of stocks. The relationship between the portfolio returns and the market returns – and indeed
other potential risk factor returns – is typically estimated using a statistical regression analysis.
And the systematic risk of the portfolio is then determined by a quadratic form, a fundamental
concept in matrix algebra that is based on the covariance matrix of the risk factor returns.
Volatility is not the only risk metric that financial risk managers need to understand. During the
last decade value-at-risk (VaR) has become the ubiquitous tool for risk capital estimation. To
understand a VaR model, risk managers require knowledge of probability distributions,
simulation methods and a host of other mathematical and statistical techniques. Market VaR is
assessed by mapping portfolios to their risk factors and forecasting the volatilities and
correlations of these factors. The diverse quantitative techniques that are commonly applied in
the assessment of market VaR include eigenvectors and eigenvalues, Taylor expansions and
partial derivatives. Credit VaR can be assessed using firm-value models that are based on the
theory of options, or statistical and/or macro-econometric models. Probability distributions are
even applied to operational risks, though they are very difficult to quantify because the data are
sparse and unreliable. Indeed, the actuarial or loss model approach has been adopted as industry
standard for operational VaR models.
Even if not directly responsible for designing and coding a risk capital model, middle office risk
managers must understand these models sufficiently well to be competent to assess them. And
the risk management role encompasses many other responsibilities. Ten years ago my best
students aspired to become traders because of the high salaries and status – risk management was
viewed (by some) as a ‘second-rate’ job that did not require very special expertise. Now, this
situation has definitely changed. Today, the middle office risk manager’s responsibility has
expanded to include the independent validation of traders’ models, as well as risk capital
assessment. And the role of risk management in the front office itself has expanded, with the
need to hedge increasingly complex options portfolios. So today, the hallmark of a good risk
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manager is not just having the statistical skills required for risk assessment – a comprehensive
knowledge of pricing and hedging financial instruments is equally important.
No wonder, therefore, that the PRM qualification includes an entire exam on mathematical and
statistical methods. However, we do recognise that many students will not have degrees in
mathematics, physics or other quantitative disciplines. So this section of the Handbook is aimed
at students having no quantitative background at all. It introduces and explains all the
mathematics and statistics that are essential for financial risk management. Every chapter is
presented in a pedagogical manner, with associated Excel spreadsheets explaining the numerous
practical examples. And, for clarity and consistency, we chose two much respected authors of the
highly acclaimed textbook Quantitative Methods in Finance to write the entire section. Keith
Parramore and Terry Watsham have put considerable effort into making the PRM material
accessible to everyone, irrespective of their quantitative background.
The first chapter, II.A (Foundations), reviews the fundamental mathematical concepts: the
symbols used and the basic rules for arithmetic, equations and inequalities, functions and graphs,
etc. Chapter II.B (Descriptive Statistics) introduces the descriptive statistics that are commonly
used to summarise the historical characteristics of financial data: the sample moments of returns
distributions, ‘downside’ risk statistics, and measures of covariation (e.g. correlation) between two
random variables. Chapter II.C (Calculus) focuses on differentiation and integration, Taylor
expansion and optimisation. Financial applications include calculating the convexity of a bond
portfolio and the estimation of the delta and gamma of an options portfolio. Chapter II.D
(Linear Mathematics and Matrix Algebra) covers matrix operations, special types of matrices and
the laws of matrix algebra, the Cholesky decomposition of a matrix, and eigenvalues and
eigenvectors. Examples of financial applications include: manipulating covariance matrices;
calculating the variance of the returns to a portfolio of assets; hedging a vanilla option position;
and simulating correlated sets of returns. Chapter II.E (Probability Theory) first introduces the
concept of probability and the rules that govern it. Then some common probability distributions
for discrete and continuous random variables are described, along with their expectation and
variance and various concepts relating to joint distributions, such as covariance and correlation,
and the expected value and variance of a linear combination of random variables. Chapter II.F
(Regression Analysis) covers the simple and multiple regression models, with applications to the
capital asset pricing model and arbitrage pricing theory. The statistical inference section deals
with both prediction and hypothesis testing, for instance, of the efficient market hypothesis.
Finally, Chapter II.G (Numerical Methods) looks at solving implicit equations (e.g. the Black–
Scholes formula for implied volatility), lattice methods, finite differences and simulation.
Financial applications include option valuation and estimating the ‘Greeks’ for complex options.
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Whilst the risk management profession is no doubt becoming increasingly quantitative, the
quantification of risk will never be a substitute for good risk management. The primary role of a
financial risk manager will always be to understand the markets, the mechanisms and the
instruments traded. Mathematics and statistics are only tools, but they are necessary tools. After
working through this part of the Handbook you will have gained a thorough and complete
grounding in the essential quantitative methods for your profession.
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Section III
Risk Management Practices
Preface to Section III: Risk Management Practices
For Exam III Learning Outcomes, see PRM Study Guide for Exam III. See PRMIA webpage for link: http://prmia.org/index.php?page=exam
Section III is the ultimate part of The PRM Handbook in both senses of the word. Not only is it
the final section, but it represents the final aims and objectives of the Handbook. Sections I
(Finance Theory, Financial Instruments and Markets) and II (Mathematical Foundations of Risk
Measurement) laid the necessary foundations for this discussion of risk management practices –
the primary concern of most readers. Here some of the foremost practitioners and academics in
the field provide an up-to-date, rigorous and lucid statement of modern risk management.
The practice of risk management is evolving at a rapid pace, especially with the impending arrival
of Basel II. Aside from these regulatory pressures, shareholders and other stakeholders
increasingly demand higher standards of risk management and disclosure of risk. In fact, it
would not be an overstatement to say that risk consciousness is one of the defining features of
modern business. Nowhere is this truer than in the financial services industry. Interest in risk
management is at an unprecedented level as institutions gather data, upgrade their models and
systems, train their staff, review their remuneration systems, adapt their business practices and
scrutinise controls for this new era.
Section III is itself split into three parts which address market risk, credit risk and operational risk
in turn. These three are the main components of risk borne by any organisation, although the
relative importance of the mix varies. For a traditional commercial bank, credit risk has always
been the most significant. It is defined as the risk of default on debt, swap, or other counterparty
instruments. Credit risk may also result from a change in the value of a security, contract or asset
resulting from a change in the counterparty’s creditworthiness. In contrast, market risk refers to
changes in the values of securities, contracts or assets resulting from movements in exchange
rates, interest rates, commodity prices, stock prices, etc. Operational risk, the risk of loss
resulting from inadequate or failed internal processes, people and systems or from external
events, is not, strictly speaking, a financial risk. Operational risks are, however, an inevitable
consequence of any business undertaking. For financial institutions and fund managers, credit
and market risks are taken intentionally with the objective of earning returns, while operational
risks are a by-product to be controlled. While the importance of operational risk management is
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increasingly accepted, it will probably never have the same status in the finance industry as credit
and market risk which are the chosen areas of competence.
For non-financial firms, the priorities are reversed. The focus should be on the risks associated
with the particular business; the production and marketing of the service or product in which
expertise is held. Market and credit risks are usually of secondary importance as they are a by-
product of the main business agenda.
The last line of defence against risk is capital, as it ensures that a firm can continue as a going
concern even if substantial and unexpected losses are incurred. Accordingly, one of the major
themes of Section III is how to determine the appropriate size of this capital buffer. How much
capital is enough to withstand unusual losses in each of the three areas of risk? The
measurement of risk has further important implications for risk management as it is increasingly
incorporated into the performance evaluation process. Since resources are allocated and bonuses
paid on the basis of performance measures, it is essential that they be appropriately adjusted for
risk. Only then will appropriate incentives be created for behaviour that is beneficial for
shareholders and other stakeholders. Chapter III.0 explores this fundamental idea at a general
level, since it is relevant for each of the three risk areas that follow.
Market Risk
Chapter III.A.1 introduces the topic of market risk as it is practised by bankers, fund managers
and corporate treasurers. It explains the four major tasks of risk management (identification,
assessment, monitoring and control/mitigation), thus setting the scene for the quantitative
chapters that follow. These days one of the major tasks of risk managers is to measure risk using
value-at-risk (VaR) models. VaR models for market risk come in many varieties. The more basic
VaR models are the topic of Chapter III.A.2, while the advanced versions are covered in III.A.3
along with some other advanced topics such as risk decomposition. The main challenge for risk
managers is to model the empirical characteristics observed in the market, especially volatility
clustering. The advanced models are generally more successful in this regard, although the basic
versions are easier to implement. Realistically, there will never be a perfect VaR model, which is
one of the reasons why stress tests are a popular tool. They can be considered an ad hoc solution
to the problem of model risk. Chapter III.A.4 explains the need for stress tests and how they
might usefully be constructed.
Credit Risk
Chapter III.B.1 introduces the sphere of credit risk management. Some fundamental tools for
managing credit risk are explained here, including the use of collateral, credit limits and credit
derivatives. Subsequent chapters on credit risk focus primarily on its modelling. Foundations for
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modelling are laid in Chapter III.B.2, which explains the three basic components of a credit loss:
the exposure, the default probability and the recovery rate. The product of these three, which
can be defined as random processes, is the credit loss distribution. Chapter III.B.3 takes a more
detailed look at the exposure amount. While relatively simple to define for standard loans,
assessment of the exposure amount can present challenges for other credit sensitive instruments
such as derivatives, whose values are a function of market movements. Chapter III.B.4 examines
in detail the default probability and how it can evolve over time. It also discusses the relationship
between credit ratings and credit spreads, and credit scoring models. Chapter III.B.5 tackles one
of the most crucial issues for credit risk modelling: how to model credit risk in a portfolio
context and thereby estimate credit VaR. Since diversification is one of the most important tools
for the management of credit risk, risk measures on a portfolio basis are fundamental. A number
of tools are examined, including the credit migration approach, the contingent claim or structural
approach, and the actuarial approach. Finally, Chapter III.B.6 extends the discussion of credit
VaR models to examine credit risk capital. It compares both economic capital and regulatory
capital for credit risk as defined under the new Basel Accord.
Operational Risk
The framework for managing operational risk is first established in Chapter III.C.1. After
defining operational risk, it explains how it may be identified, assessed and controlled. Chapter
III.C.2 builds on this with a discussion of operational risk process models. By better
understanding business processes we can find the sources of risk and often take steps to re-
engineer these processes for greater efficiency and lower risk. One of the most perplexing issues
for risk managers is to determine appropriate capital buffers for operational risks. Operational
VaR is the subject of Chapter III.C.3, including discussion of loss models, standard functional
forms, both analytical and simulation methods, and the aggregation of operational risk over all
business lines and event types.