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

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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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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

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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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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.