STEVEN ALLEN is a risk management consultant, specializing in risk measurement and valuation with a particular emphasis on illiquid and hard-to-value assets. Until his retirement in 2004, he was Managing Director in charge of risk methodology at JPMorgan Chase, where he was responsible for model validation, risk capital allocation, and the development of new measures of valuation, reserves, and risk for both market and credit risk. Previously, he was in charge of market risk for derivative products at Chase. He has been a key architect of Chase's value-at-risk and stress testing systems. Prior to his work in risk management, Allen was the head of analysis and model building for all Chase trading activities for over ten years. Since 1998, Allen has been associated with the Mathematics in Finance Master's Program at New York University's Courant Institute of Mathematical Sciences. In this program, he has served as Clinical Associate Professor and Deputy Director and has created and taught courses in risk management, derivatives mathematics, and interest rate and credit models. He was a member of the board of directors of the International Association of Financial Engineers and continues to serve as co-chair of their Education Committee.

• Foreword xviiPreface xixAcknowledgments xxiiiAbout the Author xxviiChapter 1 Introduction 11.1 Lessons from a Crisis 11.2 Financial Risk and Actuarial Risk 21.3 Simulation and Subjective Judgment 4Chapter 2 Institutional Background 72.1 Moral Hazard—Insiders and Outsiders 72.2 Ponzi Schemes 172.3 Adverse Selection 192.4 The Winner’s Curse 212.5 Market Making versus Position Taking 24Chapter 3 Operational Risk 293.1 Operations Risk 313.1.1 The Risk of Fraud 313.1.2 The Risk of Nondeliberate Incorrect Information 353.1.3 Disaster Risk 363.1.4 Personnel Risk 363.2 Legal Risk 373.2.1 The Risk of Unenforceable Contracts 373.2.2 The Risk of Illegal Actions 403.3 Reputational Risk 413.4 Accounting Risk 423.5 Funding Liquidity Risk 423.6 Enterprise Risk 443.7 Identification of Risks 443.8 Operational Risk Capital 45Chapter 4 Financial Disasters 494.1 Disasters Due to Misleading Reporting 494.1.1 Chase Manhattan Bank/Drysdale Securities 524.1.2 Kidder Peabody 534.1.3 Barings Bank 554.1.4 Allied Irish Bank (AIB) 574.1.5 Union Bank of Switzerland (UBS) 594.1.6 Société Générale 614.1.7 Other Cases 664.2 Disasters Due to Large Market Moves 684.2.1 Long‐Term Capital Management (LTCM) 684.2.2 Metallgesellschaft (MG) 754.3 Disasters Due to the Conduct of Customer Business 774.3.1 Bankers Trust (BT) 774.3.2 JPMorgan, Citigroup, and Enron 794.3.3 Other Cases 80Chapter 5 The Systemic Disaster of 2007–2008 835.1 Overview 835.2 The Crisis in CDOs of Subprime Mortgages 855.2.1 Subprime Mortgage Originators 865.2.2 CDO Creators 885.2.3 Rating Agencies 895.2.4 Investors 925.2.5 Investment Banks 935.2.6 Insurers 1065.3 The Spread of the Crisis 1085.3.1 Credit Contagion 1085.3.2 Market Contagion 1095.4 Lessons from the Crisis for Risk Managers 1115.4.1 Subprime Mortgage Originators 1115.4.2 CDO Creators 1115.4.3 Rating Agencies 1115.4.4 Investors 1115.4.5 Investment Banks 1125.4.6 Insurers 1145.4.7 Credit Contagion 1155.4.8 Market Contagion 1155.5 Lessons from the Crisis for Regulators 1155.5.1 Mortgage Originators 1165.5.2 CDO Creators 1165.5.3 Rating Agencies 1175.5.4 Investors 1185.5.5 Investment Banks 1185.5.6 Insurers 1265.5.7 Credit Contagion 1265.5.8 Market Contagion 1295.6 Broader Lessons from the Crisis 132Chapter 6 Managing Financial Risk 1336.1 Risk Measurement 1336.1.1 General Principles 1336.1.2 Risk Management of Instruments That Lack Liquidity 1446.1.3 Market Valuation 1476.1.4 Valuation Reserves 1526.1.5 Analysis of Revenue 1566.1.6 Exposure to Changes in Market Prices 1576.1.7 Risk Measurement for Position Taking 1596.2 Risk Control 161Chapter 7 VaR and Stress Testing 1697.1 VaR Methodology 1707.1.1 Simulation of the P&L Distribution 1737.1.2 Measures of the P&L Distribution 1877.2 Stress Testing 1927.2.1 Overview 1927.2.2 Economic Scenario Stress Tests 1937.2.3 Stress Tests Relying on Historical Data 1977.3 Uses of Overall Measures of Firm Position Risk 201Chapter 8 Model Risk 2098.1 How Important Is Model Risk? 2108.2 Model Risk Evaluation and Control 2128.2.1 Scope of Model Review and Control 2138.2.2 Roles and Responsibilities for Model Review and Control 2148.2.3 Model Verification 2198.2.4 Model Verification of Deal Representation 2228.2.5 Model Verification of Approximations 2238.2.6 Model Validation 2268.2.7 Continuous Review 2328.2.8 Periodic Review 2348.3 Liquid Instruments 2378.4 Illiquid Instruments 2418.4.1 Choice of Model Validation Approach 2418.4.2 Choice of Liquid Proxy 2438.4.3 Design of Monte Carlo Simulation 2458.4.4 Implications for Marking to Market 2478.4.5 Implications for Risk Reporting 2498.5 Trading Models 250Chapter 9 Managing Spot Risk 2539.1 Overview 2539.2 Foreign Exchange Spot Risk 2579.3 Equity Spot Risk 2589.4 Physical Commodities Spot Risk 259Chapter 10 Managing Forward Risk 26310.1 Instruments 27010.1.1 Direct Borrowing and Lending 27010.1.2 Repurchase Agreements 27110.1.3 Forwards 27210.1.4 Futures Contracts 27210.1.5 Forward Rate Agreements 27410.1.6 Interest Rate Swaps 27510.1.7 Total Return Swaps 27610.1.8 Asset‐Backed Securities 27810.2 Mathematical Models of Forward Risks 28210.2.1 Pricing Illiquid Flows by Interpolation 28410.2.2 Pricing Long‐Dated Illiquid Flows by Stack and Roll 29110.2.3 Flows Representing Promised Deliveries 29310.2.4 Indexed Flows 29510.3 Factors Impacting Borrowing Costs 29910.3.1 The Nature of Borrowing Demand 29910.3.2 The Possibility of Cash‐and‐Carry Arbitrage 30010.3.3 The Variability of Storage Costs 30110.3.4 The Seasonality of Borrowing Costs 30210.3.5 Borrowing Costs and Forward Prices 30310.4 Risk Management Reporting and Limits for Forward Risk 304Chapter 11 Managing Vanilla Options Risk 31111.1 Overview of Options Risk Management 31311.2 The Path Dependence of Dynamic Hedging 31811.3 A Simulation of Dynamic Hedging 32111.4 Risk Reporting and Limits 32911.5 Delta Hedging 34411.6 Building a Volatility Surface 34611.6.1 Interpolating between Time Periods 34611.6.2 Interpolating between Strikes—Smile and Skew 34711.6.3 Extrapolating Based on Time Period 35211.7 Summary 355Chapter 12 Managing Exotic Options Risk 35912.1 Single‐Payout Options 36412.1.1 Log Contracts and Variance Swaps 36712.1.2 Single‐Asset Quanto Options 36912.1.3 Convexity 37012.1.4 Binary Options 37112.1.5 Contingent Premium Options 37712.1.6 Accrual Swaps 37812.2 Time‐Dependent Options 37812.2.1 Forward‐Starting and Cliquet Options 37812.2.2 Compound Options 37912.3 Path‐Dependent Options 38112.3.1 Standard Analytic Models for Barriers 38312.3.2 Dynamic Hedging Models for Barriers 38512.3.3 Static Hedging Models for Barriers 38712.3.4 Barrier Options with Rebates, Lookback, and Ladder Options 40212.3.5 Broader Classes of Path‐Dependent Exotics 40312.4 Correlation‐Dependent Options 40412.4.1 Linear Combinations of Asset Prices 40512.4.2 Risk Management of Options on Linear Combinations 40912.4.3 Index Options 41312.4.4 Options to Exchange One Asset for Another 41512.4.5 Nonlinear Combinations of Asset Prices 41712.4.6 Correlation between Price and Exercise 42212.5 Correlation‐Dependent Interest Rate Options 42512.5.1 Models in Which the Relationship between Forwards is Treated as Constant 42612.5.2 Term Structure Models 43012.5.3 Relationship between Swaption and Cap Prices 437Chapter 13 Credit Risk 44513.1 Short‐Term Exposure to Changes in Market Prices 44613.1.1 Credit Instruments 44713.1.2 Models of Short‐Term Credit Exposure 45113.1.3 Risk Reporting for Market Credit Exposures 45613.2 Modeling Single‐Name Credit Risk 45713.2.1 Estimating Probability of Default 45813.2.2 Estimating Loss Given Default 46513.2.3 Estimating the Amount Owed at Default 46813.2.4 The Option‐Theoretic Approach 47113.3 Portfolio Credit Risk 47913.3.1 Estimating Default Correlations 47913.3.2 Monte Carlo Simulation of Portfolio Credit Risk 48213.3.3 Computational Alternatives to Full Simulation 48613.3.4 Risk Management and Reporting for Portfolio Credit Exposures 49013.4 Risk Management of Multiname Credit Derivatives 49313.4.1 Multiname Credit Derivatives 49313.4.2 Modeling of Multiname Credit Derivatives 49513.4.3 Risk Management and Reporting for Multiname Credit Derivatives 49813.4.4 CDO Tranches and Systematic Risk 500Chapter 14 Counterparty Credit Risk 50514.1 Overview 50514.2 Exchange‐Traded Derivatives 50614.3 Over‐the‐Counter Derivatives 51214.3.1 Overview 51214.3.2 The Loan‐Equivalent Approach 51314.3.3 The Collateralization Approach 51514.3.4 The Collateralization Approach—Wrong‐Way Risk 52114.3.5 The Active Management Approach 526References 533About the Companion Website 547Index 553

STEVEN ALLEN is a risk management consultant, specializing in risk measurement and valuation with a particular emphasis on illiquid and hard-to-value assets. Until his retirement in 2004, he was Managing Director in charge of risk methodology at JPMorgan Chase, where he was responsible for model validation, risk capital allocation, and the development of new measures of valuation, reserves, and risk for both market and credit risk. Previously, he was in charge of market risk for derivative products at Chase. He has been a key architect of Chase's value-at-risk and stress testing systems. Prior to his work in risk management, Allen was the head of analysis and model building for all Chase trading activities for over ten years. Since 1998, Allen has been associated with the Mathematics in Finance Master's Program at New York University's Courant Institute of Mathematical Sciences. In this program, he has served as Clinical Associate Professor and Deputy Director and has created and taught courses in risk management, derivatives mathematics, and interest rate and credit models. He was a member of the board of directors of the International Association of Financial Engineers and continues to serve as co-chair of their Education Committee.

• Foreword xviiPreface xixAcknowledgments xxiiiAbout the Author xxviiChapter 1 Introduction 11.1 Lessons from a Crisis 11.2 Financial Risk and Actuarial Risk 21.3 Simulation and Subjective Judgment 4Chapter 2 Institutional Background 72.1 Moral Hazard—Insiders and Outsiders 72.2 Ponzi Schemes 172.3 Adverse Selection 192.4 The Winner’s Curse 212.5 Market Making versus Position Taking 24Chapter 3 Operational Risk 293.1 Operations Risk 313.1.1 The Risk of Fraud 313.1.2 The Risk of Nondeliberate Incorrect Information 353.1.3 Disaster Risk 363.1.4 Personnel Risk 363.2 Legal Risk 373.2.1 The Risk of Unenforceable Contracts 373.2.2 The Risk of Illegal Actions 403.3 Reputational Risk 413.4 Accounting Risk 423.5 Funding Liquidity Risk 423.6 Enterprise Risk 443.7 Identification of Risks 443.8 Operational Risk Capital 45Chapter 4 Financial Disasters 494.1 Disasters Due to Misleading Reporting 494.1.1 Chase Manhattan Bank/Drysdale Securities 524.1.2 Kidder Peabody 534.1.3 Barings Bank 554.1.4 Allied Irish Bank (AIB) 574.1.5 Union Bank of Switzerland (UBS) 594.1.6 Société Générale 614.1.7 Other Cases 664.2 Disasters Due to Large Market Moves 684.2.1 Long‐Term Capital Management (LTCM) 684.2.2 Metallgesellschaft (MG) 754.3 Disasters Due to the Conduct of Customer Business 774.3.1 Bankers Trust (BT) 774.3.2 JPMorgan, Citigroup, and Enron 794.3.3 Other Cases 80Chapter 5 The Systemic Disaster of 2007–2008 835.1 Overview 835.2 The Crisis in CDOs of Subprime Mortgages 855.2.1 Subprime Mortgage Originators 865.2.2 CDO Creators 885.2.3 Rating Agencies 895.2.4 Investors 925.2.5 Investment Banks 935.2.6 Insurers 1065.3 The Spread of the Crisis 1085.3.1 Credit Contagion 1085.3.2 Market Contagion 1095.4 Lessons from the Crisis for Risk Managers 1115.4.1 Subprime Mortgage Originators 1115.4.2 CDO Creators 1115.4.3 Rating Agencies 1115.4.4 Investors 1115.4.5 Investment Banks 1125.4.6 Insurers 1145.4.7 Credit Contagion 1155.4.8 Market Contagion 1155.5 Lessons from the Crisis for Regulators 1155.5.1 Mortgage Originators 1165.5.2 CDO Creators 1165.5.3 Rating Agencies 1175.5.4 Investors 1185.5.5 Investment Banks 1185.5.6 Insurers 1265.5.7 Credit Contagion 1265.5.8 Market Contagion 1295.6 Broader Lessons from the Crisis 132Chapter 6 Managing Financial Risk 1336.1 Risk Measurement 1336.1.1 General Principles 1336.1.2 Risk Management of Instruments That Lack Liquidity 1446.1.3 Market Valuation 1476.1.4 Valuation Reserves 1526.1.5 Analysis of Revenue 1566.1.6 Exposure to Changes in Market Prices 1576.1.7 Risk Measurement for Position Taking 1596.2 Risk Control 161Chapter 7 VaR and Stress Testing 1697.1 VaR Methodology 1707.1.1 Simulation of the P&L Distribution 1737.1.2 Measures of the P&L Distribution 1877.2 Stress Testing 1927.2.1 Overview 1927.2.2 Economic Scenario Stress Tests 1937.2.3 Stress Tests Relying on Historical Data 1977.3 Uses of Overall Measures of Firm Position Risk 201Chapter 8 Model Risk 2098.1 How Important Is Model Risk? 2108.2 Model Risk Evaluation and Control 2128.2.1 Scope of Model Review and Control 2138.2.2 Roles and Responsibilities for Model Review and Control 2148.2.3 Model Verification 2198.2.4 Model Verification of Deal Representation 2228.2.5 Model Verification of Approximations 2238.2.6 Model Validation 2268.2.7 Continuous Review 2328.2.8 Periodic Review 2348.3 Liquid Instruments 2378.4 Illiquid Instruments 2418.4.1 Choice of Model Validation Approach 2418.4.2 Choice of Liquid Proxy 2438.4.3 Design of Monte Carlo Simulation 2458.4.4 Implications for Marking to Market 2478.4.5 Implications for Risk Reporting 2498.5 Trading Models 250Chapter 9 Managing Spot Risk 2539.1 Overview 2539.2 Foreign Exchange Spot Risk 2579.3 Equity Spot Risk 2589.4 Physical Commodities Spot Risk 259Chapter 10 Managing Forward Risk 26310.1 Instruments 27010.1.1 Direct Borrowing and Lending 27010.1.2 Repurchase Agreements 27110.1.3 Forwards 27210.1.4 Futures Contracts 27210.1.5 Forward Rate Agreements 27410.1.6 Interest Rate Swaps 27510.1.7 Total Return Swaps 27610.1.8 Asset‐Backed Securities 27810.2 Mathematical Models of Forward Risks 28210.2.1 Pricing Illiquid Flows by Interpolation 28410.2.2 Pricing Long‐Dated Illiquid Flows by Stack and Roll 29110.2.3 Flows Representing Promised Deliveries 29310.2.4 Indexed Flows 29510.3 Factors Impacting Borrowing Costs 29910.3.1 The Nature of Borrowing Demand 29910.3.2 The Possibility of Cash‐and‐Carry Arbitrage 30010.3.3 The Variability of Storage Costs 30110.3.4 The Seasonality of Borrowing Costs 30210.3.5 Borrowing Costs and Forward Prices 30310.4 Risk Management Reporting and Limits for Forward Risk 304Chapter 11 Managing Vanilla Options Risk 31111.1 Overview of Options Risk Management 31311.2 The Path Dependence of Dynamic Hedging 31811.3 A Simulation of Dynamic Hedging 32111.4 Risk Reporting and Limits 32911.5 Delta Hedging 34411.6 Building a Volatility Surface 34611.6.1 Interpolating between Time Periods 34611.6.2 Interpolating between Strikes—Smile and Skew 34711.6.3 Extrapolating Based on Time Period 35211.7 Summary 355Chapter 12 Managing Exotic Options Risk 35912.1 Single‐Payout Options 36412.1.1 Log Contracts and Variance Swaps 36712.1.2 Single‐Asset Quanto Options 36912.1.3 Convexity 37012.1.4 Binary Options 37112.1.5 Contingent Premium Options 37712.1.6 Accrual Swaps 37812.2 Time‐Dependent Options 37812.2.1 Forward‐Starting and Cliquet Options 37812.2.2 Compound Options 37912.3 Path‐Dependent Options 38112.3.1 Standard Analytic Models for Barriers 38312.3.2 Dynamic Hedging Models for Barriers 38512.3.3 Static Hedging Models for Barriers 38712.3.4 Barrier Options with Rebates, Lookback, and Ladder Options 40212.3.5 Broader Classes of Path‐Dependent Exotics 40312.4 Correlation‐Dependent Options 40412.4.1 Linear Combinations of Asset Prices 40512.4.2 Risk Management of Options on Linear Combinations 40912.4.3 Index Options 41312.4.4 Options to Exchange One Asset for Another 41512.4.5 Nonlinear Combinations of Asset Prices 41712.4.6 Correlation between Price and Exercise 42212.5 Correlation‐Dependent Interest Rate Options 42512.5.1 Models in Which the Relationship between Forwards is Treated as Constant 42612.5.2 Term Structure Models 43012.5.3 Relationship between Swaption and Cap Prices 437Chapter 13 Credit Risk 44513.1 Short‐Term Exposure to Changes in Market Prices 44613.1.1 Credit Instruments 44713.1.2 Models of Short‐Term Credit Exposure 45113.1.3 Risk Reporting for Market Credit Exposures 45613.2 Modeling Single‐Name Credit Risk 45713.2.1 Estimating Probability of Default 45813.2.2 Estimating Loss Given Default 46513.2.3 Estimating the Amount Owed at Default 46813.2.4 The Option‐Theoretic Approach 47113.3 Portfolio Credit Risk 47913.3.1 Estimating Default Correlations 47913.3.2 Monte Carlo Simulation of Portfolio Credit Risk 48213.3.3 Computational Alternatives to Full Simulation 48613.3.4 Risk Management and Reporting for Portfolio Credit Exposures 49013.4 Risk Management of Multiname Credit Derivatives 49313.4.1 Multiname Credit Derivatives 49313.4.2 Modeling of Multiname Credit Derivatives 49513.4.3 Risk Management and Reporting for Multiname Credit Derivatives 49813.4.4 CDO Tranches and Systematic Risk 500Chapter 14 Counterparty Credit Risk 50514.1 Overview 50514.2 Exchange‐Traded Derivatives 50614.3 Over‐the‐Counter Derivatives 51214.3.1 Overview 51214.3.2 The Loan‐Equivalent Approach 51314.3.3 The Collateralization Approach 51514.3.4 The Collateralization Approach—Wrong‐Way Risk 52114.3.5 The Active Management Approach 526References 533About the Companion Website 547Index 553

STEVEN ALLEN is a risk management consultant, specializing in risk measurement and valuation with a particular emphasis on illiquid and hard-to-value assets. Until his retirement in 2004, he was Managing Director in charge of risk methodology at JPMorgan Chase, where he was responsible for model validation, risk capital allocation, and the development of new measures of valuation, reserves, and risk for both market and credit risk. Previously, he was in charge of market risk for derivative products at Chase. He has been a key architect of Chase's value-at-risk and stress testing systems. Prior to his work in risk management, Allen was the head of analysis and model building for all Chase trading activities for over ten years. Since 1998, Allen has been associated with the Mathematics in Finance Master's Program at New York University's Courant Institute of Mathematical Sciences. In this program, he has served as Clinical Associate Professor and Deputy Director and has created and taught courses in risk management, derivatives mathematics, and interest rate and credit models. He was a member of the board of directors of the International Association of Financial Engineers and continues to serve as co-chair of their Education Committee.

• Foreword xviiPreface xixAcknowledgments xxiiiAbout the Author xxviiChapter 1 Introduction 11.1 Lessons from a Crisis 11.2 Financial Risk and Actuarial Risk 21.3 Simulation and Subjective Judgment 4Chapter 2 Institutional Background 72.1 Moral Hazard—Insiders and Outsiders 72.2 Ponzi Schemes 172.3 Adverse Selection 192.4 The Winner’s Curse 212.5 Market Making versus Position Taking 24Chapter 3 Operational Risk 293.1 Operations Risk 313.1.1 The Risk of Fraud 313.1.2 The Risk of Nondeliberate Incorrect Information 353.1.3 Disaster Risk 363.1.4 Personnel Risk 363.2 Legal Risk 373.2.1 The Risk of Unenforceable Contracts 373.2.2 The Risk of Illegal Actions 403.3 Reputational Risk 413.4 Accounting Risk 423.5 Funding Liquidity Risk 423.6 Enterprise Risk 443.7 Identification of Risks 443.8 Operational Risk Capital 45Chapter 4 Financial Disasters 494.1 Disasters Due to Misleading Reporting 494.1.1 Chase Manhattan Bank/Drysdale Securities 524.1.2 Kidder Peabody 534.1.3 Barings Bank 554.1.4 Allied Irish Bank (AIB) 574.1.5 Union Bank of Switzerland (UBS) 594.1.6 Société Générale 614.1.7 Other Cases 664.2 Disasters Due to Large Market Moves 684.2.1 Long‐Term Capital Management (LTCM) 684.2.2 Metallgesellschaft (MG) 754.3 Disasters Due to the Conduct of Customer Business 774.3.1 Bankers Trust (BT) 774.3.2 JPMorgan, Citigroup, and Enron 794.3.3 Other Cases 80Chapter 5 The Systemic Disaster of 2007–2008 835.1 Overview 835.2 The Crisis in CDOs of Subprime Mortgages 855.2.1 Subprime Mortgage Originators 865.2.2 CDO Creators 885.2.3 Rating Agencies 895.2.4 Investors 925.2.5 Investment Banks 935.2.6 Insurers 1065.3 The Spread of the Crisis 1085.3.1 Credit Contagion 1085.3.2 Market Contagion 1095.4 Lessons from the Crisis for Risk Managers 1115.4.1 Subprime Mortgage Originators 1115.4.2 CDO Creators 1115.4.3 Rating Agencies 1115.4.4 Investors 1115.4.5 Investment Banks 1125.4.6 Insurers 1145.4.7 Credit Contagion 1155.4.8 Market Contagion 1155.5 Lessons from the Crisis for Regulators 1155.5.1 Mortgage Originators 1165.5.2 CDO Creators 1165.5.3 Rating Agencies 1175.5.4 Investors 1185.5.5 Investment Banks 1185.5.6 Insurers 1265.5.7 Credit Contagion 1265.5.8 Market Contagion 1295.6 Broader Lessons from the Crisis 132Chapter 6 Managing Financial Risk 1336.1 Risk Measurement 1336.1.1 General Principles 1336.1.2 Risk Management of Instruments That Lack Liquidity 1446.1.3 Market Valuation 1476.1.4 Valuation Reserves 1526.1.5 Analysis of Revenue 1566.1.6 Exposure to Changes in Market Prices 1576.1.7 Risk Measurement for Position Taking 1596.2 Risk Control 161Chapter 7 VaR and Stress Testing 1697.1 VaR Methodology 1707.1.1 Simulation of the P&L Distribution 1737.1.2 Measures of the P&L Distribution 1877.2 Stress Testing 1927.2.1 Overview 1927.2.2 Economic Scenario Stress Tests 1937.2.3 Stress Tests Relying on Historical Data 1977.3 Uses of Overall Measures of Firm Position Risk 201Chapter 8 Model Risk 2098.1 How Important Is Model Risk? 2108.2 Model Risk Evaluation and Control 2128.2.1 Scope of Model Review and Control 2138.2.2 Roles and Responsibilities for Model Review and Control 2148.2.3 Model Verification 2198.2.4 Model Verification of Deal Representation 2228.2.5 Model Verification of Approximations 2238.2.6 Model Validation 2268.2.7 Continuous Review 2328.2.8 Periodic Review 2348.3 Liquid Instruments 2378.4 Illiquid Instruments 2418.4.1 Choice of Model Validation Approach 2418.4.2 Choice of Liquid Proxy 2438.4.3 Design of Monte Carlo Simulation 2458.4.4 Implications for Marking to Market 2478.4.5 Implications for Risk Reporting 2498.5 Trading Models 250Chapter 9 Managing Spot Risk 2539.1 Overview 2539.2 Foreign Exchange Spot Risk 2579.3 Equity Spot Risk 2589.4 Physical Commodities Spot Risk 259Chapter 10 Managing Forward Risk 26310.1 Instruments 27010.1.1 Direct Borrowing and Lending 27010.1.2 Repurchase Agreements 27110.1.3 Forwards 27210.1.4 Futures Contracts 27210.1.5 Forward Rate Agreements 27410.1.6 Interest Rate Swaps 27510.1.7 Total Return Swaps 27610.1.8 Asset‐Backed Securities 27810.2 Mathematical Models of Forward Risks 28210.2.1 Pricing Illiquid Flows by Interpolation 28410.2.2 Pricing Long‐Dated Illiquid Flows by Stack and Roll 29110.2.3 Flows Representing Promised Deliveries 29310.2.4 Indexed Flows 29510.3 Factors Impacting Borrowing Costs 29910.3.1 The Nature of Borrowing Demand 29910.3.2 The Possibility of Cash‐and‐Carry Arbitrage 30010.3.3 The Variability of Storage Costs 30110.3.4 The Seasonality of Borrowing Costs 30210.3.5 Borrowing Costs and Forward Prices 30310.4 Risk Management Reporting and Limits for Forward Risk 304Chapter 11 Managing Vanilla Options Risk 31111.1 Overview of Options Risk Management 31311.2 The Path Dependence of Dynamic Hedging 31811.3 A Simulation of Dynamic Hedging 32111.4 Risk Reporting and Limits 32911.5 Delta Hedging 34411.6 Building a Volatility Surface 34611.6.1 Interpolating between Time Periods 34611.6.2 Interpolating between Strikes—Smile and Skew 34711.6.3 Extrapolating Based on Time Period 35211.7 Summary 355Chapter 12 Managing Exotic Options Risk 35912.1 Single‐Payout Options 36412.1.1 Log Contracts and Variance Swaps 36712.1.2 Single‐Asset Quanto Options 36912.1.3 Convexity 37012.1.4 Binary Options 37112.1.5 Contingent Premium Options 37712.1.6 Accrual Swaps 37812.2 Time‐Dependent Options 37812.2.1 Forward‐Starting and Cliquet Options 37812.2.2 Compound Options 37912.3 Path‐Dependent Options 38112.3.1 Standard Analytic Models for Barriers 38312.3.2 Dynamic Hedging Models for Barriers 38512.3.3 Static Hedging Models for Barriers 38712.3.4 Barrier Options with Rebates, Lookback, and Ladder Options 40212.3.5 Broader Classes of Path‐Dependent Exotics 40312.4 Correlation‐Dependent Options 40412.4.1 Linear Combinations of Asset Prices 40512.4.2 Risk Management of Options on Linear Combinations 40912.4.3 Index Options 41312.4.4 Options to Exchange One Asset for Another 41512.4.5 Nonlinear Combinations of Asset Prices 41712.4.6 Correlation between Price and Exercise 42212.5 Correlation‐Dependent Interest Rate Options 42512.5.1 Models in Which the Relationship between Forwards is Treated as Constant 42612.5.2 Term Structure Models 43012.5.3 Relationship between Swaption and Cap Prices 437Chapter 13 Credit Risk 44513.1 Short‐Term Exposure to Changes in Market Prices 44613.1.1 Credit Instruments 44713.1.2 Models of Short‐Term Credit Exposure 45113.1.3 Risk Reporting for Market Credit Exposures 45613.2 Modeling Single‐Name Credit Risk 45713.2.1 Estimating Probability of Default 45813.2.2 Estimating Loss Given Default 46513.2.3 Estimating the Amount Owed at Default 46813.2.4 The Option‐Theoretic Approach 47113.3 Portfolio Credit Risk 47913.3.1 Estimating Default Correlations 47913.3.2 Monte Carlo Simulation of Portfolio Credit Risk 48213.3.3 Computational Alternatives to Full Simulation 48613.3.4 Risk Management and Reporting for Portfolio Credit Exposures 49013.4 Risk Management of Multiname Credit Derivatives 49313.4.1 Multiname Credit Derivatives 49313.4.2 Modeling of Multiname Credit Derivatives 49513.4.3 Risk Management and Reporting for Multiname Credit Derivatives 49813.4.4 CDO Tranches and Systematic Risk 500Chapter 14 Counterparty Credit Risk 50514.1 Overview 50514.2 Exchange‐Traded Derivatives 50614.3 Over‐the‐Counter Derivatives 51214.3.1 Overview 51214.3.2 The Loan‐Equivalent Approach 51314.3.3 The Collateralization Approach 51514.3.4 The Collateralization Approach—Wrong‐Way Risk 52114.3.5 The Active Management Approach 526References 533About the Companion Website 547Index 553