QUANTITATIVE FINANCE

AND

RISK MANAGEMENT

A Physicist's Approach

Second Edition

Jan W Dash

World Scientific

LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEf • CHENNAI •

Table of Contents

Acknowledgments for the 1st and 2nd Editions xxi

PART I: INTRODUCTION, OVERVIEW, AND EXERCISE 1

3. Introduction / Outline; Note for 2nd Edition; Unresolved Problems 3 Who/ How/What, "Tech. Index", Messages, Personal Note 3 Summary Outline: Book Contents 5 Note for the 2nd Edition (2015) 6 Climate Change Risk Management - NEW TOPIC 7 Evaluation - Where do we stand? What about the future? 7

2. Overview (Tech. Index 1/10) 9 Objectives of Quantitative Finance and Risk Management 9 T ools of Quantitative Finance and Risk Management 11 The Traditional Areas of Risk Management 14 When Will We Ever See Real-Time Color Movies of Risk? 16 Many People Participate in Risk Management 16 Quants in Quantitative Finance and Risk Management 18 References 21

3. An Exercise (Tech. Index 1/10) 23 Part #1: Data, Statistics, and Reporting Using a Spreadsheet 23 Part #2: Repeat Part #1 Using Programming 26 Part #3: A Few Quick and Tricky Hypothetical Questions 27 Messages and Advice 28 References 28

PART II: RISK LAB (NUTS AND BOLTS OF RISK MANAGEMENT) 29

4. Equity Options (Tech. Index 3/10) 31 Pricing and Hedging One Option 31 American Options 34 Basket Options and Index Options 35 Other Types of Equity Options; Exotics 37 Portfolio Risk (Introduction) 37 Scenario Analysis (Introduction) 37 References 38

vii

vj- Quantitative Finance and Risk Management

5. FX Options (Tech. Index 4/10) 39

FX Forwards and Options ^9 Some Practical Details for FX Options 43 Hedging FX Options with Greeks: Details and Ambiguities 44 FX Volatility Skew and/or Smile 46 Pricing Barrier Options with Skew 51 Double Barrier Option: Practical Example 52 The "Two-Country Paradox" 54

Quanto Options and Correlations 56 FX Options in the presence of Stochastic Interest Rates 57 Numerical Codes, Closed Form Sanity Checks, and Intuition 57 References 58

6. Equity Volatility Skew (Tech. Index 6/10) 59 Put-Call Parity: Theory and Violations 60 The Volatility Surface 61 Dealing with Skew 62 Perturbative Skew and Barrier Options 62 Static Replication 65 Stochastic Volatility 66 Local Volatility and Skew 69 The Skew-Implied Probability Distribution 70 Local vs. Implied Volatility Skew; Derman's Rules of Thumb 70 Option Replication with Gadgets 72 Intuitive Models and Different Volatility Regimes 75 The Macro-Micro Model and Equity Volatility Regimes 76 Jump Diffusion Processes 76 Appendix 1: Algorithm for "Perturbative Skew" Approach 76 Appendix 2: A Technical Issue for Stochastic Volatility 78 References 79

7. Forward Curves (Tech. Index 4/10) 81 Market Input Rates 81 Construction of the Forward-Rate Curve 84 References 92

8. Interest-Rate Swaps and Credit Default Swaps (Tech. Index 5/10) 93 Interest Rate Swaps: Pricing and Risk 93 Interest Rate Swaps: Pricing and Risk Details 100 Cross-Currency Swaps ] ] 5 Credit Default Swaps (CDS) ] \ 7 References j 22

9. Bonds: An Overview (Tech. Index 2/10) Types of Bonds

123 123

Table of Contents ix

Bond Issuance 127 Bond Trading 129 Flight to Quality 129 Bond Math 130 References 134

10. Interest-Rate Caps (Tech. Index 4/10) 137 introduction to Caps 137 The Black Caplet Formula 139 N'on-USD Caps 141 Relations between Caps, Floors, and Swaps 142 - iedging Delta and Gamma for Libor Caps 142 Medging Volatility and Vega Ladders 143 Ylatrices of Cap Prices 145 '• rime Caps and a Vega Trap 145

MT Rates; Volatility Dependence of CMT Products 147 References 151

11. Interest-Rate Swaptions (Tech. Index 5/10) 153 European Swaptions 153 Bermuda/American Swaption Pricing 157 j >elta and Vega Risk: Move Inputs or Forwards? 159 Swaptions and Corporate Liability Risk Management 160 : . actieal Example: A Deal Involving a Swaption 162 VUscellaneous Swaption Topics 164 •\eferences 167

! 2. Portfolios and Scenarios (Tech. Index 3/10) 169 : i;roduction to Portfolio Risk Using Scenario Analysis 169 Minitions of Portfolios 169

1 )cfinitions of Scenarios 171 ^-lany Portfolios and Scenarios 174 A Scenario Simulator 175 Risk Analyses and Presentations 175

PART III: EXOTICS, DEALS, AND GASE STÜDIES 177

13. A Complex CVR Option (Tech. Index 5/10) 179 The M&A Scenario 179 CVR Starting Point: A Put Spread 180 CVR Extension Options and Other Complications 180 The Arbs and the Mispricing of the CVR Option 182 A Simplified CVR: Two Put Spreads with Extension Logic 183 Non-Academic Corporate Decision for Option Extension 185 The CVR Option Pricing 187

x Quantitative Finance and Risk Management

Analytic CVR Pricing Methodology 191

Some Practical Aspects of CVR Pricing and Hedging ' 94 The CVR Buyback 198

A Legal Event Related to the CVR *98

References '9t'

14. Two More Case Studies (Tech. Index 5/10) 201 Case Study: DECS and Synthetic Convertibles 201 Credit Spreads, Discounting, Convertibles, and DECs 204 D)23: The Complex DEC Synthetic Convertible 20 / Case Study: Equity Call with Variable Strike and Expiration 211 References 218

15. More Exotics and Risk (Tech. Index 5/10) 219 Contingent Caps 219 Digital Options: Pricing and Hedging 223 Historical Simulations and Hedging 225 Yield-Curve Shape and Principal-Component Options 227 Principal-Component Risk Measures (Tilt Delta etc.) 228 Hybrid 2-Dimensional Barrier Options—Examples 229 Reload Options 232 References 236

16. A PotPourri of Deals (Tech. Index 5/10) 237 TIPS (Treasury Inflation Protected Securities) 237 Municipal Derivatives, Muni Issuance, Derivative Hedging 240 Difference Option on an Equity Index and a Basket of Stocks 243 Resettable Options: Cliquets 244 Power Options 248 Path-Dependent Options and Monte Carlo Simulation 249 Periodic Caps 249 ARM Caps 250 Index-Amortizing Swaps 251 A Hypothetical Repo + Options Deal 254 Convertible Issuance Risk 258 References 259

17. Single Barrier Options (Tech. Index 6/10) 261 Knock-Out Options 263 The Semi-Group Property including a Barrier 265 Calculating Barrier Options 266 Knock-ln Options 267 Useful Integrals for Barrier Options 269 Single Barrier Rebates at Touch and at Maturity 271 Other Topics Involving Single Barrier Options 272

Table of Contents xi

References 276

18. Double Barrier Options (Tech. Index 7/10) 277 Double Barrier Solution with an Infinite Set of Images 278 Double Barrier Option Pricing 280 Rebates for Double Barrier Options 282 References 284

19. Hybrid 2-D Barrier Options (Tech. Index 7/10) 285 Pricing the Barrier 2-Dimension Hybrid Options 288 'Jseful Integrals for 2D Barrier Options 289 References 290

20. Average-Rate Options (Tech. Index 8/10) 291 Arithmetic Average Rate Options in General Gaussian Models 292 Results for Average-Rate Options in the MRG Model 296 Simple Harmonie Oscillator Derivation for Average Options 297 Thermodynamic Identity Derivation for Average Options 298 Average Options with Log-Normal Rate Dynamics 298 Gaussian into Lognormal Using a Simple Trick 299 References 300

PART IV: QUANTITATIVE RISK MANAGEMENT 301

21. Fat Tail Volatility (Tech. Index 5/10) 303 Gaussian Behavior and Deviations from Gaussian 303 Review of Some Math Formalism 303 Outliers and Fat Tails 304 Üse of the Equivalent Gaussian Fat-Tail Volatility 307 Practical Considerations for the Fat-Tail Parameters 309 Overlapping vs. Non-overlapping Windows and Data 311 References 315

22. Correlation Matrix Formalism and the Jsf- Sphere (Tech. Index 8/10) 317

The Importance and Difficulty of Correlation Risk 317 One Correlation in Two Dimensions 318 Two Correlations in Three Dimensions; the Azimuthai Angle 319 Correlations in Four Dimensions - Picture 322 Correlations in Five and Higher Dimensions 324 Spherical Representation of the Cholesky Decomposition 326 References 328

23. Stressed Correlations and Random Matrices (Tech. Index 5/10) 329

xjj Quantitative Finance and Risk Management

Correlation Stress Scenarios Using Data 329 Stressed Random Correlation Matrices 335 Stochastic Correlation Matrices Using the -sphere 337

24. Optimally Stressed PD Correlation Matrices (Tech. Index 7/10) 341 Least-Squares Eitting for the Optimal PD Stressed Matrix 343 Numerical Considerations for Optimal PD Stressed Matrix 344 Example of Optimal PD Fit to a NPD Stressed Matrix 345 SVD Algorithm for the Starting PD Correlation Matrix 347 PD Stressed Correlations by "Walking through the Matrix" 350 Nearest Neighbor Technique for PD Stressed Correlations 350 References 351

25. Models for Correlation Dynamics, Uncertainties (Tech. Index 6/10)...353 "Just Make the Correlations Zero" Model; Three Versions 353 Long-Term vs. Short-Term Correlations; Macro-Micro Model 355 Macro Long-term Correlation Simulation Example 356 Macro Moves for the Whole Correlation Matrix 359 Correlation Dependence on Volatility 360 Implied, Current, and Historical Correlations for Baskets 363 SSA and Noise-Reduced Correlations - Preview 364 Factor Models, Idiosyncratic Risk, and Correlations 364 Correlated Idiosyncratic Residuais and Applications 366 References 367

26. Plain-Vanilla VAR and Component VAR (Tech. Index 4/10) 369 Historical VAR (HVAR) and Monte Carlo HVAR 372 Scenarios 375 Quadratic VAR and Component VARs (CVARs) 376 Monte-Carlo VAR 378 Backtesting VAR 379 Component VAR (CVAR) and CVAR Volatility from MC 380 Confidence Levels for Individual Variables in VAR 382 References 384

27. Enhanced/Stressed VAR (Tech. Index 5/10) 385 Improved Plain-Vanilla VAR (IPV-VAR) 385 Regulatory Stressed VAR, Turbulent VAR, VAR Uncertainty 389 Enhanced/Stressed VAR (ES- VAR) 390 Illiquidity Penalty for Enhanced VAR 392 Subadditivity, Integrated VAR, Backtesting 39g "Bayesian/Scenario VAR" 401 References ^

28. VAR, CVAR, CVAR Volatility Formalism (Tech. Index 7/10) 403

Table of Contents xiii

Set-up and Overview of the Formal VAR Results 403 Calculation of the Generating Function 405 VAR, CVARs (= Component VARs), CVAR Volatilities 408 Affective Number of SD for Underlying Variables 411 Extension to Multiple Time Steps using Rath Integrals 413

29. VAR and Component VAR for Two Variables (Tech. Index 5/10) 415 The Component VAR (CVAR) Volatility with Two Variables 415 Gcometry, Math: Risk Ellipse, VAR Line, CVAR, CVAR Vol 416

30. Corporate-Level VAR (Tech. Index 3/10) 421 •ggregation, Desks, Business Units, Corporate Hierarchy 421 >esk CVARs and Correlations between Desk Risks 423 \ged Inventory and Illiquidity 425 References 427

31. Credit Risk: Issuer, Counterparty (Tech. Index 5/10) 429 ; -.suer Credit Risk 429 i'ransition/Default Probability Matrices and Issuer Risk 431 alculation of Issuer Risk - Generic Case 435

Monte-Carlo Simulations of Credit Issuer Risk 437 vniple Example of Issuer Credit Risk Calculation 440 <uer Credit Risk and Market Risk: Separation via Spreads 443

; .parating Market and Credit Risk without Double Counting 444 Unified Credit + Market Risk Model 447

-ninterparty Credit Risk Example: Swaps 450 VA "Risk Neutral" and PFE "Real World" Simulations 453

- i l:, and the Macro-Micro Model 454 orrelated Defaults - Analytic Results for 2D Merton Model 454

•\ lisc. Topics: WWR, FVA, Factor Models, Firmwide Risk 457 Regulations 459 References 459

32. Model Risk Overview (Tech. Index 3/10) 463 Summary of Model Risk 463 Model Risk and Risk Management 464 Time Scales and Models 464 Long-Term Macro Component with Quasi-Random Behavior 465 Liquidity Model Limitations 465 Which Model Should We Use? 466 Psychology and Models 466 Model Risk, Model Reserves, and Bid-Offer Spreads 467 Model Quality Assurance 468 Models and Parameters 468 References 469

. ßwmfifoöve Finance anc/ RüA: Managcmcn'

33. Model Quality Assurance (Tech. Index 4/10) 47 f Model Quality Assurance Goals, Activities, and Procedures... 47!

Model QA: Sample Documentation 47 • User Section of Model QA Documentation 47 Quantitative Section of Model QA Documentation 47 Systems Section of Model QA Documentation 47 References ^

34. Systems Risk Overview (Tech. Index 3/10) 48 Advice and a Message to Non-Technical Managers 48 What are the "Three-Fives Systems Criteria"? 48 What is the Fundamental Theorem of Systems Risk? 48 What are Some Systems Traps and Risks? 48-The Birth and Development of a System 48', Systems Risk in Mergers and Startups 48^ Vendor Systems Risk 488 New Paradigms in Systems and Parallel Processing 490 Languages for Models: Fortran 90, C+\ C, Python, Others 490 What's the "Systems Solution"? 492 Are Software Development Risks Unique to Wall Street? 492 References 494

35. Strategie Computing (Tech. Index 3/10) 495 Introduction and Background 496 Illustration of Parallel Processing for Finance 496 Some Aspects of Parallel Processing 497 Technology, Strategy and Change 500 References 501

36. Data Risk: Qualitative, SSA, Generalized z-Score Polynomials (Tech. Index 5/10) 503

Important Qualitative Aspect of Data Risk 503 NEW TOPIC: SSA, MSSA, and Data Smoothing/Cleaning 506 NEW: Generalized z-scores: General Measure Polynomials 510 References 511

37. Correlations, Data, and Random Matrix Theory (Tech. Index 6/10) ....513 Fluctuations and Uncertainties in Measured Correlations 513 Time Windowing 514 Correlations, the Number of Data Points, and Variables 517 Intrinsic and Windowing Uncertainties: Example 518 The Fisher Transform for Correlations 519 NEW: Noise-Cleaned Correlations via SSA ZZZ" 520 Random Matrix Theory Benchmarks for Noise in Correlations...."..!"'\ZZ'Z'.52\

Table of Contents xv

NEW: Approximate Analytic Probability Distribution for ANY Eigenvalue in the Zero-Correlation Wishart Matrix 522 A Few Other Aspects of Data and Correlations 524 References 524

38. Wishart's Theorem and Fisher's Transform (Tech. Index 9/10) 527 Warm Up: The Distribution for a Volatility Estimate 528 The Wishart Distribution 530 The Probability Function for One Estimated Correlation 532 Fisher's Transform and the Correlation Probability Function 533 NEW: Hedge Fund Style-Change Risk and Correlation Changes 535 Derivation - Fourier Transform of the Wishart Distribution 535 Result - Wishart Distribution Fourier Transform 537 References 540

39. Economic Capital (Tech. Index 4/10) 541 Basic Idea of Economic Capital 541 The Classification of Risk Components of Economic Capital 545 Exposures for Economic Capital: What Should They Be? 546 Attacks on Economic Capital at High CL 546 Allocation: Standalone, Component VAR, or Other? 548 The Cost of Economic Capital 550 An Economic-Capital Utility Function 550 Firm wide Sharpe Ratio and Economic Capital 551 Revisiting Expected Losses; the Importance of Time Scales 552 Traditional Measures of Capital 554 References 555

40. Unused-Limit Risk (Tech. Index 5/10) 557 General Aspects of Risk Limits 557 The Unused Limit Risk Model: Overview 559 Unused Limit Economic Capital for Issuer Credit Risk 565

PART V: PATH INTEGRALS, GREEN FUNCTIONS, AND OPTIONS..567

4L Path Integrals and Options: Overview (Tech. Index 4/10) 569

42. Path Integrals and Options I: Introduction (Tech. Index 7/10) 573 Introduction to Path Integrals 574 Heretical Remarks on Rigor and All That 576 Path-lntegral Warm-up: The Black Scholes Model 577 Connection of Path Integral with the Stochastic Equations 589 Dividends and Jumps with Path Integrals 591 Discrete Bermuda Options 598 American Options 606

. Quantitative Finance and Risk Management

Appendix 1: Girsanov's Theorem and Path Integrals 606 Appendix 2: A Short Dictionary of Common Notations 610 Appendix 3: No-Arbitrage, Hedging and Path Integrals 611 Appendix 4: Pertubation Theory, Local Volatility, Skew 616 Figure Captions for this Chapter 6'6

References ^26

43. Path Integrals and Options II: Interest Rates (Tech. Index 8/10) 62V I. Path Integrals: Review 63 ] II. The Green Function; Discretized Gaussian Models 632 III. The Continuous-Time Gaussian Limit 636 IV. Mean-Reverting Gaussian (MRG) Models 639 IV Continued: Numeraires 643 Notation: Connection with Hull-White (HW) 646 V. The Most General Model with Memory 648 VI. Wrap-Up for this Chapter 652 Appendix A: MRG Formalism, Stochastic Equations, Etc 653 Appendix B: Rate-Dependent Volatility (Local Vol) Models 661 Appendix C: The General Gaussian Model With Memory 663 Figure Captions for This Chapter 665 References 668

44. Path Integrals and Options III: Numerical (Tech. Index 6/10) 673 Path Integrals and Common Numerical Methods 674 The Binomial Approximation to a Monte Carlo Simulation 675 Basic Numerical Procedure using Path Integrals 676 The Castresana-Hogan Path-Integral Discretization 679 Path Integrals, MC Simulation, Lattices, and Brownian Bridges 684 Monte Carlo Simulation Using Path Integrals - Illustration: 686 Smart Monte Carlo (SMC) 688 American Monte Carlo (AMC) 689 New Interpolation Methods for SMC and AMC 692 Greeks and Path Integrals 694 Normal Integral Approximations 696 Pertubation Expansion for Multivariate Gaussian Integrals 697 Appendix 1: Back-Chaining Bermuda Algorithm, Critical Path 698 Appendix 2: Some Aspects of Numerical Uncertainties 700 Appendix 3: Numerical Approximation Methods 703 Appendix 4: Some other Numerical Methods in the Literature 708 References JQQ

45. Path Integrals and Options IV: Multiple Factors (Tech. Index 9/10)....711 Calculating Options with Multidimensional Path Integrals 714 Principal-Component Path Integrals " 715 Multi-dimensional Monte Carlo Simulation 716

Table of Contents xvii

References 716

46. The Reggeon Field Theory, Markets in Crises, and "Predicting" Crises (Tech. Index 10/10) 717

Introduction to the Reggeon Field Theory (RFT) 717 Summary of the RFT in Physics 718 Aspects of Applications of the RFT to Finance 723 The RFT and Describing Financial Crises (2lld Edition) 724 RFT Scaling Without Fitting for Various Markets In Crisis 724 Rich-Cheap Analysis, the RFT, and Crises 725 RFT - the Natural Extension to Brownian Motion 725 Predicting Crises in Equity Markets; an Earthquake Analogy 726 Finance Theory is Really Phenomenology 728 References 728

PART VI: THE MACRO-MICRO MODEL 731

47. The Macro-Micro Model and Trend Risk: Overview (Tech. Index 4/10) 733

Explicit Time Scales Separating Dynamical Regions 733 L The Macro-Micro Yield-Curve Model: Ch. 48-50 734 iL Further Developments for the Macro-Micro Model: Ch. 51 738 III. A Function Toolkit: Ch. 52 739 References 740

48. A Multivariate Yield-Curve Lognormal Model and Yield-Curve Kinks (Tech. Index 6/10) 741

Summary of this Chapter 741 The Problem of Kinks in Yield Curves for Models 742 I. Introduction to this Chapter 742 IIA. Statistical Probes, Data, Quasi-Equilibrium Drift 745 IIB. Yield-Curve Kinks: Bete Noire of Yield Curve Models 747 III. EOF / Principal Component Analysis 749 IV. Simpler Lognormal Model with Three Variates 750 V. Wrap-Up and Preview of the Next Chapters 751 Appendix A: Defmitions and Stochastic Equations 752 Appendix B: EOF or Principal-Component Formalism 754 "Sub-Period Centered" Principal Components 760 Figures: Multivariate Lognormal Yield-Curve Model 761 References 775

49. Strong Mean-Reverting Multifactor YC Model and the 3rd Order Green Function (Tech. Index 7/10) 777

Summary of this Chapter 777 Introduction to this Chapter 778

KVjü Quantitative Finance and Risk Management

Short and Long Time Scales 780 Cluster Decomposition Analysis and the SMRG Model 781 Third-Order Correlation Functions 782 Historical Quasi-Equilibrium Yield Curve Path for Data 785 Large Value of the Mean Reversion in this Model 786 Physical Picture - How Interest Rates Really Seem to Behave 787 Other Statistical Tests and the SMRG Model 788 Principal Components (EOFs) and the SMRG Model 790 Wrap-Up for this Chapter 791 Appendix A: Definitions and Stochastic Equations 792 Appendix B: The Cluster-Decomposition Analysis (CDA) 794 Figures: Strong Mean-Reverting Multifactor Yield-Curve Model 798 References 812

50. The Macro-Micro Yield-Curve Model (Tech. Index 5/10) 813 Summary of this Chapter 813 Introduction to this Chapter 814 Spectral Decomposition and Time Scales 815 The Macro Component and Macroeconomics 815 The Micro Component and Short-Term Trading Activity 816 Prototype: Prime (Macro) and Libor (Macro + Micro) 817 Details of the Macro-Micro Yield-Curve Model 817 Model for the Random Macro Time Step Dynamics 818 Wrap-Up of this Chapter 820 Appendix A. No Arbitrage and Yield-Curve Dynamics 821 Figures: Macro-Micro Model 823 References 827

51. Macro-Micro Model: Further Developments (Tech. Index 6/10) 829 Summary of This Chapter 829 Using SSA to determine the Macro Component 829 Intuition: Short to Long Times - Volatility, No-Arbitrage 830 The Macro-Micro Model applied to FX and Equity Markets 831 Formal Developments in the Macro-Micro Model 833 No Arbitrage and the Macro-Micro Model: Formal Aspects 835 Hedging, Forward Prices, No Arbitrage, Options (Equities) 837 Satisfying the Interest-Rate Term-Structure Constraints 840 Chaos and the Macro-Micro Model 841 Technical Analysis and the MM Model 844 The Macro-Micro Model and Data 845 Finance Models Related to the Macro-Micro Model 848 Macroeconomics, Economics Literature, Macro-Micro Model 849 References

52. A Function Toolkit (Tech. Index 6/10) 855

Table of Contents xix

Time Thresholds; Time and Frequency; Oscillations 856 Summary ofDesirable Properties of Toolkit Functions 857 Construction of the Toolkit Functions 857 Relation of the Function Toolkit to Other Approaches 862 Example of Standard Micro "Noise" Plus Macro "Signal" 864 The Total Macro: Quasi-Random Trends + Toolkit Cycles 867 Short-Time Micro Regime, Trading, and the Function Toolkit 868 Appendix: Wavelets, Completeness, and the Function Toolkit 869 References 871

PART VII: CLIMATE CHANGE RISK MANAGEMENT 873

53. Climate Change Risk Management: Business, Economy, Finance, Society (Tech. Index 5/10) 875

Summary: Climate Change Risk Management 875 Climate Change Risk Management - Formal Structure 878 Finance, Economics, Risks, and Opportunities 885 Positive Opportunities in Mitigating Climate Change 888 Long-term discounting for climate change impacts in the future 890 Climate-Change-Induced Economic and Financial Crises? 895 Business, Investors, Regulators, and Climate Change Risks 896 Economic Models Related to Climate Change Impacts 899 Wrap Up of Climate Risk Management 902 Epilogue 902 Appendix I. The Physical Science Basis of Climate Change 903 Appendix II. Impacts of Climate Change and Vulnerabilities 906 Appendix III. Mitigation and Adaption for Climate Change 911 Appendix IV. Risk from Climate Contrarian Obstruction 919 References 932

INDEX: CH. 1 - CH. 52 967 INDEX: CLIMATE CHANGE RISK MANAGEMENT, CH. 53 981