Elements of Financial Risk Management

Value-at-Risk has emerged as the standard tool for measuring and reporting financial market risk. Currently, more than eighty commercial vendors offer enterprise or trading risk management systems that provide VAR-like measures. Risk managers are therefore often left with the daunting task of having to choose from this plethora of risk measures. While basic VAR textbooks describe average VAR situations, the vast majority of these situations are abnormal. Elements of Financial Risk Management focuses on implementation, especially recent techniques which facilitate "bridging the gap" between standard textbooks on risk and real-life risk management systems. This book will appeal to practitioners in the financial services and investment industries, as well as graduate students and advanced undergraduates who want exposure to these techniques. \*Pinpoints key features of risk asset returns and captures them in tractable statistical models in theaccompanying CD-ROM\*Presents step-by-step approaches as a means to solve problems\*Visible patterns in the data motivate the choices of tools, and when tools fall short, it presents the next tool Contents......Page 8 Preface......Page 12 Acknowledgments......Page 14 1.2. LEARNING OBJECTIVES......Page 16 1.3. RISK MANAGEMENT AND THE FIRM......Page 17 1.4. A BRIEF TAXONOMY OF RISKS......Page 19 1.5. STYLIZED FACTS OF ASSET RETURNS......Page 21 1.7. FURTHER RESOURCES......Page 24 1.8. EMPIRICAL EXERCISES ON CD-ROM......Page 25 REFERENCES 1......Page 33 2.1. CHAPTER OVERVIEW......Page 34 2.2. SIMPLE VARIANCE FORECASTING......Page 35 2.3. THE GARCH VARIANCE MODEL......Page 38 2.4. EXTENSIONS TO THE GARCH MODEL......Page 41 2.5. MAXIMUM LIKELIHOOD ESTIMATION......Page 43 2.6. VARIANCE MODEL EVALUATION......Page 45 2.7. USING INTRADAY INFORMATION......Page 47 2.9. FURTHER RESOURCES......Page 53 2.10. EMPIRICAL EXERCISES ON CD-ROM......Page 54 REFERENCES 2......Page 61 3.1. CHAPTER OVERVIEW......Page 62 3.2. VALUE AT RISK FOR SIMPLE PORTFOLIOS......Page 63 3.3. PORTFOLIO VARIANCE......Page 66 3.4. MODELING CONDITIONAL COVARIANCES......Page 67 3.5. MODELING CONDITIONAL CORRELATIONS......Page 69 3.6. QUASI-MAXIMUM LIKELIHOOD ESTIMATION......Page 73 3.7. REALIZED AND RANGE-BASED COVARIANCE......Page 74 3.9. FURTHER RESOURCES......Page 76 3.10. APPENDIX: VaR FROM LOGARITHMIC VERSUS ARITHMETIC RETURNS......Page 77 3.11. EMPIRICAL EXERCISES ON CD-ROM......Page 78 REFERENCES 3......Page 85 4.1. CHAPTER OVERVIEW......Page 86 4.2. VISUALIZING NON-NORMALITY......Page 88 4.3. THE STANDARDIZED t(d) DISTRIBUTION......Page 89 4.4. THE CORNISH-FISHER APPROXIMATION TO VAR......Page 94 4.5. EXTREME VALUE THEORY (EVT)......Page 95 4.6. THE EXPECTED SHORTFALL RISK MEASURE......Page 100 4.7. SUMMARY......Page 102 4.8. FURTHER RESOURCES......Page 103 4.9. EMPIRICAL EXERCISES ON CD-ROM......Page 104 REFERENCES 4......Page 112 5.1. CHAPTER OVERVIEW......Page 114 5.2. HISTORICAL SIMULATION (HS)......Page 115 5.3. WEIGHTED HISTORICAL SIMULATION (WHS)......Page 118 5.4. MULTI-PERIOD RISK CALCULATIONS......Page 120 5.5. MONTE CARLO SIMULATION (MCS)......Page 123 5.6. FILTERED HISTORICAL SIMULATION (FHS)......Page 125 5.7. SUMMARY......Page 127 5.9. EMPIRICAL EXERCISES ON CD-ROM......Page 128 REFERENCES 5......Page 134 6.1. CHAPTER OVERVIEW......Page 136 6.2. BASIC DEFINITIONS......Page 137 6.3. OPTION PRICING UNDER THE NORMAL DISTRIBUTION......Page 138 6.4. ALLOWING FOR SKEWNESS AND KURTOSIS......Page 144 6.5. GARCH OPTION PRICING MODELS......Page 148 6.6. IMPLIED VOLATILITY FUNCTION (IVF) MODELS......Page 153 6.7. SUMMARY......Page 154 6.8. FURTHER RESOURCES......Page 155 6.9. APPENDIX: THE OPTION PRICING FORMULA......Page 156 6.10. EMPIRICAL EXERCISES ON CD-ROM......Page 157 REFERENCES 6......Page 166 7.1. CHAPTER OVERVIEW......Page 168 7.2. THE OPTION DELTA......Page 169 7.3. PORTFOLIO RISK USING DELTA......Page 174 7.4. THE OPTION GAMMA......Page 176 7.5. PORTFOLIO RISK USING GAMMA......Page 178 7.6. PORTFOLIO RISK USING FULL VALUATION......Page 181 7.7. A SIMPLE EXAMPLE......Page 183 7.8. PITFALL IN THE DELTA AND GAMMA APPROACHES......Page 186 7.9. SUMMARY......Page 188 7.10. FURTHER RESOURCES......Page 189 7.11. EMPIRICAL EXERCISES ON CD-ROM......Page 190 REFERENCES 7......Page 195 8.1. CHAPTER OVERVIEW......Page 196 8.2. BACKTESTING VaRs......Page 199 8.3. INCREASING THE INFORMATION SET......Page 204 8.4. BACKTESTING EXPECTED SHORTFALL......Page 205 8.5. BACKTESTING THE ENTIRE DISTRIBUTION......Page 206 8.6. STRESS TESTING......Page 209 8.7. SUMMARY......Page 212 8.9. EMPIRICAL EXERCISES ON CD-ROM......Page 213 REFERENCES 8......Page 223 Index......Page 224 Elements of Financial Risk Management offers an introduction to modern risk management. It focuses on implementation, especially recent techniques which facilitate bridging the gap between standard textbooks on risk and real-life risk management systems. It identifies key features of risk asset returns and captures them in tractable statistical models in the companion website. It presents step-by-step approaches as a means to solve problems. This book is intended for three types of readers with an interest in financial risk management. First, Master's and Ph.D. students specializing in finance and economics. Second, market practitioners with a quantitative undergraduate or graduate degree. Third, a small group of advanced undergraduates majoring in either economics, engineering, finance, or another quantitative field. The book will also suit those in financial engineering courses who have strong quantitative backgrounds and those in Ph.D. courses. *Pinpoints key features of risk asset returns and captures them in tractable statistical models in the companion website *Presents step-by-step approaches as a means to solve problems *Visible patterns in the data motivate the choices of tools, and when tools fall short, it presents the next tool "Elements of Financial Risk Management pinpoints key features of risk asset returns and captures them in tractable statistical models. Written for those who measure and manage risks, Christofferson explores various types of market risk as well as the construction of conditional densities for simple assets, simulation based methods in risk management, option pricing and hedging, and risk model evaluation and comparison." "Pedagogically effective, it presents step-by-step approaches as a means to solve problems. Visible patterns in the data motivate the choices of tools, and when tools fall short, it presents the next tool. This unique approach bridges the gap between theory and practice."--BOOK JACKET This chapter begins by listing the learning objectives of the book.