A Practical Guide to Forecasting Financial Market Volatility (The Wiley Finance Series)

Financial market volatility forecasting is one of today's most important areas of expertise for professionals and academics in investment, option pricing, and financial market regulation. While many books address financial market modelling, no single book is devoted primarily to the exploration of volatility forecasting and the practical use of forecasting models. A Practical Guide to Forecasting Financial Market Volatility provides practical guidance on this vital topic through an in-depth examination of a range of popular forecasting models. Details are provided on proven techniques for building volatility models, with guide-lines for actually using them in forecasting applications. A Practical Guide to Forecasting Financial Market Volatility 4 Contents 10 Foreword by Clive Granger 16 Preface 18 1 Volatility Definition and Estimation 20 1.1 What is volatility? 20 1.2 Financial market stylized facts 22 1.3 Volatility estimation 29 1.3.1 Using squared return as a proxy for daily volatility 30 1.3.2 Using the high–low measure to proxy volatility 31 1.3.3 Realized volatility, quadratic variation and jumps 33 1.3.4 Scaling and actual volatility 35 1.4 The treatment of large numbers 36 2 Volatility Forecast Evaluation 40 2.1 The form of X(t) 40 2.2 Error statistics and the form of ε(t) 42 2.3 Comparing forecast errors of different models 43 2.3.1 Diebold and Mariano's asymptotic test 45 2.3.2 Diebold and Mariano's sign test 46 2.3.3 Diebold and Mariano's Wilcoxon sign-rank test 46 2.3.4 Serially correlated loss differentials 47 2.4 Regression-based forecast efficiency and orthogonality test 47 2.5 Other issues in forecast evaluation 49 3 Historical Volatility Models 50 3.1 Modelling issues 50 3.2 Types of historical volatility models 51 3.2.1 Single-state historical volatility models 51 3.2.2 Regime switching and transition exponential smoothing 53 3.3 Forecasting performance 54 4 Arch 56 4.1 Engle (1982) 56 4.2 Generalized ARCH 57 4.3 Integrated GARCH 58 4.4 Exponential GARCH 60 4.5 Other forms of nonlinearity 60 4.6 Forecasting performance 62 5 Linear and Nonlinear Long Memory Models 64 5.1 What is long memory in volatility? 64 5.2 Evidence and impact of volatility long memory 65 5.3 Fractionally integrated model 69 5.3.1 FIGARCH 70 5.3.2 FIEGARCH 71 5.3.3 The positive drift in fractional integrated series 71 5.3.4 Forecasting performance 72 5.4 Competing models for volatility long memory 73 5.4.1 Breaks 73 5.4.2 Components model 74 5.4.3 Regime-switching model 76 5.4.4 Forecasting performance 77 6 Stochastic Volatility 78 6.1 The volatility innovation 78 6.2 The MCMC approach 79 6.2.1 The volatility vector H 80 6.2.2 The parameter w 81 6.3 Forecasting performance 82 7 Multivariate Volatility Models 84 7.1 Asymmetric dynamic covariance model 84 7.2 A bivariate example 86 7.3 Applications 87 8 Black–Scholes 90 8.1 The Black–Scholes formula 90 8.1.1 The Black–Scholes assumptions 91 8.1.2 Black–Scholes implied volatility 92 8.1.3 Black–Scholes implied volatility smile 93 8.1.4 Explanations for the 'smile' 94 8.2 Black–Scholes and no-arbitrage pricing 96 8.2.1 The stock price dynamics 96 8.2.2 The Black–Scholes partial differential equation 96 8.2.3 Solving the partial differential equation 98 8.3 Binomial method 99 8.3.1 Matching volatility with u and d 102 8.3.2 A two-step binomial tree and American-style options 104 8.4 Testing option pricing model in practice 105 8.5 Dividend and early exercise premium 107 8.5.1 Known and finite dividends 107 8.5.2 Dividend yield method 107 8.5.3 Barone-Adesi and Whaley quadratic approximation 108 8.6 Measurement errors and bias 109 8.6.1 Investor risk preference 110 8.7 Appendix: Implementing Barone-Adesi and Whaley's efficient algorithm 111 9 Option Pricing with Stochastic Volatility 116 9.1 The Heston stochastic volatility option pricing model 117 9.2 Heston price and Black–Scholes implied 118 9.3 Model assessment 121 9.3.1 Zero correlation 122 9.3.2 Nonzero correlation 122 9.4 Volatility forecast using the Heston model 124 9.5 Appendix: The market price of volatility risk 126 9.5.1 Ito's lemma for two stochastic variables 126 9.5.2 The case of stochastic volatility 126 9.5.3 Constructing the risk-free strategy 127 9.5.4 Correlated processes 129 9.5.5 The market price of risk 130 10 Option Forecasting Power 134 10.1 Using option implied standard deviation to forecast volatility 134 10.2 At-the-money or weighted implied? 135 10.3 Implied biasedness 136 10.4 Volatility risk premium 138 11 Volatility Forecasting Records 140 11.1 Which volatility forecasting model? 140 11.2 Getting the right conditional variance and forecast with the 'wrong' models 142 11.3 Predictability across different assets 143 11.3.1 Individual stocks 143 11.3.2 Stock market index 144 11.3.3 Exchange rate 145 11.3.4 Other assets 146 12 Volatility Models in Risk Management 148 12.1 Basel Committee and Basel Accords I & II 148 12.2 VaR and backtest 150 12.2.1 VaR 150 12.2.2 Backtest 151 12.2.3 The three-zone approach to backtest evaluation 152 12.3 Extreme value theory and VaR estimation 154 12.3.1 The model 155 12.3.2 10-day VaR 156 12.3.3 Multivariate analysis 157 12.4 Evaluation of VaR models 158 13 VIX and Recent Changes in VIX 162 13.1 New definition for VIX 162 13.2 What is the VXO? 163 13.3 Reason for the change 165 14 Where Next? 166 Appendix 168 References 220 Index 234 A Practical Guide to Forecasting Financial Market Volatility......Page 4 Contents......Page 10 Foreword by Clive Granger......Page 16 Preface......Page 18 1.1 What is volatility?......Page 20 1.2 Financial market stylized facts......Page 22 1.3 Volatility estimation......Page 29 1.3.1 Using squared return as a proxy for daily volatility......Page 30 1.3.2 Using the high–low measure to proxy volatility......Page 31 1.3.3 Realized volatility, quadratic variation and jumps......Page 33 1.3.4 Scaling and actual volatility......Page 35 1.4 The treatment of large numbers......Page 36 2.1 The form of X(t)......Page 40 2.2 Error statistics and the form of ε(t)......Page 42 2.3 Comparing forecast errors of different models......Page 43 2.3.1 Diebold and Mariano's asymptotic test......Page 45 2.3.3 Diebold and Mariano's Wilcoxon sign-rank test......Page 46 2.4 Regression-based forecast efficiency and orthogonality test......Page 47 2.5 Other issues in forecast evaluation......Page 49 3.1 Modelling issues......Page 50 3.2.1 Single-state historical volatility models......Page 51 3.2.2 Regime switching and transition exponential smoothing......Page 53 3.3 Forecasting performance......Page 54 4.1 Engle (1982)......Page 56 4.2 Generalized ARCH......Page 57 4.3 Integrated GARCH......Page 58 4.5 Other forms of nonlinearity......Page 60 4.6 Forecasting performance......Page 62 5.1 What is long memory in volatility?......Page 64 5.2 Evidence and impact of volatility long memory......Page 65 5.3 Fractionally integrated model......Page 69 5.3.1 FIGARCH......Page 70 5.3.3 The positive drift in fractional integrated series......Page 71 5.3.4 Forecasting performance......Page 72 5.4.1 Breaks......Page 73 5.4.2 Components model......Page 74 5.4.3 Regime-switching model......Page 76 5.4.4 Forecasting performance......Page 77 6.1 The volatility innovation......Page 78 6.2 The MCMC approach......Page 79 6.2.1 The volatility vector H......Page 80 6.2.2 The parameter w......Page 81 6.3 Forecasting performance......Page 82 7.1 Asymmetric dynamic covariance model......Page 84 7.2 A bivariate example......Page 86 7.3 Applications......Page 87 8.1 The Black–Scholes formula......Page 90 8.1.1 The Black–Scholes assumptions......Page 91 8.1.2 Black–Scholes implied volatility......Page 92 8.1.3 Black–Scholes implied volatility smile......Page 93 8.1.4 Explanations for the 'smile'......Page 94 8.2.2 The Black–Scholes partial differential equation......Page 96 8.2.3 Solving the partial differential equation......Page 98 8.3 Binomial method......Page 99 8.3.1 Matching volatility with u and d......Page 102 8.3.2 A two-step binomial tree and American-style options......Page 104 8.4 Testing option pricing model in practice......Page 105 8.5.2 Dividend yield method......Page 107 8.5.3 Barone-Adesi and Whaley quadratic approximation......Page 108 8.6 Measurement errors and bias......Page 109 8.6.1 Investor risk preference......Page 110 8.7 Appendix: Implementing Barone-Adesi and Whaley's efficient algorithm......Page 111 9 Option Pricing with Stochastic Volatility......Page 116 9.1 The Heston stochastic volatility option pricing model......Page 117 9.2 Heston price and Black–Scholes implied......Page 118 9.3 Model assessment......Page 121 9.3.2 Nonzero correlation......Page 122 9.4 Volatility forecast using the Heston model......Page 124 9.5.2 The case of stochastic volatility......Page 126 9.5.3 Constructing the risk-free strategy......Page 127 9.5.4 Correlated processes......Page 129 9.5.5 The market price of risk......Page 130 10.1 Using option implied standard deviation to forecast volatility......Page 134 10.2 At-the-money or weighted implied?......Page 135 10.3 Implied biasedness......Page 136 10.4 Volatility risk premium......Page 138 11.1 Which volatility forecasting model?......Page 140 11.2 Getting the right conditional variance and forecast with the 'wrong' models......Page 142 11.3.1 Individual stocks......Page 143 11.3.2 Stock market index......Page 144 11.3.3 Exchange rate......Page 145 11.3.4 Other assets......Page 146 12.1 Basel Committee and Basel Accords I & II......Page 148 12.2.1 VaR......Page 150 12.2.2 Backtest......Page 151 12.2.3 The three-zone approach to backtest evaluation......Page 152 12.3 Extreme value theory and VaR estimation......Page 154 12.3.1 The model......Page 155 12.3.2 10-day VaR......Page 156 12.3.3 Multivariate analysis......Page 157 12.4 Evaluation of VaR models......Page 158 13.1 New definition for VIX......Page 162 13.2 What is the VXO?......Page 163 13.3 Reason for the change......Page 165 14 Where Next?......Page 166 Appendix......Page 168 References......Page 220 Index......Page 234 This Book Gives Clear And Practical Guidance On How To Model And Forecast Volatility Using Only Volatility Models That Have Been Tested For Their Forecasting Performance. The Book Focuses On Describing, Evaluating And Comparing Research In Volatility Forecasting And Provides Some Background On Volatility Definition, Estimation And Some Principles On Forecasts Evaluation. This Book Covers Both Time Series Econometric Volatility Models And Implied Volatility Models Based On Black-scholes And Continuous Time Stochastic Volatility Option Pricing Models.--book Jacket. Volatility Definition And Estimation -- Volatility Forecast Evaluation -- Historial Volatility Models -- Arch -- Linear And Nonlinear Long Memory Models -- Stochastic Volatility -- Multivariate Volatility Models -- Black-scholes -- Option Pricing With Stochastic Volatility -- Option Forecasting Power -- Volatility Forecasting Records -- Volatility Models In Risk Management -- Vix And Recent Changes In Vix -- Where Next? Ser-huang Poon. Includes Bibliographical References (p. [201]-213) And Index. Volatility forecasting is crucial for option pricing, risk management and portfolio management. This book gives clear and practical guidance on how to model and forecast volatility using only volatility models that have been tested for their forecasting performance. The book focuses on describing, evaluating and comparing research in volatility forecasting and provides some background on volatility definition, estimation and some principles on forecasts evaluation. The book covers both time series econometric volatility models and implied volatility models based on Black-Scholes and continuous time stochastic volatility option pricing models. To give a brief appreciation of the amount of variation across different financial assets, Figure 1.1 plots the returns distributions of a normally distributed random variable, and the respective daily returns on the US Standard and Poor market index (S&P100), the yen-sterling exchange rate, the share of Legal & General (a major insurance company in the UK), the UK Index for Small Capitalisation Stocks (i.e. small companies), and silver traded at the commodity exchange.