About the author Dr SER-HUANG POON was promoted to Professor of Finance at Manchester University in 2003. Prior to that, she was a senior lecturer at Strathclyde University. Ser-Huang graduated from the National University of Singapore and obtained her masters and PhD from Lancaster University, UK. She has researched financial market volatility for many years and has published in many top ranking peer reviewed finance and financial econometric journals with many co-authors from around the world. Her financial market volatility work was cited as a reference reading on the Nobel web site in 2003.

• Foreword by Clive Granger xiiiPreface xv1 Volatility Definition and Estimation 11.1 What is volatility? 11.2 Financial market stylized facts 31.3 Volatility estimation 101.3.1 Using squared return as a proxy for daily volatility 111.3.2 Using the high–low measure to proxy volatility 121.3.3 Realized volatility, quadratic variation and jumps 141.3.4 Scaling and actual volatility 161.4 The treatment of large numbers 172 Volatility Forecast Evaluation 212.1 The form of Xt 212.2 Error statistics and the form of εt 232.3 Comparing forecast errors of different models 242.3.1 Diebold and Mariano’s asymptotic test 262.3.2 Diebold and Mariano’s sign test 272.3.3 Diebold and Mariano’sWilcoxon sign-rank test 272.3.4 Serially correlated loss differentials 282.4 Regression-based forecast efficiency and orthogonality test 282.5 Other issues in forecast evaluation 303 Historical Volatility Models 313.1 Modelling issues 313.2 Types of historical volatility models 323.2.1 Single-state historical volatility models 323.2.2 Regime switching and transition exponential smoothing 343.3 Forecasting performance 354 Arch 374.1 Engle (1982) 374.2 Generalized ARCH 384.3 Integrated GARCH 394.4 Exponential GARCH 414.5 Other forms of nonlinearity 414.6 Forecasting performance 435 Linear and Nonlinear Long Memory Models 455.1 What is long memory in volatility? 455.2 Evidence and impact of volatility long memory 465.3 Fractionally integrated model 505.3.1 FIGARCH 515.3.2 FIEGARCH 525.3.3 The positive drift in fractional integrated series 525.3.4 Forecasting performance 535.4 Competing models for volatility long memory 545.4.1 Breaks 545.4.2 Components model 555.4.3 Regime-switching model 575.4.4 Forecasting performance 586 Stochastic Volatility 596.1 The volatility innovation 596.2 The MCMC approach 606.2.1 The volatility vector H 616.2.2 The parameter w 626.3 Forecasting performance 637 Multivariate Volatility Models 657.1 Asymmetric dynamic covariance model 657.2 A bivariate example 677.3 Applications 688 Black–Scholes 718.1 The Black–Scholes formula 718.1.1 The Black–Scholes assumptions 728.1.2 Black–Scholes implied volatility 738.1.3 Black–Scholes implied volatility smile 748.1.4 Explanations for the ‘smile’ 758.2 Black–Scholes and no-arbitrage pricing 778.2.1 The stock price dynamics 778.2.2 The Black–Scholes partial differential equation 778.2.3 Solving the partial differential equation 798.3 Binomial method 808.3.1 Matching volatility with u and d 838.3.2 A two-step binomial tree and American-style options 858.4 Testing option pricing model in practice 868.5 Dividend and early exercise premium 888.5.1 Known and finite dividends 888.5.2 Dividend yield method 888.5.3 Barone-Adesi and Whaley quadratic approximation 898.6 Measurement errors and bias 908.6.1 Investor risk preference 918.7 Appendix: Implementing Barone-Adesi and Whaley’s efficient algorithm 929 Option Pricing with Stochastic Volatility 979.1 The Heston stochastic volatility option pricing model 989.2 Heston price and Black–Scholes implied 999.3 Model assessment 1029.3.1 Zero correlation 1039.3.2 Nonzero correlation 1039.4 Volatility forecast using the Heston model 1059.5 Appendix: The market price of volatility risk 1079.5.1 Ito’s lemma for two stochastic variables 1079.5.2 The case of stochastic volatility 1079.5.3 Constructing the risk-free strategy 1089.5.4 Correlated processes 1109.5.5 The market price of risk 11110 Option Forecasting Power 11510.1 Using option implied standard deviation to forecast volatility 11510.2 At-the-money or weighted implied? 11610.3 Implied biasedness 11710.4 Volatility risk premium 11911 Volatility Forecasting Records 12111.1 Which volatility forecasting model? 12111.2 Getting the right conditional variance and forecast with the ‘wrong’ models 12311.3 Predictability across different assets 12411.3.1 Individual stocks 12411.3.2 Stock market index 12511.3.3 Exchange rate 12611.3.4 Other assets 12712 Volatility Models in Risk Management 12912.1 Basel Committee and Basel Accords I & II 12912.2 VaR and backtest 13112.2.1 VaR 13112.2.2 Backtest 13212.2.3 The three-zone approach to backtest evaluation 13312.3 Extreme value theory and VaR estimation 13512.3.1 The model 13612.3.2 10-day VaR 13712.3.3 Multivariate analysis 13812.4 Evaluation of VaR models 13913 VIX and Recent Changes in VIX 14313.1 New definition for VIX 14313.2 What is the VXO? 14413.3 Reason for the change 14614 Where Next? 147Appendix 149References 201Index 215