Forecasting Volatility in Financial Markets: A Review

Financial market volatility is an important input for investment, option pricing, and financial market regulation. The emphasis of this review article is on forecasting instead of modelling; it compares the volatility forecasting findings in 93 papers published and written in the last two decades. Provided in this paper as well are volatility definitions, insights into problematic issues of forecast evaluation, data frequency, extreme values and the measurement of "actual" volatility. We compare volatility forecasting performance of two main approaches; historical volatility models and volatility implied from options. Forecasting results are compared across different asset classes and geographical regions.

[1]  C. B. Tilanus,et al.  Applied Economic Forecasting , 1966 .

[2]  P. Clark.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices , 1973 .

[3]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[4]  Richard J. Rendleman,et al.  STANDARD DEVIATIONS OF STOCK PRICE RATIOS IMPLIED IN OPTION PRICES , 1976 .

[5]  R. Trippi,et al.  COMMON STOCK VOLATILITY EXPECTATIONS IMPLIED BY OPTION PREMIA , 1978 .

[6]  Donald P. Chiras,et al.  The information content of option prices and a test of market efficiency , 1978 .

[7]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[8]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[9]  L. Hansen,et al.  Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis , 1980, Journal of Political Economy.

[10]  S. Beckers.  Standard deviations implied in option prices as predictors of future stock price variability , 1981 .

[11]  R. Whaley.  Valuation of American call options on dividend-paying stocks: Empirical tests , 1982 .

[12]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[13]  Philip R. Perry.  The Time‐Variance Relationship of Security Returns: Implications for the Return‐Generating Stochastic Process , 1982 .

[14]  George Tauchen,et al.  THE PRICE VARIABILITY-VOLUME RELATIONSHIP ON SPECULATIVE MARKETS , 1983 .

[15]  Walter N. Torous,et al.  The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing , 1984 .

[16]  G. Gemmill,et al.  The Forecasting Performance of Stock Options On the London Traded Options Market , 1986 .

[17]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[18]  Thomas H. McCurdy,et al.  Tests of the Martingale Hypothesis for Foreign Currency Futures with Time-Varying Volatility , 1986 .

[19]  F. Diebold,et al.  Structural change and the combination of forecasts , 1986 .

[20]  D. Hendry,et al.  Econometric Evaluation of Linear Macro-Economic Models , 1986 .

[21]  H. Iemoto.  Modelling the persistence of conditional variances , 1986 .

[22]  R. Carroll,et al.  Variance Function Estimation , 1987 .

[23]  Anders Milhøj,et al.  A Conditional Variance Model for Daily Deviations of an Exchange Rate , 1987 .

[24]  James B. Wiggins.  Option values under stochastic volatility: Theory and empirical estimates , 1987 .

[25]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[26]  Jonathan M. Karpoff.  The Relation between Price Changes and Trading Volume: A Survey , 1987, Journal of Financial and Quantitative Analysis.

[27]  K. French,et al.  Expected stock returns and volatility , 1987 .

[28]  T. Bollerslev,et al.  A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN , 1987 .

[29]  Stephen L Taylor,et al.  Modelling Financial Time Series , 1987 .

[30]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[31]  F. Diebold.  Empirical modeling of exchange rate dynamics , 1988 .

[32]  M. Rothschild,et al.  Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills , 1988 .

[33]  Edward W. Frees,et al.  Estimating the Volatility of Discrete Stock Prices , 1988 .

[34]  R. Shiller,et al.  The Informational Content of Ex Ante Forecasts , 1988 .

[35]  Alan L. Tucker,et al.  Predicting currency return volatility , 1989 .

[36]  Adrian Pagan,et al.  Alternative Models for Conditional Stock Volatility , 1989 .

[37]  David I. Laibson,et al.  Economic Implications of Extraordinary Movements in Stock Prices , 1989 .

[38]  V. Akgiray.  Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts , 1989 .

[39]  R. Baillie,et al.  A Conditional-Variance Tale , 1989 .

[40]  Ray C. Fair,et al.  The Informational Context of Ex Ante Forecasts , 1989 .

[41]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[42]  David A. Hsieh,et al.  Modeling Heteroscedasticity in Daily Foreign-Exchange Rates , 1989 .

[43]  William L. Silber,et al.  Financial Options: From Theory to Practice , 1990 .

[44]  Christopher G. Lamoureux,et al.  Persistence in Variance, Structural Change, and the GARCH Model , 1990 .

[45]  Ray C. Fair,et al.  Comparing Information in Forecasts from Econometric Models , 1990 .

[46]  Elroy Dimson,et al.  Volatility forecasting without data-snooping , 1990 .

[47]  D. Duffie,et al.  Simulated Moments Estimation of Markov Models of Asset Prices , 1990 .

[48]  Hung-Gay Fung,et al.  The Forecasting Performance of the Implied Standard Deviation in Currency Options , 1990 .

[49]  Yiu Kuen Tse,et al.  Stock returns volatility in the Tokyo stock exchange , 1991 .

[50]  Mohammad Najand,et al.  A test of two models in forecasting stock index futures price volatility , 1991 .

[51]  S. Wei,et al.  Are Option-Implied Forecasts of Exchange Rate Volatility Excessively Variable? , 1991 .

[52]  D. Reeve,et al.  Scale models. , 1991, The Health service journal.

[53]  K. Lee,et al.  Are the GARCH models best in out-of-sample performance? , 1991 .

[54]  A. Hodgson,et al.  INDEX FUTURES OPTIONS IN AUSTRALIA ‐AN EMPIRICAL FOCUS ON VOLATILITY , 1991 .

[55]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[56]  Estimating the volatility of S&P 500 futures prices using the extreme‐value method , 1992 .

[57]  Forecasting volatility in the Singapore stock market , 1992 .

[58]  T. Day,et al.  Stock market volatility and the information content of stock index options , 1992 .

[59]  Ruey S. Tsay,et al.  Nonlinear Time-Series Analysis of Stock Volatilities , 1992 .

[60]  Dean P. Foster,et al.  Filtering and Forecasting with Misspecified Arch Models Ii: Making the Right Forecast with the Wrong Model , 1992 .

[61]  Daniel B. Nelson,et al.  Filtering and Forecasting with Misspecified Arch Models Ii: Making the Right Forecast with the Wrong Model , 1992 .

[62]  K. West,et al.  A Utility Based Comparison of Some Models of Exchange Rate Volatility , 1992 .

[63]  Stephen L Taylor,et al.  Stock returns and volatility: An empirical study of the UK stock market , 1992 .

[64]  Campbell R. Harvey,et al.  Market volatility prediction and the efficiency of the S & P 100 index option market , 1992 .

[65]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[66]  R. Whaley.  Derivatives on Market Volatility , 1993 .

[67]  Stephen Figlewski,et al.  Forecasting Volatilities and Correlations with EGARCH Models , 1993 .

[68]  G. Karolyi.  A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation , 1993, Journal of Financial and Quantitative Analysis.

[69]  Stephen Figlewski,et al.  The Informational Content of Implied Volatility , 1993 .

[70]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[71]  T. Nijman,et al.  Temporal Aggregation of GARCH Processes. , 1993 .

[72]  A. Pagan,et al.  Australian Stock Market Volatility: 1875–1987* , 1993 .

[73]  Predicting stock-market volatility , 1993 .

[74]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[75]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[76]  Christopher G. Lamoureux,et al.  Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities , 1993 .

[77]  Peter E. Rossi,et al.  Nonlinear dynamic structures , 1993 .

[78]  Anil K. Bera,et al.  ARCH Models: Properties, Estimation and Testing , 1993 .

[79]  K. West,et al.  The Predictive Ability of Several Models of Exchange Rate Volatility , 1994 .

[80]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[81]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[82]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models: Comments: Reply , 1994 .

[83]  G. C. Tiao,et al.  Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance , 1994 .

[84]  Jón Dańıelsson.  Stochastic volatility in asset prices estimation with simulated maximum likelihood , 1994 .

[85]  Eric Ghysels,et al.  Periodic Autoregressive Conditional Heteroskedasticity , 1996 .

[86]  Daniel B. Nelson,et al.  ARCH MODELS a , 1994 .

[87]  Tim Bollerslev,et al.  Chapter 49 Arch models , 1994 .

[88]  R. Engle,et al.  Forecasting Volatility and Option Prices of the S&P 500 Index , 1994 .

[89]  N. Shephard,et al.  Multivariate stochastic variance models , 1994 .

[90]  K. West,et al.  Asymptotic Inference about Predictive Ability , 1996 .

[91]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[92]  Harry M. Kat,et al.  Volatility Prediction , 1994 .

[93]  Jose A. Lopez.  Evaluating the Predictive Accuracy of Volatility Models , 2001 .

[94]  Stephen L Taylor,et al.  Conditional volatility and the informational efficiency of the PHLX currency options market , 1995 .

[95]  F. Diebold,et al.  Modeling Volatility Dynamics , 1995 .

[96]  David S. Bates.  Testing Option Pricing Models , 1995 .

[97]  Philippe Jorion.  Predicting Volatility in the Foreign Exchange Market , 1995 .

[98]  Jeff Fleming,et al.  Predicting stock market volatility: A new measure , 1995 .

[99]  K. Kroner,et al.  Forecasting volatility in commodity markets , 1995 .

[100]  Dajiang Guo.  The Information Content of Implied Stochastic Volatility from Currency Options , 1996 .

[101]  T. Andersen.  Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility , 1996 .

[102]  Stephen Gray.  Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process , 1996 .

[103]  T. Brailsford,et al.  An evaluation of volatility forecasting techniques , 1996 .

[104]  T. Bollerslev,et al.  MODELING AND PRICING LONG- MEMORY IN STOCK MARKET VOLATILITY , 1996 .

[105]  Dajiang Guo,et al.  The predictive power of implied stochastic variance from currency options , 1996 .

[106]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[107]  N. Meade,et al.  FORECASTING VOLATILITY FOR PORTFOLIO SELECTION , 1996 .

[108]  Robin L. Lumsdaine,et al.  Macroeconomic News and Bond Market Volatility , 1998 .

[109]  P. Franses,et al.  Forecasting stock market volatility using (non‐linear) Garch models , 1996 .

[110]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[111]  F. Diebold,et al.  How Relevant is Volatility Forecasting for Financial Risk Management? , 1997 .

[112]  Kaushik I. Amin,et al.  Inferring Future Volatility from the Information in Implied Volatility in Eurodollar Options: A New Approach , 1997 .

[113]  Stephen L Taylor,et al.  The incremental volatility information in one million foreign exchange quotations , 1997 .

[114]  Jacob Boudoukh,et al.  Investigation of a Class of Volatility Estimators , 1997 .

[115]  M. Pitt,et al.  Likelihood analysis of non-Gaussian measurement time series , 1997 .

[116]  Bent E. Sørensen,et al.  GMM and QML asymptotic standard deviations in stochastic volatility models: Comments on Ruiz (1994) , 1997 .

[117]  Hany A. Shawky,et al.  Stock market volatility and the business cycle , 1997 .

[118]  Anil K. Bera,et al.  ARCH and Bilinearity as Competing Models for Nonlinear Dependence , 1997 .

[119]  L. Harris,et al.  A maximum likelihood approach for non-Gaussian stochastic volatility models , 1998 .

[120]  Franc J. G. M. Klaassen,et al.  Improving GARCH Volatility Forecasts , 1998 .

[121]  Siem Jan Koopman,et al.  Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives , 1999 .

[122]  Jeffrey R. Russell,et al.  Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data , 1998 .

[123]  N. Prabhala,et al.  The relation between implied and realized volatility , 1998 .

[124]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[125]  Forecasting index v olatility : sampling inter v al and non-trading e ff ects , 1998 .

[126]  Stephen E. Satchell,et al.  Implied Volatility Forecasting: A Comparison of Different Procedures , 1998 .

[127]  Jeff Fleming.  The quality of market volatility forecasts implied by S&P 100 index option prices , 1998 .

[128]  M. Subrahmanyam,et al.  WHO BUYS AND WHO SELLS OPTIONS : THE ROLE OF OPTIONS IN AN ECONOMY WITH BACKGROUND RISK , 1998 .

[129]  Per Frennberg,et al.  An Evaluation of Alternative Models for Predicting Stock Volatility: Evidence from a Small Stock Market , 1998 .

[130]  Clive W. J. Granger,et al.  Empirical Modeling in Economics: Specification and Evaluation , 1999 .

[131]  Michael D. McKenzie,et al.  Power transformation and forecasting the magnitude of exchange rate changes , 1999 .

[132]  Michael Y. Hu,et al.  Combining conditional volatility forecasts using neural networks: an application to the EMS exchange rates , 1999 .

[133]  C. Inclan,et al.  Volatility in Emerging Stock Markets , 1997, Journal of Financial and Quantitative Analysis.

[134]  P. Franses,et al.  Additive outliers, GARCH and forecasting volatility , 1999 .

[135]  Stephen Taylor,et al.  Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High Frequency Index Returns , 2000 .

[136]  Clive W. J. Granger,et al.  Occasional Structural Breaks and Long Memory , 1999 .

[137]  T. C. Green,et al.  Market Risk and Model Risk for a Financial Institution Writing Options , 1999 .

[138]  S. Satchell,et al.  Forecasting Volatility in the Financial Markets , 1999 .

[139]  L. Ederington,et al.  The Information Frown in Option Prices , 1999 .

[140]  T. Bollerslev,et al.  Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon , 1999 .

[141]  E. Ghysels,et al.  A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation , 2000 .

[142]  Turan G. Bali.  Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate , 2000, Journal of Financial and Quantitative Analysis.

[143]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[144]  Geoffrey F. Loudon,et al.  An empirical analysis of alternative parametric ARCH models , 2000 .

[145]  Clive W. J. Granger,et al.  STYLIZED FACTS ON THE TEMPORAL AND DISTRIBUTIONAL PROPERTIES OF ABSOLUTE RETURNS: AN UPDATE , 2000 .

[146]  S. Koopman,et al.  Forecasting the Varibility of Stock Index Returns with Stochastic Volatility Models and Implied Volatility , 2000 .

[147]  Allen M. Poteshman.  Forecasting Future Volatility from Option Prices , 2000 .

[148]  YU JUN,et al.  Institutional Knowledge at Singapore Management University Institutional Knowledge at Singapore Management University Forecasting Volatility in the New Zealand Stock Market Forecasting Volatility in the New Zealand Stock Market , 2000 .

[149]  Chris Kirby,et al.  The Economic Value of Volatility Timing , 2000 .

[150]  Chris Kirby,et al.  The Economic Value of Volatility Timing Using 'Realized' Volatility , 2001 .

[151]  F. Diebold,et al.  The Distribution of Realized Exchange Rate Volatility , 2000 .

[152]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[153]  Jun Yu,et al.  Forecasting Volatility:Evidence from the German Stock Market , 2001 .

[154]  K. Singleton.  Estimation of affine asset pricing models using the empirical characteristic function , 2001 .

[155]  Jae Ha Lee,et al.  Intraday Volatility in Interest‐Rate and Foreign‐Exchange Markets: ARCH, Announcement, and Seasonality Effects , 2001 .

[156]  J. Hull.  Fundamentals of Futures and Options Markets , 2001 .

[157]  P. Hansen,et al.  A Forecast Comparison of Volatility Models: Does Anything Beat a Garch(1,1)? , 2004 .

[158]  Mikhail Chernov.  Implied Volatilities as Forecasts of Future Volatility, Time-Varying Risk Premia, and Returns Variability , 2001 .

[159]  Oliver Masutti,et al.  Genetic Programming with Syntactic Restrictions Applied to Financial Volatility Forecasting , 2001 .

[160]  Stephen L Taylor,et al.  Forecasting Currency Volatility: A Comparison of Implied Volatilities and AR(FI)MA Models , 2003 .

[161]  Kai Li.  Long-Memory versus Option-Implied Volatility Predictions , 2002 .

[162]  Jun Yu,et al.  Forecasting volatility in the New Zealand stock market , 2002 .

[163]  M. Martens,et al.  Predicting Financial Volatility: High-Frequency Time-Series Forecasts Vis-a-Vis Implied Volatility , 2002 .

[164]  Gilles O. Zumbach,et al.  Volatility processes and volatility forecast with long memory , 2002 .

[165]  Wei Guan,et al.  Is implied volatility an informationally efficient and effective predictor of future volatility , 2002 .

[166]  Jon Vilasuso.  Forecasting exchange rate volatility , 2002 .

[167]  Christopher J. Neely.  Forecasting foreign exchange volatility: why is implied volatility biased and inefficient? and does it matter? , 2002 .

[168]  Asger Lunde,et al.  Choosing the Best Volatility Models: The Model Confidence Set Approach , 2003 .

[169]  P. Garcia,et al.  The Term Structure of Implied Forward Volatility: Recovery and Informational Content in the Corn Options Market , 2007 .

[170]  Ludger Hentschel,et al.  Errors in Implied Volatility Estimation , 2003, Journal of Financial and Quantitative Analysis.

[171]  Forecasting Volatility in Financial Markets , 2003 .

[172]  W. Davidson,et al.  The predictive power of implied volatility: Evidence from 35 futures markets , 2003 .

[173]  Fabio Trojani,et al.  Estimating and Predicting Multivariate Volatility Thresholds in Global Stock Markets , 2003 .

[174]  Chris Kirby,et al.  The economic value of volatility timing using “realized” volatility ☆ , 2003 .

[175]  C. S. Jones.  The dynamics of stochastic volatility: evidence from underlying and options markets , 2003 .

[176]  P. Hansen,et al.  Consistent Ranking of Volatility Models , 2006 .

[177]  L. Ederington,et al.  Forecasting Volatility , 2004 .

[178]  N. Ṣabrī.  Stock Return Volatility and Market Crisis in Emerging Economies , 2004 .

[179]  T. Bollerslev,et al.  Volatility Puzzles: A Simple Framework for Gauging Return-Volatility Regression , 2004 .

[180]  Volatility processes and volatility forecast with long memory , 2004 .

[181]  Long memory stochastic volatility in option pricing , 2004, cond-mat/0403761.

[182]  Stavros Degiannakis,et al.  Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model , 2004 .

[183]  James W. Taylor.  Volatility forecasting with smooth transition exponential smoothing , 2004 .

[184]  Constantino Tsallis,et al.  Bridging a paradigmatic financial model and nonextensive entropy , 2005 .