It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as an auxiliary model a time-varying generalization of the HAR model for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights the robustness of the methodology adopted in tracking the dynamics of the parameters.

[1]  Peter F. Christoffersen,et al.  Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach , 2012 .

[2]  Rodney W. Strachan,et al.  On the evolution of the monetary policy transmission mechanism , 2009 .

[3]  Rodney W. Strachan,et al.  On the evolution of monetary policy , 2007 .

[4]  Paolo Santucci de Magistris,et al.  Estimation of Long Memory in Integrated Variance , 2011 .

[5]  Michael McAleer,et al.  Forecasting Realized Volatility with Linear and Nonlinear Univariate Models , 2011 .

[6]  S. Laurent,et al.  Modelling Daily Value-at-Risk Using Realized Volatility and Arch Type Models , 2001 .

[7]  Christian Gourieroux,et al.  Simulation-based econometric methods , 1996 .

[8]  R. Dahlhaus,et al.  A recursive online algorithm for the estimation of time-varying ARCH parameters , 2007, 0708.4081.

[9]  S. Mittnik,et al.  The Volatility of Realized Volatility , 2005 .

[10]  Sveriges Riksbank.  Forecast Combination and Model Averaging using Predictive Measures , 2005 .

[11]  T. Sargent,et al.  Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S. , 2005 .

[12]  C. Liu,et al.  Are There Structural Breaks in Realized Volatility , 2008 .

[13]  Peter Carr,et al.  Variance Risk Premiums , 2009 .

[14]  N. Meddahi,et al.  A theoretical comparison between integrated and realized volatility , 2002 .

[15]  J. Geweke,et al.  Contemporary Bayesian Econometrics and Statistics , 2005 .

[16]  Mark Podolskij,et al.  Asymptotic theory for Brownian semi-stationary processes with application to turbulence , 2012, 1211.4221.

[17]  Kris Jacobs,et al.  Nonlinear Kalman Filtering in Affine Term Structure Models , 2013, Manag. Sci..

[18]  E. Ghysels,et al.  Série Scientifique Scientific Series Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies , 2022 .

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

[20]  R. Engle,et al.  And Now, The Rest of the News: Volatility and Firm Specific News Arrival , 2012 .

[21]  Jana Eklund,et al.  Forecast Combination and Model Averaging Using Predictive Measures , 2005 .

[22]  P. Carr,et al.  Stochastic Skew in Currency Options , 2004 .

[23]  Lan Zhang,et al.  A Tale of Two Time Scales , 2003 .

[24]  Thomas H. McCurdy,et al.  Série Scientifique Scientific Series Nonlinear Features of Realized Fx Volatility Nonlinear Features of Realized Fx Volatility , 2022 .

[25]  Fulvio Corsi,et al.  A Simple Approximate Long-Memory Model of Realized Volatility , 2008 .

[26]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[27]  F. Diebold,et al.  Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility , 2005, The Review of Economics and Statistics.

[28]  Luca Benzoni,et al.  An Empirical Investigation of Continuous-Time Equity Return Models , 2001 .

[29]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

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

[31]  S. Lahiri,et al.  A Nonstandard Empirical Likelihood for Time Series , 2013, 1401.1026.

[32]  Francesco Audrino,et al.  Lassoing the Har Model: A Model Selection Perspective on Realized Volatility Dynamics , 2013 .

[33]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[34]  Remco C. J. Zwinkels,et al.  Modelling structural changes in the volatility process , 2011 .

[35]  Drew D. Creal,et al.  Generalized autoregressive score models with applications ∗ , 2010 .

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

[37]  G. Serna,et al.  Why do we smile? On the determinants of the implied volatility function , 1999 .

[38]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

[39]  Marco Riani,et al.  The Selection of ARIMA Models With or Without Regressors , 2012 .

[40]  Dick van Dijk,et al.  Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic announcements , 2009 .

[41]  M. Medeiros,et al.  A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries , 2008 .

[42]  Alain Guay,et al.  Indirect inference and calibration of dynamic stochastic general equilibrium models , 2007 .

[43]  Anders Rahbek,et al.  Multivariate Variance Targeting in the BEKK-GARCH Model , 2012 .

[44]  Francesco Ravazzolo,et al.  Real-Time Inflation Forecasting in a Changing World , 2009 .

[45]  J. Jacod,et al.  A Test for the Rank of the Volatility Process: The Random Perturbation Approach , 2012, 1212.5490.

[46]  Bjørn Eraker.  Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices , 2004 .

[47]  T. Teräsvirta,et al.  Global Hemispheric Temperature Trends and Co–Shifting: A Shifting Mean Vector Autoregressive Analysis , 2012 .

[48]  E. Ghysels,et al.  Why Do Absolute Returns Predict Volatility So Well , 2006 .

[49]  Mikko S. Pakkanen.  Limit theorems for power variations of ambit fields driven by white noise , 2013, 1301.2107.

[50]  R. Dahlhaus,et al.  Statistical inference for time-varying ARCH processes , 2006, math/0607799.

[51]  P. Phillips,et al.  Refined Inference on Long Memory in Realized Volatility , 2006 .

[52]  Predicting Returns and Rent Growth in the Housing Market Using the Rent-to-Price Ratio: Evidence from the OECD Countries , 2015 .

[53]  A. Gallant,et al.  Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance , 1999, Review of Economics and Statistics.

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

[55]  Eric Zivot,et al.  Long Memory Versus Structural Breaks in Modeling and Forecasting Realized Volatility , 2008 .

[56]  Nicholas G. Polson,et al.  The Impact of Jumps in Volatility and Returns , 2000 .

[57]  Roberto Renò,et al.  Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling , 2010 .

[58]  Arnaud Dufays.  Modeling structural changes in volatility , 2013 .

[59]  Silvano Bordignon,et al.  Long Memory and Nonlinearities in Realized Volatility: A Markov Switching Approach , 2010, Comput. Stat. Data Anal..

[60]  Luc Bauwens,et al.  A Component GARCH Model With Time Varying Weights , 2006 .

[61]  N. Meddahi,et al.  ARMA representation of integrated and realized variances , 2003 .

[62]  T. Bollerslev,et al.  A Reduced Form Framework for Modeling Volatility of Speculative Prices Based on Realized Variation Measures , 2008 .

[63]  T. Bollerslev,et al.  Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility , 2001 .

[64]  Adrian E. Raftery,et al.  Prediction under Model Uncertainty Via Dynamic Model Averaging : Application to a Cold Rolling Mill 1 , 2008 .

[65]  Michael McAleer,et al.  Modelling and Forecasting Noisy Realized Volatility , 2009, Comput. Stat. Data Anal..

[66]  R. Engle,et al.  The Spline-Garch Model for Low Frequency Volatility and its Global Macroeconomic Causes , 2006 .

[67]  N. Shephard,et al.  Estimating quadratic variation using realized variance , 2002 .

[68]  T. Sargent,et al.  Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S. , 2003 .

[69]  Almut E. D. Veraart,et al.  Risk premia in energy markets , 2013 .

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

[71]  G. Koop,et al.  Forecasting In ation Using Dynamic Model Averaging , 2009 .

[72]  R. Kohn,et al.  Efficient Bayesian Inference for Dynamic Mixture Models , 2000 .

[73]  Giorgio E. Primiceri.  Time Varying Structural Vector Autoregressions and Monetary Policy , 2002 .

[74]  A. Gallant,et al.  Alternative models for stock price dynamics , 2003 .

[75]  M. Medeiros,et al.  Forecasting Realized Volatility with Linear and Nonlinear Models , 2009 .

[76]  Gustavo A. Suarez,et al.  The Evolution of a Financial Crisis: Collapse of the Asset-Backed Commercial Paper Market: Collapse of the ABCP Market , 2013 .

[77]  Gustavo A. Suarez,et al.  The Evolution of a Financial Crisis: Collapse of the Asset-Backed Commercial Paper Market , 2012 .

[78]  Indirect Inference, Nuisance Parameter, and Threshold Moving Average Models , 2003 .

[79]  N. Shephard,et al.  Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation , 2005 .

[80]  Almut E. D. Veraart,et al.  Stochastic Volatility of Volatility and Variance Risk Premia , 2011 .