The Value of Multivariate Model Sophistication: An Application to Pricing Dow Jones Industrial Average Options

We assess the predictive accuracy of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set 248 multivariate models that differ in their specification of the conditional variance, conditional correlation, and innovation distribution. All models belong to the dynamic conditional correlation class which is particularly suited because it allows to consistently estimate the risk neutral dynamics with a manageable computational effort in relatively large scale problems. It turns out that the most important gain in pricing accuracy comes from increasing the sophistication in the marginal variance processes (i.e. nonlinearity, asymmetry and component structure). Enriching the model with more complex correlation models, and relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a smaller way. Apart from investigating directly the value of model sophistication in terms of dollar losses, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performance.

[1]  Andrew J. Patton.  Volatility Forecast Comparison Using Imperfect Volatility Proxies , 2006 .

[2]  Michael McAleer,et al.  Ranking Multivariate GARCH Models by Problem Dimension * , 2010 .

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

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

[5]  Kris Jacobs,et al.  Which GARCH Model for Option Valuation? , 2004, Manag. Sci..

[6]  G. Schwert.  Why Does Stock Market Volatility Change Over Time? , 1988 .

[7]  Pascal J. Maenhout,et al.  The Price of Correlation Risk: Evidence from Equity Options , 2006 .

[8]  Michael McAleer,et al.  ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL , 2003, Econometric Theory.

[9]  A. Arize,et al.  Asymmetric mean-reversion and contrarian profits: ANST-GARCH approach , 2002 .

[10]  Lars Stentoft,et al.  Convergence of the Least Squares Monte Carlo Approach to American Option Valuation , 2004, Manag. Sci..

[11]  Francis X. Dieobold.  Modeling The persistence Of Conditional Variances: A Comment , 1986 .

[12]  Paul Belleflamme,et al.  Industrial Organization: Markets and Strategies , 2010 .

[13]  Christian M. Hafner,et al.  Econometric analysis of volatile art markets , 2012, Comput. Stat. Data Anal..

[14]  S. Satchell,et al.  GARCH processes — some exact results, some difficulties and a suggested remedy , 2007 .

[15]  Lars Stentoft,et al.  Pricing American options when the underlying asset follows GARCH processes , 2005 .

[16]  Tim Bollerslev,et al.  Glossary to ARCH (GARCH) , 2008 .

[17]  P. Boyle.  Options: A Monte Carlo approach , 1977 .

[18]  Valeri Voev.  On the Economic Evaluation of Volatility Forecasts , 2009 .

[19]  Roxana Halbleib,et al.  Modelling and Forecasting Multivariate Realized Volatility , 2008 .

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

[21]  R. Engle.  Dynamic Conditional Correlation : A Simple Class of Multivariate GARCH Models , 2000 .

[22]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[23]  Halbert White,et al.  Tests of Conditional Predictive Ability , 2003 .

[24]  C. Gouriéroux,et al.  Derivative Pricing With Wishart Multivariate Stochastic Volatility , 2010 .

[25]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[26]  J. Diebolt,et al.  Probabilistic properties of the Béta-ARCH model , 1994 .

[27]  Ludger Hentschel.  All in the family Nesting symmetric and asymmetric GARCH models , 1995 .

[28]  T. Mayer,et al.  The Economics of Clusters: Lessons from the French Experience , 2011 .

[29]  Peter Christoffersen,et al.  Série Scientifique Scientific Series Option Valuation with Conditional Skewness Option Valuation with Conditional Skewness , 2022 .

[30]  R. Engle,et al.  Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns , 2003, SSRN Electronic Journal.

[31]  Tim Bollerslev,et al.  Volatility and Time Series Econometrics , 2010 .

[32]  Peter F. Christoffersen,et al.  Option Valuation with Long-Run and Short-Run Volatility Components , 2008 .

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

[34]  Timo Terasvirta,et al.  Multivariate GARCH Models , 2008 .

[35]  Riccardo Colacito,et al.  Testing and Valuing Dynamic Correlations for Asset Allocation , 2005 .

[36]  T. Bollerslev,et al.  Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model , 1990 .

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

[38]  R. Engle.  Dynamic Conditional Correlation , 2002 .

[39]  J. Zakoian.  Threshold heteroskedastic models , 1994 .

[40]  Peter H. Ritchken,et al.  An empirical comparison of GARCH option pricing models , 2006 .

[41]  S. Laurent,et al.  On the Forecasting Accuracy of Multivariate GARCH Models , 2010 .

[42]  C. Tebaldi,et al.  Option pricing with Correlation Risk , 2007 .

[43]  F. Audrino,et al.  A General Multivariate Threshold GARCH Model With Dynamic Conditional Correlations , 2007 .

[44]  C. Granger,et al.  Modeling volatility persistence of speculative returns: A new approach , 1996 .

[45]  Daniel Bienstock,et al.  Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice , 2002 .

[46]  A. Melé,et al.  Modeling the changing asymmetry of conditional variances , 1996 .

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

[48]  Thresholds, news impact surfaces and dynamic asymmetric multivariate GARCH , 2011 .

[49]  David S. Bates.  Post-'87 crash fears in the S&P 500 futures option market , 2000 .

[50]  Anil K. Bera,et al.  A Class of Nonlinear ARCH Models , 1992 .

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

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

[53]  P. Pestieau,et al.  Social Security and Family Support (Sécurité Sociale et Support de la Famille) , 2014 .

[54]  M. Lubrano.  Smooth Transition Garch Models: a Bayesian Perspective , 1998, Recherches économiques de Louvain.

[55]  Francesco Audrino,et al.  Forecasting correlations during the late-2000s financial crisis: The short-run component, the long-run component, and structural breaks , 2014, Comput. Stat. Data Anal..

[56]  Matthias R. Fengler,et al.  A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew , 2012 .

[57]  Lars Stentoft,et al.  Multivariate Option Pricing with Time Varying Volatility and Correlations , 2010 .

[58]  Peter Christoffersen,et al.  Volatility Components, Affine Restrictions, and Nonnormal Innovations , 2008 .

[59]  Jun Pan.  The Jump-Risk Premia Implicit in Options : Evidence from an Integrated Time-Series Study , 2001 .

[60]  Fabio Fornari,et al.  SIGN- AND VOLATILITY-SWITCHING ARCH MODELS: THEORY AND APPLICATIONS TO INTERNATIONAL STOCK MARKETS , 1997 .

[61]  Jeroen V.K. Rombouts,et al.  Série Scientifique Scientific Series on Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models on Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models , 2022 .

[62]  Robert F. Engle,et al.  Stock Volatility and the Crash of '87: Discussion , 1990 .

[63]  Long Kang,et al.  Volatility and time series econometrics: essays in honor of Robert Engle , 2011 .

[64]  S. Heston,et al.  A Closed-Form GARCH Option Valuation Model , 2000 .

[65]  Jan Korbel,et al.  Modeling Financial Time Series , 2013 .

[66]  Francesco Audrino,et al.  Forecasting correlations during the late-2000 s financial crisis : short-run component , long-run component , and structural breaks , 2011 .

[67]  J. Huriot,et al.  Economics of Cities , 2000 .

[68]  G. González-Rivera,et al.  Smooth-Transition GARCH Models , 1998 .

[69]  Michael McAleer,et al.  GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION , 2008, Econometric Theory.

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

[71]  A. Koulakiotis,et al.  Volatility and error transmission spillover effects: Evidence from three European financial regions , 2009 .

[72]  Jun Pan.  The jump-risk premia implicit in options: evidence from an integrated time-series study $ , 2002 .

[73]  M. Crouhy,et al.  Volatility Clustering, Asymmetry and Hysteresis in Stock Returns: International Evidence , 1998 .

[74]  A. Lo,et al.  When are Contrarian Profits Due to Stock Market Overreaction? , 1989 .

[75]  Bruno Feunou,et al.  Série Scientifique Scientific Series 2009 s-32 Option Valuation with Conditional Heteroskedasticity and Non-Normality , 2009 .

[76]  Peter Christoffersen,et al.  Volatility Components, Affine Restrictions and Non-Normal Innovations , 2008 .

[77]  Lars Stentoft,et al.  American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution , 2007 .

[78]  M. Fleurbaey,et al.  A Theory of Fairness and Social Welfare , 2011 .

[79]  Te-Won Lee,et al.  On the multivariate Laplace distribution , 2006, IEEE Signal Processing Letters.

[80]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

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

[82]  Claudio Tebaldi,et al.  Option pricing when correlations are stochastic: an analytical framework , 2006 .

[83]  C. Genest,et al.  Multivariate Option Pricing Using Dynamic Copula Models , 2005 .

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

[85]  Peter Reinhard Hansen,et al.  The Model Confidence Set , 2010 .

[86]  R. Engle,et al.  A Permanent and Transitory Component Model of Stock Return Volatility , 1993 .

[87]  David S. Bates.  The Crash of ʼ87: Was It Expected? The Evidence from Options Markets , 1991 .

[88]  Dominique Guegan,et al.  Pricing bivariate option under GARCH processes with time-varying copula , 2008 .

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

[90]  M. V. Vyve,et al.  Linear prices for non-convex electricity markets: models and algorithms , 2011 .

[91]  C. Czado,et al.  Multivariate option pricing using copulae , 2012 .