Alternative Models for Stock Price Dynamics

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(1)2002s-58. Alternative Models for Stock Price Dynamics Mikhail Chernov, A.Ronald Gallant, Eric Ghysels, George Tauchen. Série Scientifique Scientific Series. Montréal Juin 2002. © 2002 Mikhail Chernov, A. Ronald Gallant, Eric Ghysels, George Tauchen. Tous droits réservés. All rights reserved. Reproduction partielle permise avec citation du document source, incluant la notice ©. Short sections may be quoted without explicit permission, if full credit, including © notice, is given to the source..

(2) CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des comp agnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisationsmembres, d’une subvention d’infrastructure du ministère de la Recherche, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère de la Recherche, de la Science et de la Technologie, and grants and research mandates obtained by its research teams. Les organisations-partenaires / The Partner Organizations •École des Hautes Études Commerciales •École Polytechnique de Montréal •Université Concordia •Université de Montréal •Université du Québec à Montréal •Université Laval •Université McGill •Ministère des Finances du Québec •MRST •Alcan inc. •AXA Canada •Banque du Canada •Banque Laurentienne du Canada •Banque Nationale du Canada •Banque Royale du Canada •Bell Canada •Bombardier •Bourse de Montréal •Développement des ressources humaines Canada (DRHC) •Fédération des caisses Desjardins du Québec •Hydro-Québec •Industrie Canada •Pratt & Whitney Canada Inc. •Raymond Chabot Grant Thornton •Ville de Montréal. Les cahiers de la série scientifique (CS) visent à rendre accessibles des résultats de recherche effectuée au CIRANO afin de susciter échanges et commentaires. Ces cahiers sont écrits dans le style des publications scientifiques. Les idées et les opinions émises sont sous l’unique responsabilité des auteurs et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners.. ISSN 1198-8177.

(3) Alternative Models for Stock Price Dynamics * Mikhail Chernov †, A. Ronald Gallant ‡, Eric Ghysels§, George Tauchen ** Résumé / Abstract. Nous examinons un ensemble de diffusions avec volatilité stochastique et de sauts afin de modéliser la distribution des rendements d'actifs boursiers. Puisque certains modèles sont nonemboîtés, nous utilisons la méthode EMM afin d'étudier et de comparer le comportement des différents modèles. This paper evaluates the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions. We use estimation technology that facilitates non-nested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns. We consider two broad families of models: (1) the multifactor loglinear family, and (2) the affine-jump family. Both classes of models have attracted much attention in the derivatives and econometrics literatures. There are various trade-offs in considering such diverse specifications. If pure diffusion SV models are chosen over jump diffusions, it has important implications for hedging strategies. If logaritmic models are chosen over affine ones, it may seriously complicate option pricing. Comparing many different specifications of pure diffusion multi-factor models and jump diffusion models, we find that (1) log linear models have to be extented to 2 factors with feedback in the mean reverting factor, (2) affine models have to have a jumps in returns, stochastic volatility and probably both. Models (1) and (2) are observationally equivalent on the data set in hand. In either (1) or (2) the key is that the volatility can move violently. As we obtain models with comparable empirical fit, one must make a choice based on arguments other than statistical goodness of fit criteria. The considerations include facility to price options, to hedge and parsimony. The affine specification with jumps in volatility might therefore be preferred because of the closed-form derivatives prices. * We would like to thank Torben Andersen, the Editor, two anonymous referees and Nour Medahi, the third referee, for comments that substantially improved the paper. We are also grateful to Luca Benzoni, Paul Glasserman, Micheal Johannes, David Robinson, the conference and seminar participants at the CAP Mathematical Finance Workshop, Columbia University, the Conference on Risk Neutral and Objective Probability Distributions, Fuqua School of Business, Duke University, CIRANO and Vanderbilt University for their comments. All remaining errors are our own. This paper subsumes part of the material presented in the working paper titled. “A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation.” † Columbia Business School ‡ University of North Carolina § University of North Carolina and CIRANO ** Duke University.

(4) Codes JEL : G13; C14, C52, C53 Mots clés : Processus de diffusions, processus Poisson, volatilité stochastique Keywords : Efficient method of moments, Poisson jump processes, stochastic volatility models.

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