Alternative models for stock price dynamics

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 r eturns, 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."

The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk

“…9 To the best of our knowledge there does not exist a suitable reference estimate for an average number of jumps in the default intensity of an obligor, so we rely on the co-movement observed between the CDS and equity markets (as evidenced, e.g., in Berndt, Douglas, Duffie, Ferguson, and Schranz (2008), Carr and Wu (2006)) and draw on equity-based estimates in our parameter choice. Chernov, Gallant, Ghysels, and Tauchen (2003), Eraker, Johannes, andPolson (2003), andEraker (2004) estimate jump intensities for equity (index) time series in the range of approx. 1 to 1.7 jumps per year.…”

Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics

“…Much of the option and bond pricing literature estimates jumps by various parametric inference methods such as the Calibration method, (Implied State) Generalized Method of Moments (GMM), (Simulated) Maximum Likelihood Estimation (MLE), Efficient Method of Moment (EMM), or Bayesian approach (see Bakshi et al, 1997;Bates, 2000;Pan 2002;Schaumburg 2001;Chernov et al, 2003;Eraker, Johannes, and Polson, 2003;Aït-Sahalia, 2004;Piazzesi, 2003;and Aït-Sahalia and Jacod, 2005). As is well known, parametric approaches run the risk of incorrect specification for functionals in their chosen models.…”

“…They also conclude that the models can be improved by introducing the stochastic jump intensity that captures the timevarying nature of the financial markets. Some studies allow jump arrival rates to depend on variables such as latent volatility, latent jump size, or market information in an Affine or non-Affine fashion (see Chernov et al, 2003;Piazzesi, 2003;and Dubinsky and Johannes, 2006, for instance). Though incorporating state variables is intuitively attractive, these existing (computationally intensive) parametric procedures become quite complicated to implement due to the discontinuity introduced by jumps and the increased number of parameters.…”

Sequential calibration of options

“…Today, models use a combination of jumps, stochastic volatility and local volatility, see e.g. Bates (1996), Duffie et al (2000), Carr et al (2003b), Chernov et al (2004), and Carr and Wu (2004). The purpose of this paper is to outline a framework in which these advanced models can be adaptively calibrated to data.…”