An Empirical Investigation of Continuous-Time Equity Return Models

This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices. MUCH ASSET AND DERIVATIVE PRICING THEORY is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. A possible explanation could be that analytic formulas for pricing and hedging are available for only a limited set of continuous-time representations for asset returns and risk-free discount rates. It has become increasingly evident that such “classical” models fail to account adequately for the underlying dynamic evolution of asset prices and interest rates. Not surprisingly, the inadequacy of these specifications also shows up in bond and derivatives pricing, where the standard representations falter systematically. For example, the Black– Scholes pricing formula, although widely used by practitioners, is well known to produce pronounced and persistent biases in the pricing of options. Devi* Torben G. Andersen is at the Kellogg Graduate School of Management, Northwestern University and the NBER. Luca Benzoni is at the Carlson School of Management, University of Minnesota. Jesper Lund is at the Nykredit Bank, Denmark. We are grateful to Alexandre Baptista; David Bates; Menachem Brenner; Sanjiv Das; Bjørn Eraker; Ron Gallant; Rick Green; Jack Kareken; Marti Subrahmanyam; George Tauchen; Harold Zhang; an anonymous referee; and seminar participants at Atlanta FED, University of Arizona, Boston College, Brown University, University of Chicago, CIRANO, Harvard University, Iowa State University, University of Maryland, Michigan State University, University of Michigan, University of Minnesota, the Newton Institute at Cambridge ~UK!, University of North Carolina, Northwestern University ~Finance and Statistics Departments!, NYU, the Center for NonLinear Methods in Economics at Svinkløv, Denmark, the Econometric Society Winter Meeting 1999, and the Option Pricing Conference in Montreal, March 2000, for helpful comments and suggestions. Also, we would like to thank the MSI center at the University of Minnesota for providing computing resources. Of course, all errors remain our sole responsibility. Previous versions of this paper were circulated under the title “Estimating Jump-Diffusions for Equity Returns.” THE JOURNAL OF FINANCE • VOL. LVII, NO. 3 • JUNE 2002