Conditional Jump Dynamics in Stock Market Returns

This article develops a new conditional jump model to study jump dynamics in stock market returns. We propose a simple filter to infer ex post the distribution of jumps. This permits construction of the shock affecting the time t conditional jump intensity and is the main input into an autoregressive conditional jump intensity model. The model allows the conditional jump intensity to be time-varying and follows an approximate autoregressive moving average (ARMA) form. The time series characteristics of 72 years of daily stock returns are analyzed using the jump model coupled with a generalized autoregressive conditional heteroscedasticity (GARCH) specification of volatility. We find significant time variation in the conditional jump intensity and evidence of time variation in the jump size distribution. The conditional jump dynamics contribute to good in-sample and out-of-sample fits to stock market volatility and capture the rally often observed in equity markets following a significant downturn.

[1]  Alan L. Tucker,et al.  The Probability Distribution of Foreign Exchange Price Changes: Tests of Candidate Processes , 1988 .

[2]  Philippe Jorion.  On Jump Processes in the Foreign Exchange and Stock Markets , 1988 .

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

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

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

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

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

[8]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[9]  Franz C. Palm,et al.  The message in weekly exchange rates in the European Monetary System: mean reversion , 1993 .

[10]  B. LeBaron,et al.  Simple Technical Trading Rules and the Stochastic Properties of Stock Returns , 1992 .

[11]  W. Torous,et al.  A Simplified Jump Process for Common Stock Returns , 1983, Journal of Financial and Quantitative Analysis.

[12]  Jeremy Berkowitz.  Evaluating the Forecasts of Risk Models , 1999 .

[13]  David Hsieh.  Testing for Nonlinear Dependence in Daily Foreign Exchange Rates , 1989 .

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

[15]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[16]  P. Fortune.  Are Stock Returns Different over Weekends? A Jump Diffusion Analysis of the "Weekend Effect" , 1999 .

[17]  G. Geoffrey Booth,et al.  Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements , 1988 .

[18]  Stephen Gray,et al.  Target Zones and Exchange Rates: An Empirical Investigation , 1996 .

[19]  James D. Hamilton,et al.  Autoregressive conditional heteroskedasticity and changes in regime , 1994 .

[20]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[21]  Christian C. P. Wolff,et al.  Stochastic trends and jumps in EMS exchange rates , 1994 .

[22]  Jeffrey R. Russell,et al.  Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data , 1998 .

[23]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[24]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options , 1998 .

[25]  Franz C. Palm,et al.  Simple diagnostic procedures for modeling financial time series , 1997 .

[26]  A. Gallant,et al.  Estimation of Stochastic Volatility Models with Diagnostics , 1995 .

[27]  Bruce E. Hansen,et al.  Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis , 1996 .

[28]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

[29]  R. Craine,et al.  Estimation of a Stochastic-Volatility Jump-Diffusion Model , 2000 .

[30]  James D. Hamilton,et al.  A Model for the Federal Funds Rate Target , 1999 .

[31]  R. Sundaram,et al.  Taming the Skew: Higher-Order Moments in Modeling Asset Price Processes in Finance , 1997 .

[32]  Christopher J. Neely.  Target zones and conditional volatility: the role of realignments , 1999 .

[33]  K. West,et al.  The Predictive Ability of Several Models of Exchange Rate Volatility , 1994 .

[34]  A. Gallant,et al.  A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation , 1999 .

[35]  R. Sundaram,et al.  Of Smiles and Smirks: A Term Structure Perspective , 1998, Journal of Financial and Quantitative Analysis.