A Mixture Model for Stock Prices

Building on a Lucas tree asset pricing model, this paper relates the tail risk of asset prices to the component-density of a Normal-Laplace mixture distribution and proposes a new method to measure extreme event behavior in financial markets. The hidden state of the model represents the underlying state of the macroeconomy, which follows a two-state Markov regime switching process. Conditional on the state being “normal” or “extreme”, the log dividend is subject to Normal or Laplace (fat-tailed) shocks respectively. The asset’s price is derived from discounted dividend values, where the stochastic discount factor is determined by the utilility maximization of a representative agent who holds the asset. Finally, the identifiability of the model parameters, Maximum Likelihood estimation techniques and asymptotic properties of the MLE are discussed, and the estimation results are illustrated using S&P index returns. Department of Economics, University of Southern California The author thanks C. Hsiao, G. Ridder, S. Sakata, M. H. Pesaran (Department of Economics, USC), C. Jones (Marshall Scholl of Business, USC), T. W. Lee (Department of Economics, University of California, Riverside) and participants in USC econometrics seminar for comments. All errors are mine.