STOCHASTIC VOLATILITY MODELS WITH PERSISTENT LATENT FACTORS:
THEORY AND ITS APPLICATIONS TO ASSET PRICES

A Dissertation by HYOUNG IL LEE
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
August 2008

122pages

TABLE OF CONTENTS

I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1

II STOCHASTIC VOLATILITY MODELS WITH SMOOTH TRANSITION REGIMES . . . . . . . . . . . . . . . . . . . . . 6
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 6
B. The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
  1. A Stochastic Volatility Model . . . . . . . . . . . . . . 10
  2. Comparisons with the Existing Models . . . . . . . . . 13
C. Conventional Approach Using Density-Based Filter . . . . 17
  1. Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 18
  2. Monte-Carlo Experiments . . . . . . . . . . . . . . . . 23
D. Bayesian Approach Using Gibbs Sampling . . . . . . . . . 23
  1. Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 25
  2. Simulation Study of Gibbs Sampling . . . . . . . . . . 27
E. Empirical Applications . . . . . . . . . . . . . . . . . . . . 29
  1. Data Description . . . . . . . . . . . . . . . . . . . . . 29
  2. Stock Returns and Volatility Factor . . . . . . . . . . 30
  3. Dividend Growth and Volatility Factor . . . . . . . . 36
F. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

III MACROECONOMIC UNCERTAINTY AND ASSET PRICES:
A STOCHASTIC VOLATILITY MODEL . . . . . . . . . . . . 44
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 44
B. Asset Pricing Model . . . . . . . . . . . . . . . . . . . . . 47
C. Identifying Macroeconomic Uncertainty . . . . . . . . . . . 53
  1. A Bayesian Algorithm . . . . . . . . . . . . . . . . . . 53
  2. Data and Gibbs Sampling Results . . . . . . . . . . . 57
D. Equity Premium: Estimation Results . . . . . . . . . . . . 64
E. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

IV NONLINEAR FILTERING WITH A LATENT AUTOREGRESSIVE STATE: A NUMERICAL COMPARISON OF FOUR TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . 68

A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 68
B. Nonlinear Filtering in Theory and Practice . . . . . . . . . 71
  1. Kalman Filter . . . . . . . . . . . . . . . . . . . . . . 74
  2. Extended Kalman Filter . . . . . . . . . . . . . . . . . 75
  3. Unscented Kalman Filter . . . . . . . . . . . . . . . . 77
  4. Density-Based Nonlinear Filter . . . . . . . . . . . . . 78
C. Experimental Design . . . . . . . . . . . . . . . . . . . . . 80
  1. Simulation . . . . . . . . . . . . . . . . . . . . . . . . 80
  2. Estimation . . . . . . . . . . . . . . . . . . . . . . . . 82
  3. Criteria for Comparison . . . . . . . . . . . . . . . . . 83
D. Experimental Results and Conclusions . . . . . . . . . . . 84
V CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
APPENDIX B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
APPENDIX C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
APPENDIX D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
APPENDIX E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111