Financial Economics
Applied Econometrics

Finance Theory
Empirical Finance
Applied Econometrics
Industrial Organization

October 1999 (Oral) Econometrics, Finance
May 1998 (Written) Macroeconomics and Microeconomics (with distinction)

Estimation of the Information Time Stock Return Model

Professor Peter C.B. Phillips
Professor Robert Shiller
Professor Stephano Athanasoulis

May 2004

Ph.D., Economics, Yale University, May 2004, Expected
M.Phil, Economics, Yale University, December 2000
M.A., Economics, University of Iowa, May 1997
B.A. Investment Economics and Management, People’s University of China, July 1993

Yale University
     Summer Fellowship, 2002
     Dissertation Fellowship, 2001
     Cowles Foundation Prize, 1998
     Yale University Fellowship, 1997-2000
University of Iowa
     Tuition Fellowship, 1996
People’s University of China
     Guang Hua Fellowship, 1993

Doctoral Courses
     Econometrics I, Teaching assistant for Professor J. Park, Fall 1998
     Econometrics II, Teaching assistant for Professor Y.S. Whang, Spring 1999
Undergraduate Courses
     Financial Theory, Teaching assistant for Professor John Geanakoplos, Fall 1999 and 2000
Financial Market, Head teaching assistant for Professor Robert Shiller, Spring 2001

Research Assistant for Professor Oliver Linton, Yale University, 1999
Designed and implemented simulation study of nonparametric censored regression

Estimation of Information Time in Stock Returns, 2002.
Estimation of Intrinsic Time CAPM, 2003.
Information Time Option Pricing Model and its Estimation, in progress.
Nonparametric Estimation of Highway Construction Auction, 1999.

My dissertation is centered on the use of information time or stochastic time changes in modeling stock returns. According to this model, stock returns are modeled as a Brownian motion in information time instead of calendar time. Considering models of stock returns in information time is of interest for several reasons. First, from a market microstructure perspective, price movements arise with the arrival of information and the pace of the trading is related to the speed of the information flow. Stochastic time changes can be used to represent information flow in the market. Second, stochastic time change models are supported by no arbitrage pricing theory, since under no arbitrage pricing theory asset returns are semimartingales and can be written as time changed Brownian motion. Third, in the stochastic time change model, stock returns are in effect modeled as a continuous mixture of normal distributions. This captures the well-documented "fat tail" feature of financial return series, and is a better description of reality than the normality assumption that forms the basis of many financial models. This dissertation concerns the empirical testing and estimation of the stochastic time change stock return model and its applications in asset pricing and option pricing.

Chapter I: Estimation of Information Time in Stock Returns addresses the problem of the identification of information time in the stochastic time change model. The main purpose of the paper is to investigate whether the information time can be identified as an observable process. In this paper I consider three possible variables: cumulative trading volume, cumulative number of transactions and cumulative realized volatility. I correct a mistake in Ane and Geman (2000), which changes their GMM results and their conclusion that the cumulative number of transactions is the unique information time. Using the modified method, I conduct a GMM test to compare the moments of estimated information time with those of the three variables considered. I also conduct conditional and unconditional nonparametric density estimation and standard normality tests to test the normality assumption under information time. Previous works have focused on testing normality of stock returns in information time. In this paper I also test the uncorrelated increment property implied by the Brownian motion assumption. The data considered in the paper include 10 stocks at 15 minute, 2 hour and daily frequencies. While the modified GMM tests reject all variables as the information time, the nonparametric tests, normality tests and uncorrelated increment tests suggest that all of the three variables help to restore normality in information time at 2 hour and daily frequencies.

Chapter II: Estimation of the Intrinsic Time CAPM tests the Intrinsic Time CAPM developed by Derman (2002). Based on the assumption that stocks with the same risk measured in information time receive the same return in information time, the information time CAPM suggests that calendar time excess stock returns should be linear to the stocks "temperature", which is the standard CAPM beta adjusted by trading frequencies. This paper tests the information time CAPM using daily individual stock returns. I use trading volume to approximate the trading frequency in the model. Tests analogous to those in the context of traditional CAPM testing are conducted and the results confirm the intrinsic time CAPM.

Chapter III: Option Pricing in Information Time and its Estimation (in progress) considers the implication of the stochastic time change model in option pricing. I derive an option pricing model assuming that the stock return is a Brownian Motion under information time and the information time increment has a known density. The result of the option pricing model is a sum of a standard Black-Scholes model solution weighted by the density of the information time increment. I use the realized volatility as the information time here and estimate its density both nonparametrically and under parametric assumptions. Then I compare the estimation results with the Black-Scholes benchmark model and attempt to confirm empirical findings such as the volatility smile effect.