Source: Dissertation Abstracts International, Volume: 65-11, Section: A, page: 4291.

Director: Peter C. B. Phillips.

My dissertation is centered on the use of information time or stochastic time changes in modeling stock returns. In this model, stock returns are modeled as a Brownian motion in information time instead of calendar time.

Part 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 this chapter is to investigate whether the information time can be identified as an observable process. I consider three possible variables: cumulative trading volume, cumulative number of transactions and cumulative realized volatility. I address an identification problem in a previous study and modify their GMM test to study these three variables. I also conduct conditional and unconditional nonparametric density estimation and standard normality tests to test the normality assumption under information time. The uncorrelated increment property implied by the Brownian motion assumption is also examined.

Part 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 standard CAPM betas adjusted by trading frequencies. This chapter 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.

Part III. Option Pricing in Iinformation Time and its Estimation considers the implication of the information time stock return model in option pricing. I study an option pricing model assuming that the stock return is a Brownian Motion under information time and the information time increment has a log-normal distribution. 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. Numerical simulation and calibration are used to compare the estimation results with the Black-Scholes benchmark model in an attempt to confirm the volatility smile effect.