Statistical analysis of dynamic risk neutral density, dynamic cross-sectional distribution and portfolio optimization
Creators: name: Yan, Xi
Publisher: name: No Publisher Supplied
Year: 2019

description: This dissertation focuses on developing new statistical methods for analyzing and modeling financial time series. The first part of this dissertation discusses modeling of functional and distributional time series, assuming the series are driven by a finite dimensional underlying feature process. Functional time series are commonly observed in finance and difficult to model mainly due to high dimensionality. We instead focus on a low-dimensional latent feature process and connect it with the original functional time series through generalized state-space models. A state-space model assumes that observations are driven by an underlying dynamic state process and is widely used in many fields. We propose a generalized two-stage Sequential Monte Carlo (SMC) joint estimation framework to model functional time series driven by its feature process through state-space models and perform on-line estimations and predictions. In order to improve computation efficiency, we also implement parallel computing and re-design computation algorithms to integrate with non-linear optimization and SMC calculations.Two financial applications are presented to demonstrate the robustness and efficiency of our proposed framework. The first application aims to extract and model the daily implied risk neutral densities from observed call option prices. We view the underlying risk neutral density as a functional time series driven by its feature process and model it with a parametric mixed log-normal distribution through a state-space model. We conduct both simulation and empirical studies and compare prediction performance of our models with that of random walk models. Empirically, the proposed models improves prediction performance significantly. The second financial application studies daily cross-sectional distribution of 1000 largest market capitalization stock returns from year 1991 to year 2002. Similarly we view cross-sectional distribution as a functional time series driven by its feature process and model it with a four-parameter generalized skewed $t$-distribution. Using proposed two-stage SMC joint estimation framework, we build models separately for different market conditions, including the dot-com crisis. In both bearish and bullish markets, prediction performances of our models gain substantial improvement comparing with random walk models.The second part of dissertation presents a new portfolio optimization strategy for minimum variance portfolios with constraints on short-sale and transaction costs. Unlike traditional mean-variance theory, our method minimizes only the portfolio risk and uses analysts' consensus ratings to pre-screen stocks. An empirical study of S&amp;P 500 stocks from year 1990 to year 2009 is conducted to demonstrate effectiveness. We show that portfolios constructed and optimized using our strategy deliver considerable improvement of performance in terms of Sharpe ratio comparing with benchmark portfolios and portfolios in past literatures.