Measuring The Risk Aversion Based On Semi-parametric ARCH-M Model

In this thesis, we focus on the study of measuring the risk aversion, namely how to find a more practicable method to estimate the aggregate risk aversion of the stock market, which makes great points in the realistic word. To begin with, in the exordium, we introduce the concepts of individual risk aversion and the aggregate risk aversion and the inner relations between the two concepts. In chapter 2, we illustrate the constant-parametric ARCH-M model and the time-varying parameter ARCH-M model, both of which were used to measure the risk aversion. We also point out some drawbacks about the above two models.In the subsequent chapter 3, we propose a semi-parametric ARCH-M model to measure the risk aversion. To avoid restricting the variety of the risk aversion to a certain process, we consider the risk aversion as the unknown function of some economical variables. Two step estimates are suggested to estimate the nonparametric function in the price of volatility and parameters in volatility, in which the first step estimate is based on local linear smoothing and the second step estimate on the maximum likelihood method. Asymptotic properties of the estimators are discussed. We also give the ways to choose the window widths and construct the confidence intervals.In chapter 4, we do some simulations about the proposed model and find that our method performs well. Then we apply the proposed model to analyze Shanghai stock market and Hongkong stock market to measure risk aversion and explain the estimated results. We also make a comparison between two markets based the estimated results.In chapter 5, we extend the proposed semi-parametric ARCH-M model by allowing the density of the errors to belong a more broad set besides the Normal distributions. Some extra conditions and the asymptotic results are given in the article. We also discuss the potential problems and where need to be improved.