Essay on semiparametric efficient adaptive estimation and empirical applications in finance

Abstract

This thesis is composed of three chapters. The first two chapters construct semiparametric efficient adaptive estimators: one is for asymmetric GARCH-in-mean models; the other is for single-index models. However, estimation methodologies are different. The first chapter is related to maximum likelihood; and the second chapter minimizes mean square errors.

In Chapter 1, without imposing additional restrictions on the distribution of disturbances other than some regular assumptions, I show that parameters appearing in the conditional standard deviation function can be adaptively estimated. The kernel smoothing parameter is calculated by minimizing mean squared errors between estimated score functions and target score functions. Significant asymmetric effects are identified with daily value-weighted stock index returns on NYSE/AMEX. Monte Carlo simulation results support my theory.

In Chapter 2, conditional expectation function is estimated by k − nearest neighbor method. I show that semiparametric efficient estimate of parameters of single-index models and k can be calculated simultaneously. Monte Carlo experiments results show that the semiparametric estimator performs equally well across different data generating mechanisms even for small samples.

In Chapter 3, catastrophe-linked securities whose payoffs are tied to the occurrence of natural disasters allow insurers to better diversify their risks through capital markets while at the same time offering an attractive new asset class to investors. Up to now, this class of assets is still under development, and few empirical applications have been carefully analyzed. This chapter examines one of the catastrophe-linked instruments—PCS options traded at the CBOT. Two main issues are explored: (a) Theoretical prices are derived by assuming complete and arbitrage free market. Comparing market prices to theoretical prices, three puzzles are observed. (b) Comparing PCS call spread option contracts to traditional excess-of-loss catastrophe reinsurance contracts; I find that pricing patterns of these two types of assets are similar. Other factors, not limited capacity, are capable of explaining these special pricing patterns.