In this thesis, the regime dependent mean and abnormal returns are studied to examine whether socially responsible mutual funds have a different performance from traditional mutual funds, since there may be different patterns in the economy. Five economic factors - stock returns, treasury yield spread, credit spread, economic confidence and building permits - are used to identify the market regimes, which are determined as bear and bull markets. The regime-dependent abnormal returns are calculated with a regime-switching Fama & French three factor asset-pricing model. The empirical results show that socially responsible mutual funds have statistically higher mean return than non-socially responsible mutual funds in both bear and bull markets. However, using the measurement of the abnormal returns, socially responsible mutual funds statistically underperform non-socially responsible mutual funds in bull market, while the performance of the two types of funds are not statistically differentiable in the bear market.

This dissertation consists of two essays: one looks at the time-varying relationship between earnings and price momentum, and the other looks at how liquidity and transparency affect the pricing differential between Chinese A-and Hong Kong H-share. The first essay presented in Chapter I investigates the time varying relationship between earnings momentum and price momentum. Using a Markov-switching framework, allowing for variation between high volatility and low volatility states, I find that price momentum is significantly more influenced by earnings momentum in the high volatility state. Further for price momentum I find that loser firms display a higher degree of differential response to earnings momentum across the low and high volatility states than winner firms. Limited financing and investor’s sensitivity to future investment opportunities might explain these two results. A further analysis indeed indicates that loser firms tend to be more financially constrained. Additionally, I investigate the relationship between investor sentiment and the two momentums and find that sentiment only has predictive power for price momentum profits in the low volatility state. Finally, the results are robust regardless of instrument variables. The second essay presented in Chapter 2 examines the impact of liquidity and transparency on the discount attached to H-shares from 2003 to 2011. The higher the relative illiquidity of an H-share, the more the H-share is discounted relative to the underlying A-share price. In addition, more actively traded A-shares and infrequently traded H-shares are associated with a higher H-share discount. Further, increases in the number of analysts following a firm, both in the A-and H- market, are accompanied by a lower H-share discount. Also, a firm with a higher percentage of A-share holdings by mutual funds is associated with a smaller H-share discount. Overall, the results provide support for the notion that liquidity and transparency affect the relative pricing of A- and H-shares.

The purpose of this thesis is to examine the nonlinear relationships between financial (and economic) variables within the field of financial econometrics. The thesis comprises two reviews of literatures, one on nonlinear time series models andthe other one on term structure of interest rates, and four empirical essays on financialapplications using nonlinear modelling techniques. The first empirical essay compares different model specifications of a Markov switching CIR model on the term structure of UK interest rates. We find the least restricted model provides the best in-sample estimation results. Although models with restrictive specifications may provide slightly better out-of-sample forecasts in directional movements of the yields, the economic gains seem to be small. In the second essay, we jointly model the nominal and real term structure of the UK interest rates using a three-factor essentially affine no-arbitrage term structure model. The model-implied expected inflation rates are then used in the subsequent analysis on its nonlinear relationship with the FTSE 100 index return premiums, utilizing a smooth transition vector autoregressive model. We find the model implied expected inflation rates remain below the actual inflation rates after the independence of the Bank of England in 1997, and the recent sharp decline of the expected inflation rates may lend support to the standing ground of the central bank for keeping interest rates low. The nonlinearity test on the relationship between the FTSE 100 index return premiums and the expected inflation rates shows that there exists a nonlinear adjustment on the impact from lagged expected inflation rates to current return premiums. The third essay provides us additional insight into the nature of the aggregate stock market volatilities and its relationship to the expected returns, in a Markov switching model framework, using centuries-long aggregate stock market data from six countries (Australia, Canada, Sweden, Switzerland, UK and US). We find that the Markov switching model assuming both regime dependent mean and volatility with a 3-regime specification is capable to captures the extreme movements of the stock market which are short-lived. The volatility feedback effect that we studied on each of these six countries shows a positive sign on anticipating a high volatility regime of the current trading month. The investigation on the coherence in regimes over time for the six countries shows different results for different pairs of countries. In the last essay, we decompose the term premium of the North American CDX investment grade index into a permanent and a stationary component using a Markov switching unobserved component model. We explain the evolution of the two components in relating them to monetary policy and stock market variables. We establish that the inversion of the CDX index term premium is induced by sudden changes in the unobserved stationary component, which represents the evolution of the fundamentals underpinning the risk neutral probability of default in the economy. We find strong evidence that the unprecedented monetary policy response from the Fed during the crisis period was effective in reducing market uncertainty and helped to steepen the term structure of the CDX index, thereby mitigating systemic risk concerns. The impact of stock market volatility on flattening the term premium was substantially more robust in the crisis period. We also show that equity returns make a significant contribution to the CDX term premium over the entire sample period.

Neste trabalho analisaremos a utilização dos modelos de mudança de regime markoviano para a variância condicional. Estes modelos podem estimar de maneira fácil e inteligente a variância condicional não observada em função da variância anterior e do regime. Isso porque, é razoável ter coeficientes variando no tempo dependendo do regime correspondentes à persistência da variância (variância anterior) e às inovações. A noção de que uma série econômica possa ter alguma variação na sua estrutura é antiga para os economistas. Marcucci (2005) comparou diferentes modelos com e sem mudança de regime em termos de sua capacidade para descrever e predizer a volatilidade do mercado de valores dos EUA. O trabalho de Hamilton (1989) foi uns dos mais importantes para o desenvolvimento de modelos com mudança de regime. Inicialmente mostrou que a série do PIB dos EUA pode ser modelada como um processo que tem duas formas diferentes, uma na qual a economia encontra-se em crescimento e a outra durante a recessão. O câmbio de uma fase para outra da economia pode seguir uma cadeia de Markov de primeira ordem. Utilizamos as séries de índice Bovespa e S&P500 entre janeiro de 2003 e abril de 2012 e ajustamos o modelo GARCH(1,1) com mudança de regime seguindo uma cadeia de Markov de primeira ordem, considerando dois regimes. Foram consideradas as distribuições gaussiana, t de Student e generalizada do erro (GED) para modelar as inovações. A distribuição t de Student com mesmo grau de liberdade para ambos os regimes e graus distintos se mostrou superior à distribuição normal para caracterizar a distribuição dos retornos em relação ao modelo GARCH com mudança de regime. Além disso, verificou-se um ganho no percentual de cobertura dos intervalos de confiança para a distribuição normal, bem como para a distribuição t de Student com mesmo grau de liberdade para ambos os regimes e graus distintos, em relação ao modelo GARCH com mudança de regime quando comparado ao modelo GARCH usual. / In this work we analyze heterocedastic financial data using Markov regime switching models for conditional variance. These models can estimate easily the unobserved conditional variance as function of the previous variance and the regime. It is reasonable to have time-varying coefficients corresponding to the persistence of variance (previous variance) and innovations. The economic series notion may have some variation in their structure is usual for economists. Marcucci (2005) compared different models with and without regime switching in terms of their ability to describe and predict the volatility of the U.S. market. The Hamiltons (1989) work was the most important one in the regime switching models development. Initially showed that the series of U.S. GDP can be modeled as a process that has two different forms one in which the economy is growing and the other during the recession. The change from one phase to another economy can follow a Markov first order chain. We use the Bovespa series index and S&P500 between January 2003 and April 2012 and fitted the GARCH (1,1) models with regime switching following a Markov first order chain, considering two regimes. We considered Gaussian distribution, Student-t and generalized error (GED) to model innovations. The t-Student distribution with the same freedom degree for both regimes and distinct degrees showed higher than normal distribution for characterizing the distribution of returns relative to the GARCH model with regime switching. In addition, there was a gain in the percentage of coverage of the confidence intervals for the normal distribution, as well as the t-Student distribution with the same freedom degree for both regimes and distinct degrees related to GARCH model with regime switching when compared to the usual GARCH model.

本篇論文主要在檢視Fong與See (2001) 所提出的假說，將其應用於道瓊歐洲石油天然氣指數期貨 (DJ EURO STOXX OIL & GAS Index Futures) 上，是否能得到相同的驗證。 　　在是否加入狀態轉換考量的檢定中，本文採用AIC與BIC準則為判斷的基準，而由於雙狀態下BIC準則易有樣本參數過大的懲罰特性，因此其中又以AIC為較佳判斷的準則。研究結果顯示，有考量狀態轉換的Regime Switching GARCH模型配適度會較無考量狀態轉換的GARCH模型為佳。而在納入狀態轉換的考量下，在Regime Switching GARCH模型及其相關衍生模型的比較中，主要是採用RS-GARCH(1,1)-N，RS-GARCH(1,1)-t以及RS-ARCH(1,1)-t模型作為比較。這裡同樣以AIC與BIC準則為判斷的基準，研究結果顯示，在三模型中，是以RS-GARCH(1,1)-t模型具有最佳的配適度。 　　在預測能力的檢定中，本研究是利用MSE、MAE與R2，來判斷何者具有較佳的解釋能力，並且以DM檢定來進一步驗證。研究結果顯示，在有考量狀態轉換的Regime Switching GARCH模型與無考量狀態轉換的GARCH模型中，是以有考量狀態轉換的Regime Switching GARCH模型具有較佳的預測能力；而在RS-GARCH(1,1)-N，RS-GARCH(1,1)-t以及RS-ARCH(1,1)-t三種衍生模型的比較中，又以同時考量t分配以及有狀態轉換的RS-GARCH(1,1)-t模型具有較佳的預測能力。

A general methodology is described in which policyholder behaviour is decoupled from the pricing of a variable annuity based on the cost of hedging it, yielding two sequences of weakly coupled systems of partial differential equations (PDEs): the pricing and utility systems. The utility systems are used to generate policyholder withdrawal behaviour, which is in turn fed into the pricing systems as a means to determine the cost of hedging the contract. This approach allows us to incorporate the effects of utility-based pricing and factors such as taxation. As a case study, we consider the Guaranteed Lifelong Withdrawal and Death Benefits (GLWDB) contract. The pricing and utility systems for the GLWDB are derived under the assumption that the underlying asset follows a Markov regime-switching process. An implicit PDE method is used to solve both systems in tandem. We show that for a large class of utility functions, the two systems preserve homogeneity, allowing us to decrease the dimensionality of solutions. We also show that the associated control for the GLWDB is bang-bang, under which the work required to compute the optimal strategy is significantly reduced. We extend this result to provide the reader with sufficient conditions for a bang-bang control for a general variable annuity with a countable number of events (e.g. discontinuous withdrawals). Homogeneity and bang-bangness yield significant reductions in complexity and allow us to rapidly generate numerical solutions. Results are presented which demonstrate the sensitivity of the hedging expense to various parameters. The costly nature of the death benefit is documented. It is also shown that for a typical contract, the fee required to fund the cost of hedging calculated under the assumption that the policyholder withdraws at the contract rate is an appropriate approximation to the fee calculated assuming optimal consumption.

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

Hidden Markov models have become a popular tool for modeling long-term investment guarantees. Many different variations of hidden Markov models have been proposed over the past decades for modeling indexes such as the S&P 500, and they capture the tail risk inherent in the market to varying degrees. However, goodness-of-fit testing, such as residual-based testing, for hidden Markov models is a relatively undeveloped area of research. This work focuses on hidden Markov model assessment, and develops a stochastic approach to deriving a residual set that is ideal for standard residual tests. This result allows hidden-state models to be tested for goodness-of-fit with the well developed testing strategies for single-state models. This work also focuses on parameter uncertainty for the popular long-term equity hidden Markov models. There is a special focus on underlying states that represent lower returns and higher volatility in the market, as these states can have the largest impact on investment guarantee valuation. A Bayesian approach for the hidden Markov models is applied to address the issue of parameter uncertainty and the impact it can have on investment guarantee models. Also in this thesis, the areas of portfolio optimization and portfolio replication under a hidden Markov model setting are further developed. Different strategies for optimization and portfolio hedging under hidden Markov models are presented and compared using real world data. The impact of parameter uncertainty, particularly with model parameters that are connected with higher market volatility, is once again a focus, and the effects of not taking parameter uncertainty into account when optimizing or hedging in a hidden Markov are demonstrated.

In order to catch up the international trend, ¡§Expensing employee bonus¡¨ has been implemented in Taiwan since year 2008. Hence, all the cost concerning employees¡¦ bonuses have been recorded as expense in the income statement and recognized by fair market value. Since the company decides total amount of employees¡¦ bonuses after authorized by the board and annual general meeting, it can distribute the proportion of cash and stock bonuses. As the result of calculating the stock bonus by stock¡¦s fair value, employees gain much less stocks than before, which lessen the encouragement effect. Therefore, enterprises begin to increase the standard salary of employee or proportion of cash bonus. This study collects the data from the fourth quarter of year 1989 to the third quarter of 2009, and chooses the Taiwan Weighted Stock Index and the stock prices of listed electronic firms in Taiwan. Using the Markov Regime Switching Model as the research method, and add the macroeconomic and financial variables to separate the stock price into two regimes- recession and expansion regime. This research is in the employee¡¦s shoes, and to study what stock incentives strategies the company should adopt under the required expensing of employee stock bonus. The empirical results are summarized as follows: 1.Under the expansion regime, if the company¡¦s stock price was affected by both macroeconomic and financial variables, it will more likely rise further, which leads to the large gap between two regimes. For example: Cyberlink, Acer and Mediatec, which stock price gaps are over ten dollars. 2.According to the two arguments of this study: the company with long duration of expansion regime and is influenced by macroeconomic and financial variables should adopt the strategies based on stock bonus. Therefore, according to the empirical results, the study suggests that Acer is the suitable company to do the strategies.