One of the most famous problem of finding optimal weight to maximize an agent's expected terminal utility in finance literature is Merton's optimal portfolio problem. Classic solution to this problem is given by stochastic Hamilton-Jacobi-Bellman Equation where we briefly review it in chapter 1. Similar idea has found many applications in other finance literatures and we will focus on its application to the high-frequency trading using limit orders in this thesis. In [1], major analysis using the constant volatility arithmetic Brownian motion stock price model with exponential utility function is described. We re-analyze the solution of HJB equation in this case using different asymptotic expansion. And then, we extend the model to the regime-switching volatility model to capture the status of market more accurately.

One of the most famous problem of finding optimal weight to maximize an agent's expected terminal utility in finance literature is Merton's optimal portfolio problem. Classic solution to this problem is given by stochastic Hamilton-Jacobi-Bellman Equation where we briefly review it in chapter 1. Similar idea has found many applications in other finance literatures and we will focus on its application to the high-frequency trading using limit orders in this thesis. In [1], major analysis using the constant volatility arithmetic Brownian motion stock price model with exponential utility function is described. We re-analyze the solution of HJB equation in this case using different asymptotic expansion. And then, we extend the model to the regime-switching volatility model to capture the status of market more accurately.

Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples. We develop a number of techniques for pricing American options by solving the system of partial differential equations in a general \mathcal{K}-state regime-switching model. The linear complementarity problem is replaced by either the penalty or the direct control formulations. With an implicit discretization, we compare a number of iterative procedures (full policy iteration, fixed point-policy iteration, and local American iteration) for the associated nonlinear algebraic equations. Specifically, a linear system appears in the full policy iteration which can be solved directly or iteratively. Numerical tests indicate that the fixed point-policy iteration and the full-policy iteration (using a simple iteration for the linear system), both coupled with a penalty formulation, results in an efficient method. In addition, using a direct solution method to solve the linear system appearing in the full policy iteration is usually computationally very expensive depending on the jump parameters. A Fourier transform is applied to the system of partial differential equations for pricing American options to obtain a linear system of ordinary differential equations that can be solved explicitly at each timestep. We develop the Fourier space timestepping algorithm which incorporates a timestepping scheme in the frequency domain, in which the frequency domain prices are obtained by applying the discrete Fourier transform to the spatial domain. Close to quadratic convergence in time and space is observed for all regimes when using a second order Crank-Nicolson scheme for approximation of the explicit solution of the ordinary differential equation.

Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples. We develop a number of techniques for pricing American options by solving the system of partial differential equations in a general \mathcal{K}-state regime-switching model. The linear complementarity problem is replaced by either the penalty or the direct control formulations. With an implicit discretization, we compare a number of iterative procedures (full policy iteration, fixed point-policy iteration, and local American iteration) for the associated nonlinear algebraic equations. Specifically, a linear system appears in the full policy iteration which can be solved directly or iteratively. Numerical tests indicate that the fixed point-policy iteration and the full-policy iteration (using a simple iteration for the linear system), both coupled with a penalty formulation, results in an efficient method. In addition, using a direct solution method to solve the linear system appearing in the full policy iteration is usually computationally very expensive depending on the jump parameters. A Fourier transform is applied to the system of partial differential equations for pricing American options to obtain a linear system of ordinary differential equations that can be solved explicitly at each timestep. We develop the Fourier space timestepping algorithm which incorporates a timestepping scheme in the frequency domain, in which the frequency domain prices are obtained by applying the discrete Fourier transform to the spatial domain. Close to quadratic convergence in time and space is observed for all regimes when using a second order Crank-Nicolson scheme for approximation of the explicit solution of the ordinary differential equation.

For the empirical macroeconomist, accounting for nonlinearities in data series by using regime switching techniques has a long history. Over the past 25 years, there have been tremendous advances in both the estimation of regime switching and the incorporation of regime switching into macroeconomic models. In this dissertation, I apply techniques from this literature to study two topics that are of particular relevance to the conduct of monetary policy: asset bubbles and the Federal Reserve’s policy reaction function. My first chapter utilizes a recently developed Markov-Switching model in order to test for asset bubbles in simulated data. I find that this flexible model is able to detect asset bubbles in about 75% of simulations. In my second and third chapters, I focus on the Federal Reserve’s policy reaction function. My second chapter advances the literature in two important directions. First, it uses meeting- based timing to more properly account for the target Federal Funds rate; second, it allows for the inclusion of up to 14 economic variables. I find that the long-run inflation response coefficient is larger than had been found in previous studies, and that increasing the number of economic variables that can enter the model improves both in-sample fit and out-of-sample forecasting ability. In my third chapter, I introduce a new econometric model that allows for Markov-Switching, but can also remove variables from the model, or enforce a restriction that there is no regime switching. My findings indicate that the majority of coefficients in the Federal Reserve’s policy reaction function have not changed over time.

In this paper, focus is on the global vector autoregressive (GVAR) model. Its attractiveness stems from an ability to incorporate global interdependencies when modeling local economies. The model is based on a collection of local models, which in general are estimated as regular VAR models. This paper examines alternative specifications of the local models by estimating them as regime-switching VAR models, where transition probabilities between different states are studied using both constant and time-varying settings. The results show that regime-switching models are appealing as they yield inferences about the states of the economy, but these inferences are not guaranteed to be reasonable from an economic point of view. Furthermore, the global solution of the model is in some cases non-stationary when local models are regime-switching. The conclusion is that the regime-switching alternatives, while theoretically reasonable, are sensitive to the exact specification used. At the same time, the issue of specifying the regime-switching models in such a way that they perform adequately speaks in favor of the simpler, yet functional, basic GVAR model.

In retrospect, telecommunication technology and services have seen incessant renovation and development. The wave of liberalization is also the inexorable trend in the global telecommunications industry, the telecommunications industry in Taiwan can not be excluded itself from the trend. The telecommunications industry in Taiwan has been opened by degrees and sought to establish a fair competitive environment. In the meantime, there are several important changes no matter in facets of regulatory regimes, industrial structure, technology, or market demand, etc. The environment of telecommunications industry became more volatile than the monopoly one's. We extend the opinion of Noam (2006) who observed the long-term upturn and downturn in the American telecommunications industry and concluded that that volatility and cyclicality will be an inherent part of the telecommunication sector in the future. First, in our thesis we explore the cyclical behavior of Taiwan telecommunications industry. As the turning point of the telecommunications industry may be obscure, we adopt a Markov Regime-Switching model with two regimes representing contraction and expansion. This nonlinear, two states, regime-switching model shows that Taiwan telecommunications industry has suffered from the cyclic fluctuation since the liberalization had been followed out. We focus on the mobile phone industry thereafter in this study. Since three telecommunication-related laws passed in 1996, the mobile phone industry is the first industry implemented the liberalization policy. In the process of the mobile phone industry's evolution, the carriers in this industry all experience the rapid growth in the mobile phone penetration rate and the fierce competition. Hence, to identify the main explanatory factors of the mobile phone industry fluctuation and cycles we introduce an 11-variable vector autoregressive (VAR) model. The empirical results confirm that the mobile phone industry' output can be influenced by five factors mainly including the macroeconomic status, demand, network effect, relative equipment import price, and output price, and furthermore, the impetus of the liberalization policy and the progress of the technology also play an important role beyond the five main factors in terms of the separate carriers' analysis.

Asset allocation and portfolio decisions are at the heart of money management and draw great attention from both academics and practitioners. In addition, the segmentation of fund investors (i.e., the clientele effect) in the money management industry is well known but poorly understood. The objective of this dissertation is to study the implications of regime switching behaviors in asset returns on asset allocation and to analyze the clientele effect as well as the impact of portfolio management contracts on fund investment. Chapter 2 presents an innovative regime switching multi-factor model accounting for the different regime switching behaviors in the systematic and idiosyncratic components of asset returns. A Gibbs sampling approach for estimation is proposed to deal with the computational challenges that arise from a large number of assets and multiple Markov chains. In the empirical analysis, the model is applied to study sector exchange-traded funds (ETFs). The idiosyncratic volatilities of different sector ETFs exhibit a strong degree of covariation and state-dependent patterns, which are different from the dynamics of their systematic component. In a dynamic asset allocation problem, the certainty equivalent return is computed and compared across various models for an investor with constant relative risk aversion. The out-of-sample asset allocation experiments show that the new regime switching model statistically significantly outperformed the linear multi-factor model and conventional regime switching models driven by a common Markov chain. The results suggest that it is not only important to account for regimes in portfolio decisions, but correct specification about the structure and number of regimes is of equal importance. Chapter 3 proposes a rational explanation for the existence of clientele effects under commonly used portfolio management contracts. It shows that although a fund manager always benefits from his market timing skill, which comes from his private information about future market returns, the value of the manager's private information to an investor can be negative when the investor is sufficiently more risk-averse than the manager. This suggests different clienteles for skilled and unskilled funds. Investors in skilled funds are uniformly more risk-tolerant than investors in unskilled funds. Moreover, a comparative statics analysis is conducted to investigate the effects of the manager's skill level, contract parameters, and market conditions on an investor's fund choice. The results suggest that the investors who are sufficiently more risk-averse than the manager should include fulcrum fees in the contract to benefit from the skilled manager's information advantage.

This paper studies the predictive performance and in-sample dynamics of three regime switching models for Swedish macroeconomic time series. The models discussed are threshold autoregressive (TAR), Markov switching autoregressive (MSM-AR), and smooth-transition autoregressive (STAR) regime switching models. We perform recursive out-of-sample forecasting to study the predictive performance of the models. We also assess the in-sample dynamics correspondence to the forecast performance and find that there is not always a relationship. Furthermore, we seek to explore if these unrestricted models yield interpretable results regarding the regimes from an macroeconomic standpoint. We assess GDP-growth, the unemployment rate, and government bond yields and find evidence of Teräsvirta's claims that even when the data has non-linear dynamics, non-linear models might not improve the forecast performance of linear models when the forecast window is linear.

過去文獻在探究利率波動行為時多採用現貨市場利率做為研究對象，思及期貨市場交易成本較低且流動性也較高使其對新資訊的反應更為迅速下，本文改以短期利率期貨，三個月期歐洲美元定存利率期貨、三個月歐元存款利率期貨以及三十天期商業本票利率期貨的隱含利率作為樣本資料，進而探討美國、歐洲及台灣的利率波動行為。研究方法以Gray(1996)提出的一般化狀態轉換模型為基礎並加入可以反應不對稱性的Dispersion設定，此設定有二個優點，其一為當面臨極大衝擊時，可減少衝擊所造成的變異數持續性而產生波動度均數復歸的現象，此設計乃考量到樣本期間一半時期均處於高峰度狀態的情形不常見，當波動度處於高峰時，預期市場波動度會反轉成近似常態水準；其二為易於Student’s t分配之狀態轉換模型下自由度的參數化設定，使峰態可隨狀態轉換。另外亦加入槓桿效果設定來反應市場上正負消息對資產報酬波動度所造成的不對稱影響。 由AIC模型配適度選擇準則下，適合描述美國、歐洲以及台灣的利率模型分別為RS-GARCH-L-DF, RS-GJR-GARCH-L-DF與RS-GJR-GARCH模型，這三個模型在DM預測力檢定下亦顯示具較佳模型預測力，本文進一步透過此些模型來探測歷年來重大經濟事件與央行利率政策對利率波動度的影響與關聯性。 研究結果顯示美國、歐洲及台灣的利率波動行為均具有顯著的高低兩波動狀態，台灣與歐洲的利率處於高低波動期間的機率較平均，但台灣處於高波動度狀態的機率遠高於歐洲，相形之下，美國普遍處於低波動度狀態；三者的利率長期皆會回歸於某一均衡水準，且顯著存在波動度叢聚的現象，其中，台灣利率的波動最為劇烈，而美國與歐洲的利率行為則具有波動度長期會回歸某一均衡水準的現象。當利率水準較高時，可清楚窺知歐洲的利率波動度也會較大，此現象亦存在於美國的高波動時期，但不適用於台灣利率動態行為上的描述。