This study includes three issues about the dynamic of 30-days Taiwan Commercial Paper rate (CP2).The first issue focuses on the estimation of continuous-time short-term interest rate models. We discretize the continuous-time models by using two different approaches, and then use weekly and monthly data to estimate the parameters. The models are evaluated by data fit. We find that the estimated parameters are similar for different discretization approaches and would be more stable and efficient under quasi-maximum likelihood (QML) with weekly data. There exists mean reversion for Taiwan CP rate and the relationship between the volatility and the level of interest rates are less than 1 and smaller than that of American T-Bill rates reported by CKLS (1992) and Nowman (1997). We also find that CIR-SR model performs best for Taiwan CP rate. The second issue compares the continuous-time short-term interest rate models empirically both by predictive accuracy test and encompassing test. Having the estimated parameters of the models by discretization of Nowman(1997) and QML, we produce the forecasts on conditional mean and volatility for the interest rate over multiple-step-ahead horizons. The results indicate that the sophisticated models outperform the simpler models in the in-sample data fit, but have a distinct performance in the out-of-sample forecasting. The models equipped with mean reversion can produce better forecasts on conditional means during some period, and the heteroskedasticity variance model with outperform counterparts in volatility forecasting in some periods. The third issue concerns the persistent and massive volatility of short-term interest rates. This part inquires how the realizations on Taiwan short-term interest rates can be best described empirically. Various popular volatility specifications are estimated and tested. The empirical findings reveal that the mean reversion is an important characteristic for the Taiwan interest rates, and the level effect exists. Overall, the GARCH-L model fits well to Taiwan interest rates.

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.

Although the Black-Scholes (BS) model and its alternatives have been widely applied in finance, their flaws have drawn the attention of many investors and risk managers. The Black-Scholes (BS) model fails to explain the volatility smile. Its alternatives, such as the BS model with a Poisson jump process, fail to explain the volatility clustering. Based on the literature, a novel dynamic regime-switching option-pricing model is developed in this thesis, to overcome the flaws of the traditional option pricing models. Five macroeconomic indicators are identified as the drivers of economic states over time. Two regimes are selected among all likely numbers of regimes under the Bayes Information Criterion (BIC). Both in-sample and out-of-sample tests are constructed to examine the prediction of the model. Empirical results show that the two-state regime-switching option-pricing model exhibits significant prediction power.

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.

過去文獻在探究股市報酬率波動行為時，多採用GARCH/ARCH等傳統時間序列模型，但這些模型不能解決波動度的高持續性(persistence)。本文以Gray(1996)提出的一般化狀態轉換模型(GRS-GARCH)為基礎並加入Dueker(1997)所提出的Dispersion設定，建立GRS-GARCH-K以及GRS-GRACH-DF模型來預測股市報酬率波動行為。GRS-GARCH-K模型設定最大的優點是加入Student’s t分配之自由度可隨狀態轉換，使峰態亦可隨狀態轉換，另外GRS-GRACH-DF模型除了擁有GRS-GARCH-K的特性外，還擁有均數復歸的特色。本文以單一狀態下的GARCH-N、GARCH-t模型，以及雙狀態下的GRS-GARCH、GRS-GARCH-K以及GRS-GARCH-DF模型做研究，並以台灣股價加權股價指數為研究樣本，探討並預測股價日報酬率的波動度，最後將波動度代入Black-Scholes選擇權訂價模型，探討模型之其評價效果。 研究顯示，在樣本內以AIC和SBC檢定法則下，GRS-GARCH-DF有最好的配適能力，樣本外的預測能力在MAE、MASE、MAPE三種誤差比較法下，GRS-GARCH-DF相較於GARCH-N、GARCH-t、GRS-GARCH和GRS-GARCH-K四種模型，在訂價方面與市場價格誤差最小，並以DM檢定法證實其統計上的顯著性。因此擁有均數復歸特色的GRS-GARCH-DF在波動度的估計上相較於其他模型來的優異。

@Frankfurt (Main), University, Diss., 2007.

This thesis improves our understanding of asset prices and returns as it documents a regime shift risk premium in currencies, corrects the estimation bias in the term premium of bond yields, and shows the impact of ambiguity aversion towards parameter uncertainty on equities. The thesis consists of three essays. The first essay "The Yen Risk Premiums: A Story of Regime Shifts in Bond Markets" documents a new monetary mechanism, namely the shift of monetary policies, to account for the forward premium puzzle in the USD-JPY currency pair. The shift of monetary policy regimes is modelled by a regime switching dynamic term structure model where the risk of regime shifts is priced. Our model estimation characterises two policy regimes in the Japanese bond market---a conventional monetary policy regime and an unconventional policy regime of quantitative easing. Using foreign exchange data from 1985 to 2009, we find that the shift of monetary policies generates currency risk: the yen excess return is predicted by the Japanese regime shift premium, and the emergence of the yen carry trade in the mid 1990s is associated with the transition from the conventional to the unconventional monetary policy in Japan. The second essay "Correcting Estimation Bias in Regime Switching Dynamic Term Structure Models" examines the small sample bias in the estimation of a regime switching dynamic term structure model. Using US data from 1971 to 2009, we document two regimes driven by the conditional volatility of bond yields and risk factors. In both regimes, the process of bond yields is highly persistent, which is the source of estimation bias when the sample size is small. After bias correction, the inference about expectations of future policy rates and long-maturity term premia changes dramatically in two high-volatility episodes: the 1979--1982 monetary experiment and the recent financial crisis. Empirical findings are supported by Monte Carlo simulation, which shows that correcting small sample bias leads to more accurate inference about expectations of future policy rates and term premia compared to before bias correction. The third essay "Learning about the Persistence of Recessions under Ambiguity Aversion" incorporates ambiguity aversion into the process of parameter learning and assess the asset pricing implications of the model. Ambiguity is characterised by the unknown parameter that governs the persistence of recessions, and the representative investor learns about this parameter while being ambiguity averse towards parameter uncertainty. We examine model-implied conditional moments and simulated moments of asset prices and returns, and document an uncertainty effect that characterises the difference between learning under ambiguity aversion and learning under standard recursive utility. This uncertainty effect is asymmetric across economic expansions and recessions, and this asymmetry generates in simulation a sharp increase in the equity premium at the onset of recessions, as in the recent financial crisis.

This thesis examines stock price bubbles in the Stock Exchange of Thailand (SET) from its establishment in April 1975 until December 2012 using regime-switching bubble models, on the main aggregated market index, called the SET Index, and several disaggregated stock indices by industrial sector. The results suggest some evidence of bubble-like behaviour in these indices, most especially when a structural break is included at July 1997, the date when Thailand switched to adopting a managed floating exchange rate system. Given the limitations of published stock price indices in Thailand a new, consistent index was computed the K-NI. The econometric test results using this new index indicate strong evidence of stock price bubbles in several industrial sectors and at least some evidence of bubbles in all industry groups in the SET. Finally, the standard model is extended to study the transmission of bubbles between industry groups. The results indicate some levels of contagion in the Technology sector, as well as, in several other industry groups, while the Resources sector seems to be relatively isolated.

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.

This study examines price formation in one of the largest wholesale electricity markets in the world: the Pennsylvania Jersey Maryland Interconnection, which serves 13 states and the District of Columbia with over 60 million consumers. The contribution of this thesis is to apply a variety of time series models offered in the literature to a large data set describing a single market, allowing for a comparison of their performance as well as demonstrating their validity. A central question that drives market deregulation is if it has created efficiency gains. To formalize this notion of efficiency, we implement tests for stationarity to measure the degree of randomness over time, finding that short run volatility can result in the outcomes for these tests that are inconclusive. We explore this volatility structure using Asymmetrical Power Autoregressive Conditional Heteroskedastic (APARCH) framework which captures the asymmetric nature of price shocks, finding that this behavior is unique to electricity returns, and that APARCH offers a better modelling alternative than simpler representations. Additionally, we account for long memory given the seasonal drivers of electricity prices which are persistent using Autoregressive Fractionally Integrated Moving Averages (ARFIMA). Temperature related market drivers are further modelled using Fourier based seasonality functions which enable us to capture cycles over multiple frequencies. Lastly, we provide an application of Markov Regime Switching models to account for the possibility of multiple states. Although appealing from a theoretical perspective, we find that the increased complexity of the model does not necessarily translate to better performance over simpler non-switching alternatives. These findings highlight the importance of establishing the features of the time series before selecting an appropriate model, and motivating it with economic rationale. / Graduate