國內外股市普遍發現：在多頭市場下，個股與市場關連性低；空頭市場下，個股與市場關連度高。造成多數投資人往往在股市多頭上方獲利受阻，反而在空頭市場下承擔更多的下方風險。最早將此議題至入資產分配的是Ang and Bekaert (2002)之馬可夫狀態轉換模型，他們將相關程度高、波動度高、預期報酬低視為一種狀態；相關程度低、波動度低、預期報酬高視為另一種狀態。然而考慮這種絕對關係在台灣可能不明顯下，本研究僅僅將狀態設定為高相關程度與低相關程度，因為我們希望能透過馬可夫狀態轉換模型，根據台灣個別產業與市場相關之特性，尋找出由產業組成之投資組合，同時具有風險分散並追求高獲利能力，以因應不同的市場環境。本研究並會針對歸類出的產業，提供投資台股組合配置的建議。

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。

在國際間的股票市場中，股票報酬常存在有不對稱的相關結構，而其會造成許多極度地尾端風險。Copula函數常被用來描述多變數之間的聯合相關程度。多數的文獻均以二元copula函數為架構，去描述多種不同資產，像是股票、債券、匯率等之間的關係。我們討論多元copula的應用，本文以四元copula為主軸，並輔以狀態轉換 (regime-switching) 之機率過程，建構出四資產的投資組合之相關結構模型。 考慮了狀態轉換之copula的配適性後，我們以此模型來做資產投資策略。在模擬過程中，我們嘗試根據不同的未來目標做出最佳的投資組合權重，並採用動態預期模型 (dynamic anticipative model) 來藉由資訊的不斷更新，重新估計模型的參數來做資產評估。實證結果上，我們發現考慮狀態轉換之copula模型可以捕捉到更多股票報酬波動的情形，因此能減少在股市共跌時造成的重大損失。 / The correlation of returns in international stock markets exist asymmetric structure, which cause extremely tail dependence. The copula functions are commonly used to describe the dependence between random variables. Most literatures use basic pair-copulas to model the dependence of two variables, like stocks, bonds and exchange rates. This article try to use multivariate copulas, mainly 4-copula, and regime-switching method to construct a portfolio dependence, and extend to asset allocation. Given the fitting regime-switching copula, we use the model to decide investment strategy. We try to select the optimal weights of portfolio by different objective function, and we adapt a dynamic anticipative model, which can take all new information for parameters estimation. Empirically, we find that the copula-based model with regime-switching can capture more variation, and decrease the return loss from downside co-movement.

雖然技術分析的爭議非常的多，在市場上卻仍然被廣泛應用，原因即是因為容易被理解且方便應用，不過當馬可夫轉換模型出現時，技術分析便面臨的挑戰。馬可夫轉換模型又稱為隨機分段趨勢模型(stochastic segmented trend model)，預測方法也類似於技術分析，利用一段期間內的趨勢來判斷未來走勢。 本研究利用馬可夫轉換模型以及技術分析中相當受歡迎的移動平均轉換法相互作比較，研究標的則選擇國內的兩種期貨：臺股期貨與黃金期貨和國外的五種商品期貨：紐約黃金、布蘭特原油、芝加哥小麥、玉米和大豆共七種期貨，相互比較後，我們發現馬可夫轉換模型在樣本內的獲利績效比均線轉換法的績效要來得好，其中平滑推論又比濾嘴推論的績效好。 另外，馬可夫轉換模型在樣本外的績效並不亮眼，原因可能是估計參數的不穩定性過高，不過在臺灣黃金期貨的部分，樣本外表現也是非常的亮眼。

學術上不接受技術分析等方法，認為股價已經在市場上充分反應，過去的歷史股價不能對未來進行預測。然而，業界或一般的投資人，卻往往把技術分析拿來做為買賣的依據。實際上以歷史資料做模擬交易，卻可以發現許多技術分析的法則在某些市場、股票、期間之中，可以獲得相對於買進賣出更好的報酬。有趣的是，任何一種操作法則或是特定一組參數選擇，在樣本外的操作則無法完全發現同樣的結果。故以技術分析所獲得的超額報酬，究竟是此機制有效還是單純運氣成分，許多技術分析的文獻以及著作往往著墨甚少。 本論文利用狀態轉換模型(Regime Switching Model)捕捉台灣加權股價指數，將股價的動態分為上漲以及下跌兩種狀態，並估計其市場參數—漲跌速度、漲跌速度標準差、轉換機率。其次將所估計的市場參數做為模擬的依據，可發現在單純隨機的環境下，某些市場參數組合存在移動平均線的交易策略明顯優於買進持有策略。研究中以敏感度分析的方法，呈現各個單一市場參數的改變情形，對於操作績效影響的方向。 最後將2001~2010的的台灣加權股價指數，估計市場參數並找尋當下最適的移動平均組合，允許每季重新調整參數，並實際以收盤價做為買賣模擬。結果發現移動平均線操作，確實能提供比買進持有更好的報酬，並減低每年報酬率變異。

Hamilton (1989)發展出馬可夫轉換模型，假設模型母體參數會隨某一無法觀察得到的狀態變數變動而改變，並用馬可夫鏈的機制來掌控狀態間切換，可適當掌握金融與經濟變數所面臨的結構改變，因此是一個十分重要的財務模型。Schwert (1989)觀察股價波動狀況，發現經濟衰退期的股價波動比經濟擴張期大，因此認為Hamilton (1989)所提出的馬可夫轉換模型亦可應用於股票市場。然而，發現當市場上有重大訊息來臨時，大部分標的資產報酬率會產生跳躍現象，因此汪昱頡 (2008)提出跳躍風險下馬可夫轉換模型，以改善馬可夫模型所無法反映之股價不正常跳躍現象。在探討股價指數報酬率之敘述統計量與動態圖後，本文認為跳躍幅度也會受狀態影響，因此進一步拓展周家伃 (2010)跳躍獨立風險下狀態轉換模型，期望對股市報酬率動態過程提供更佳的分析。實證部分使用1999到2010年的國際股價指數之S&P500、道瓊工業指數與日經225三檔作為研究資料，來說明股價指數具有狀態轉換及跳躍的現象，並利用EM(Expectation Maximization)演算法來估計模型的參數，以SEM(Supplemented Expectation Maximization )演算法估計參數的標準差，且使用概似比(Likelihood ratio)檢定結果顯示跳躍相關風險下狀態轉換模型比跳躍獨立風險下狀態轉換模型更適合描述股價指數報酬率。最後，驗證跳躍相關風險下狀態轉換模型能捕捉其報酬率不對稱、高狹峰與波動聚集之特性。 / Hamilton (1989) proposed Markov switching models to suppose the model parameters change with unobserved state variables which control the switch between states by Markov chain. It can be appropriate to grasp the financial and economic variables which facing structural changes, so it’s a very important financial model. Schwert (1989) observed stock prices, and discovered that the volatilities of recession are higher than the volatilities of expansion. Hence, Schwert (1989) suggested to apply the Markov switching models to stock market. However, most of underlying asset return have jump phenomenon when abnormal events occur to financial market. Wong (2008) proposed Markov switching models with jump risks to improve Markov switching models which can not capture the jump risk of asset price. According to stock index return’s descriptive statistics and dynamic graph, we argue that states will impact jump sizes. In this paper, we extend the regime-switching model with independent jump risks (Chou, 2010) to provide better analysis for the dynamic of return. This paper use stock indices of the study period from 1999 to 2010 to estimate the parameters of the model and variance of parameter estimators by Expectation-Maximization (EM) algorithm and SEM(Supplemented Expectation Maximization ) , respectively. And use the likelihood ratio statistics to test which model is appropriate.Finally, the empirical results show that regime-switching model with jump sizes dependency risk can capture leptokurtic feature of the asset return distribution and volatility clustering phenomenon.

本文研究美國退休福利保險公司(PBGC)保險價值的計算,延伸 Marcus (1987)模型,提出狀態轉換過程保險價值模型計算,也就是將市場分為兩種情況,正成長率視為正常狀態,負成長率為衰退狀態,利用狀態轉換過程評價 PBGC 契約在經濟困難而終止和介入終止下合理的保險價值。在參數估計方面,本文以 S&P500股價指數和一年期國庫券資料參數估計值及Marcus(1987)和Pennacchi and Lewis(1994)的方式給定參數,以 EM-PSO-Gradient 延伸 EM-Gradient 方法並以最大概似函數值、AIC 準則和 BIC 準則比較估計結果。最後固定其他參數, 探討狀態轉換過程保險價值模型對參數調整後保險價值的影響之敏感度分析。 / In this paper, we evaluate Pension Benefit Guaranty Corporation insurance values through regime switching models, which is the extension of the models of Marcus (1987). That is, we can separate periods of economy with faster growth from those with slower growth when observing long-term trends in economy and calculate the reasonable PBGC insurance values under distress termination and intervention termination by regime switching processes. We set parameters by estimating S&P 500 index and 1-year treasury bills by EM-PSO-Gradient, which is the extensive method of EM-Gradient and refer the methods of setting parameters from Marcus (1987) and Pennacchi and Lewis (1994). After that, we compare the maximum likelihood estimates, AIC and BIC of the estimative results. Finally, we do sensitivity analysis through given the other parameters and look into what would impact on our models of insurance values when adjusting one parameter.

此篇論文利用馬可夫狀態轉換模型實證出在歐元區的股票市場中，以規模溢酬、價值溢酬以及市場溢酬建構的投資組合存在兩個不同的情境狀態。以歐元區市場溢酬和規模溢酬建構的投資組合(SMB portfolios)在牛市存在較高的平均報酬，另一方面以價值溢酬建構的投資組合(HML portfolios)則在熊市有較高的平均報酬。而以規模溢酬、價值溢酬以及歐元區市場溢酬建構的投資組合，其報酬率變異數在熊市皆比牛市來得高。由於此篇論文實證出不論在樣本內或樣本外的測試中，以規模溢酬以及價值溢酬建構的投資組合，其特色反轉投資策略皆優於買入並持有的投資策略，因此本篇論文建議，在歐元區以規模因素（size factor）及帳面價值與市價比因素（book-to-market factor）為考量建構投資組合時，考慮規模溢酬以及價值溢酬在不同情境狀態下的反轉異常現象是重要且不可忽視的課題。 / This paper documents the presence of two regimes in the joint distribution of stock returns on European market premium portfolio and portfolios tracking size- and value effects in the Euro area. The mean returns of the EMU market portfolio and SMB portfolios are higher in the bull state while the mean return of the HML portfolio is larger in the bear state. Volatilities of the EMU market portfolio, SMB portfolio and the HML portfolio are all larger in the bear state compared to the bull state. This paper uses the Markov regime-switching model to generate the switching signal of market, size and value portfolios in the stock market and reallocates the market, size and value portfolios in the stock market by the mean-variance approach. Since both in the in-sample and out-sample test, the performance of the style rotation strategy outperforms style consistent strategy of the SMB portfolio and HML portfolio, this paper proposes that when analyzing investments in returns of size and value portfolios in the European market, it is important for us to account for anomalies for size and value effects in European market under different regimes. In the regime-switching VAR(1) model to account for the net capital flow predictability on the stock returns of EMU market, SMB and HML portfolios and the interrelationships among these variables. The result shows that adding the European Union net capital flow in relation to the economy's size as the predictor variable to the regime switching VAR(1) model, it improves the asset allocation outcomes both in the in-sample and out-sample test. Furthermore, this paper has found that both in the bull and bear states, the impulse response function shows that a shock of one standard deviation of net capital inflows last month will reduce the EMU market return up to near three months. Besides, the net capital inflow shock in European stock market will generates appreciation of companies with low book-to-market ratios (growth stocks) and large-sized firms in the bull state, while it generates appreciation of companies with high book-to-market ratios (value stocks) in the bear state.

本篇論文使用了LHP的近似方法去評價擔保債權憑證，並推導出漸進極值因子模型，又稱單因子copula模型，單因子copula模型被廣泛運用在CDO之風險管理與一些風險因子模擬之應用，但由於2008年之金融海嘯造成市場標準模型Gaussian copula model會有評價上的誤差，所以為了能在市場不穩定時能更精確的求算出分券價差，我們必須找到一個更簡單且快速捕捉到市場不穩定性的模型。在這篇論文中，我們引用了Anna Schloesser在2009年所提出以NIG copula model為基礎的兩個延伸，讓模型更穩健和且擁有良好的性質去進行模擬，NIG Regime-Switch 模型有兩大特色: (i)可以用一致的方法去評價不同到期日的分券，放寬了同一分券必須是相同到期日的假設，和(ii)有不同的相關係數狀態，對於金融風暴來說，狀態轉換可以有效地降低市場不穩定所帶來的評價誤差。本文也對不同模型下的CDO進行風險分析與避險，分券的期望損失廣泛被信評公司視為一項審定信用評等重要的風險衡量指標，但是並無法真實反映出擔保債權憑證分券之間相對風險之大小，因此本文採用期望損失率的觀念，利用期望損失佔本金的比例來比較各分券之相對風險，且本文也求算出CDO之避險參數，讓投資人了解對合成行擔保債權憑證分券避險時所需之避險部位，分券持有人也可依據所要規避的風險類型，選擇市場上現有的信用違約交換指數或是單一資產之信用違約交換(single-name credit default swap)來進行避險。 / This paper presents the Large Homogeneous Portfolio (LHP) approach to the pricing of CDOs and we derive the one-factor copula model. It is popular that the one-factor copula models are very useful for risk management and measurement applications involving the generation of scenarios for the complete universe of risk factors. However, since the financial crisis in 2008 induces some errors in the valuation by Gaussian copula model, which is originally adopted by credit rating firms, it is necessary to have a simple and fast model that can capture the market unstableness. In this paper we apply two extensions of the NIG copula model, which are first present by Anna Schloesser (2009), since they make the model well defined and powerful for scenario simulation. The NIG Regime-Switch copula model allows for two important features: (i) tranches with different maturities modeled in a consistent way, and (ii) different correlation regimes. The regime-switching component of the NIG copula model is especially important in view of the financial crisis. This paper also targets on different models to conduct risk analysis and hedging strategy. The expected loss of tranches is widely used by credit rating organizations as one of the important indicators for risk measurement. However, it can’t reflect the relative risk level between CDO’s tranches. Therefore, our research adopts the concept of expected loss rate, which use the proportion of expected loss to total principal amount to compare the relative risk of each tranche. Moreover, when we want to hedge the spread risk of synthetic CDO tranches, the holders of tranches can choose the existing CDS index or the single-name CDS based on different risks types to hedge. The employment of the NIG Regime-Switch copula model not only has more precise estimation for the spread of tranches but also possess more stable hedge ratio to hedge.

本研究探討VIX 期貨價格所隱含的資訊對於S&P 500 指數波動度預測的解釋力。過去許多文獻主要運用線性預測模型探討歷史波動度、隱含波動度和風險中立偏態對於波動度預測的資訊內涵。然而過去研究顯示，波動度具有長期記憶與非線性的特性，因此本文主要研究非線性預測模型對於波動度預測的有效性。本篇論文特別著重在不同市場狀態下(高波動與低波動)的實現波動度及隱含波動度異質自我迴歸模型(HAR-RV-IV model)。因此，本研究以考慮馬可夫狀態轉化下的異質自我迴歸模型(MRS-HAR model)進行實證分析。 本研究主要目的有以下三點: (1) 以VIX期貨價格所隱含的資訊提升S&P 500波動度預測的準確性。(2) 結合風險中立偏態與VIX期貨的資訊內涵，進一步提升S&P 500 波動度預測的準確性。(3) 考慮狀態轉換後的波動度預測模型是否優於過去文獻的線性迴歸模型。 本研究實證結果發現: (1) 相對於過去的實現波動度及隱含波動度，VIX 期貨可以提供對於預測未來波動度的額外資訊。 (2) 與其他模型比較，加入風險中立偏態和VIX 期貨萃取出的隱含波動度之波動度預測模型，只顯著提高預測未來一天波動度的準確性。 (3) 考慮狀態轉換後的波動度預測模型優於線性迴歸模型。 / This paper explores whether the information implied from VIX futures prices has incremental explanatory power for future volatility in the S&P 500 index. Most of prior studies adopt linear forecasting models to investigate the usefulness of historical volatility, implied volatility and risk-neutral skewness for volatility forecasting. However, previous literatures find out the long-memory and nonlinear property in volatility. Therefore, this study focuses on the nonlinear forecasting models to examine the effectiveness for volatility forecasting. In particular, we concentrate on Heterogeneous Autoregressive model of Realized Volatility and Implied Volatility (HAR-RV-IV) under different market conditions (i.e., high and low volatility state). This study has three main goals: First, to investigate whether the information extracted from VIX futures prices could improve the accuracy for future volatility forecasting. Second, combining the information content of risk-neutral skewness and VIX futures to enhance the predictive power for future volatility forecasting. Last, to explore whether the nonlinear models are superior to the linear models. This study finds that VIX futures prices contain additional information for future volatility, relative to past realized volatilities and implied volatility. Out-of-sample analysis confirms that VIX futures improves significantly the accuracy for future volatility forecasting. However, the improvement in the accuracy of volatility forecasts is significant only at daily forecast horizon after incorporating the information of risk-neutral skewness and VIX futures prices into the volatility forecasting model. Last, the volatility forecasting models are superior after taking the regime-switching into account.