This dissertation is devoted to studying a fast and analytic approximation method, called the variational Bayesian (VB) method, and aims to give insight into its general applicability and usefulness, and explore its applications to various real-world problems. This work has three main foci: 1) The general applicability and properties; 2) Diagnostics for VB approximations; 3) Variational applications. Generally, the variational inference has been developed in the context of the exponential family, which is open to further development. First, it usually consider the cases in the context of the conjugate exponential family. Second, the variational inferences are developed only with respect to natural parameters, which are often not the parameters of immediate interest. Moreover, the full factorization, which assumes all terms to be independent of one another, is the most commonly used scheme in the most of the variational applications. We show that VB inferences can be extended to a more general situation. We propose a special parameterization for a parametric family, and also propose a factorization scheme with a more general dependency structure than is traditional in VB. Based on these new frameworks, we develop a variational formalism, in which VB has a fast implementation, and not be limited to the conjugate exponential setting. We also investigate its local convergence property, the effects of choosing different priors, and the effects of choosing different factorization scheme. The essence of the VB method relies on making simplifying assumptions about the posterior dependence of a problem. By definition, the general posterior dependence structure is distorted. In addition, in the various applications, we observe that the posterior variances are often underestimated. We aim to develop diagnostics test to assess VB approximations, and these methods are expected to be quick and easy to use, and to require no sophisticated tuning expertise. We propose three methods to compute the actual posterior covariance matrix by only using the knowledge obtained from VB approximations: 1) To look at the joint posterior distribution and attempt to find an optimal affine transformation that links the VB and true posteriors; 2) Based on a marginal posterior density approximation to work in specific low dimensional directions to estimate true posterior variances and correlations; 3) Based on a stepwise conditional approach, to construct and solve a set of system of equations that lead to estimates of the true posterior variances and correlations. A key computation in the above methods is to calculate a uni-variate marginal or conditional variance. We propose a novel way, called the VB Adjusted Independent Metropolis-Hastings (VBAIMH) method, to compute these quantities. It uses an independent Metropolis-Hastings (IMH) algorithm with proposal distributions configured by VB approximations. The variance of the target distribution is obtained by monitoring the acceptance rate of the generated chain. One major question associated with the VB method is how well the approximations can work. We particularly study the mean structure approximations, and show how it is possible using VB approximations to approach model selection tasks such as determining the dimensionality of a model, or variable selection. We also consider the variational application in Bayesian nonparametric modeling, especially for the Dirichlet process (DP). The posterior inference for DP has been extensively studied in the context of MCMC methods. This work presents a a full variational solution for DP with non-conjugate settings. Our solution uses a truncated stick-breaking representation. We propose an empirical method to determine the number of distinct components in a finite dimensional DP. The posterior predictive distribution for DP is often not available in a closed form. We show how to use the variational techniques to approximate this quantity. As a concrete application study, we work through the VB method on regime-switching lognormal models and present solutions to quantify both the uncertainty in the parameters and model specification. Through a series numerical comparison studies with likelihood based methods and MCMC methods on the simulated and real data sets, we show that the VB method can recover exactly the model structure, gives the reasonable point estimates, and is very computationally efficient.

在真實世界中，我們可以觀察到許多財務或經濟變數(股價、匯率、利率等)有時波動幅度非常微小，呈現相對穩定的狀態(Regime)；有時會由於政治因素或經濟環境的變動，突然一段期間呈現瘋狂震盪的狀態。針對這種現象，已有學者提出狀態轉換波動度模型(Regime Switching Volatility Model，簡稱RSV)來捕捉此一現象。 本篇論文選擇每年交易金額非常龐大的外匯選擇權市場，以RSV模型為基礎，採用馬可夫鏈蒙地卡羅法 ( Markov Chain Monte Carlo，簡稱MCMC ) 中的吉普斯抽樣(Gibbs Sampling)法來估計RSV模型的參數，依此預測外匯選擇權在RSV模型下的價格。我們再將此價格與Black and Scholes(BS)法及實際市場交易的價格資料作比較，最後並提出笑狀波幅與隱含波動度平面的結果。結果顯示經由RSV模型與MCMC演算法所計算出來的選擇權價格確實優於傳統的BS方法，且能有效解釋波動率期間結構 (Volatility Term Structure) 與笑狀波幅 (Volatility Smile) 的現象，確實反應且捕捉到了市場上選擇權價格所應具備的特色。

Diss. (sammanfattning) Stockholm : Handelshögskolan, 2008 Sammanfattning jämte 3 uppsatser

Techn. Univ., Diss.--München, 2002.

Univ., Diss.--Kiel, 2001.

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.

Dans cette thèse, nous nous intéressons aux questions de l’hétérogénéité inobservée et des solutions en coin dans les modèles de choix d’assolements. Pour répondre à ces questions, nous nous appuyons sur un modèle de choix de production multicultures avec choix d’assolement de forme NMNL, dont nous proposons des extensions. Ces extensions conduisent à des problèmes spécifiques d’estimation, auxquels nous apportons des solutions. La question de l’hétérogénéité inobservée est traitée en considérant une spécification à paramètres aléatoires. Ceci nous permet de tenir compte des effets de l’hétérogénéité inobservée sur l’ensemble des paramètres du modèle. Nous montrons que les versions stochastiques de l’algorithme EM sont particulièrement adaptées pour estimer ce type de modèle.Nos résultats d’estimation et de simulation montrent que les agriculteurs réagissent de façon hétérogène aux incitations économiques et que ne pas tenir compte de cette hétérogénéité peut conduire à des effets simulés de politiques publique biaisés.Pour tenir compte des solutions en coin dans les choix d’assolement, nous proposons une modélisation basée sur les modèles à changement de régime endogène avec coûts fixes associés aux régimes. Contrairement aux approches basées sur des systèmes de régression censurées, notre modèle est cohérent d’un point de vue micro-économique. Nos résultats montrent que les coûts fixes associés aux régimes jouent un rôle important dans le choix des agriculteurs de produire ou non certaines cultures et qu’ils constituent, à court terme, un déterminant important des c / In this thesis, we are interested in questions of unobserved heterogeneity and corner solutions in acreage choice models. To answer these questions, we rely on a NMNL acreage share multi-crop models, of which we propose extensions. These extensions lead to specific estimation problems, to which we provide solutions.The question of unobserved heterogeneity is dealt with by considering a random parameter specification. This allows us to take into account the effects of the unobserved heterogeneity on all the parameters of the model. We show that the stochastic versions of the EM algorithm are particularly suitable for estimating this type of modelOur estimation and simulation results show that farmers react heterogeneously to economic incentives and that ignoring this heterogeneity can lead to biased simulated effects of public policies.In order to take account of the corner solutions in acreage choices, we propose modelling based on endogenous regime switching models with regime fixed costs. Unlike approaches based on censored regression systems, our model is “fully” consistent from a micro-economic viewpoint. Our results show that the regime fixed costs play an important role in farmers’ choice to produce or not some crops and they are, in the short term, an important determinant of acreage choices.

Cette thèse développe différents modèles à changements de régimes de la structure par terme des taux d'intérêt. Un cadre général de modélisation des taux associés à différents émetteurs y est présenté (chapitre 2). Ce cadre est exploité afin d’analyser les taux d’État de dix pays de la zone euro entre 1999 et 2012 (chapitre 3). Un régime de crise permet d’expliquer l’accroissement de la volatilité des taux pendant la crise financière. Cette étude montre en outre que la liquidité des titres est déterminante pour leur valorisation. Le cadre de modélisation est complété afin d’étudier le lien de causalité entre deux types de tensions: celles liées à des motifs de liquidité et celles liées à des motifs de crédit (chapitre 4). Enfin, l'influence de la politique monétaire sur la courbe des taux est examinée grâce à un modèle dans lequel une utilisation innovante des changements de régime permet de produire des trajectoires réalistes des taux directeurs de la banque centrale (chapitre 5). / This doctoral thesis develops regime-switching models of the term structure of interest rates. A general framework is proposed to model the joint dynamics of yield curves associated with different debtors (Chapter 2). This framework is exploited to analyse the fluctuations of ten euro-area sovereign yield curves over the period 1999-2012 (Chapter 3). In this model, a crisis regime is key to account for the increase in spread volatility during the financial crisis. Also, this study shows that market liquidity is an important determinant of bond prices. The model is then completed in order to explore potential causality relationships between two kinds of stresses: liquidity- and credit-related stresses (Chapter 4). Finally, the influence of monetary policy on the yield curve is investigated by means of a term structure model where an innovative use of regime-switching techniques makes it possible to capture salient features of the dynamics of monetary-policy rates (chapter 5).

Depuis une dizaine d'années, une part croissante de fonds de pension rencontrent des difficultés financières. Cette détérioration a soulevé des questions sur la gestion de ces institutions et sur l'efficacité du cadre réglementaires. Cette thèse a pour objet d'analyser les comportements financiers et la gestion des risques opérés par les fonds de pension à prestation définies et les institutions assimilées. En premier lieu, nous relions les choix d'investissement à la question du contrôle managériale. Notre analyse suggère que la bonne gestion des fonds de pension nécessite un partage optimal des droits de contrôle entre les participants du plan et l'entreprise sponsor. Nous montrons alors comment cette répartition affecte les décisions d'investissement. Notre seconde analyse étudie l'impact des fluctuations financières sur la gestion des fonds de pension. Nos résultats suggèrent que le cadre réglementaire actuel conduit à de larges effets pro-cycliques, en particulier sur les exigences de capital et les décisions d'investissement. Finalement, nous analysons comment les changement structurels de la mortalité affectent le risque et les politiques de risque des fonds de pension. / Since ten years, an increasing proportion of pension funds faces to severe financial difficulties, addressing some questions about the management of these institutions and the effectiveness of the regulatory framework. This thesis aims to analyze the investment decisions and financial risk management made by the pension fund defined benefit and assimilated institutions, in order to address some advances for the regulation purpose. First, we address the question of the pension funds management by analyzing the implications of the managerial control problem. Our analysis suggests that the efficient management may require an optimal splitting of control rights between plan participants and the sponsoring company. We then show how this splitting of right controls can affects investment decisions in pension funds. Second, we analyze the implications of financial cycles for pension fund management. Our results suggest that the regulatory framework produces large pro-cyclical, including regime-dependent capital requirement and regime-dependent investment decisions. Finally, we analyze how the structural change in mortality affect the risk and the risk management of pension funds.

L’Europe a subi la crise la plus sévère de sa récente histoire à la suite de la crise financière globale de 2008. C’est pourquoi cette thèse a l’objectif d’identifier de façon empirique les déterminants de cette crise dans le cadre de 15 principaux membres de l’UE. Dans ce sens, nous développons d’abord un index de pression fiscale continu, contrairement aux travaux empiriques précédents, afin d’identifier des périodes de crise dans les pays UE-15 de 2003 à 2015. Ensuite, nous utilisons trois différentes techniques d’estimation, à savoir Cartes auto-organisatrices, Logit et Markov. Nos résultats d’estimation démontrent que notre indicateur de crise identifie le timing et la durée de la crise de dette dans chacun des pays de UE-15. Résultats empiriques indiquent également que l’occurrence de la crise de dette dans l’UE-15 est la conséquence de la détérioration de balances macroéconomiques et financières sachant que les variables comme le ratio des prêts non-performants sur les crédits totaux du secteur bancaire, la croissance du PIB, chômage, balance primaire / PIB, le solde ajusté du cycle PIB. De plus, variables démontrant la qualité de gouvernance tel que participation et responsabilisation, qualité de la réglementation, et de l'efficacité gouvernementale, jouent également un rôle important dans l’occurrence et sur la durée de la crise de dette dans le cadre de l’UE-15. Étant donne que les résultats économétriques indiquent l’importance de la détérioration fiscale dans l’occurrence de la crise de dette européenne, nous testons la convergence fiscale des pays membre de l’UE. Les résultats montrent que Portugal, Irlande, Italie, Grèce et Espagne diverge des autres pays de l’UE-15 en termes de dette publique / PIB alors qu’ils convergent, à part la Grèce, avec les autres pays membres de l’UE-15 en termes de déficit budgétaires / PIB. / Europe went through the most severe economic crisis of its recent history following the global financial crisis of 2008. Hence, this thesis aims to empirically identify the determinants of this crisis within the framework of 15 core EU member countries (EU-15). To do so, the study develops a continuous fiscal stress index, contrary to previous empirical studies that tend to use event-based crisis indicators, which identifies the debt crises in the EU-15 and the study employs three different estimation techniques, namely Self-Organizing Map, Multivariate Logit and Panel Markov Regime Switching models. Our estimation results show first that the study identifies correctly the time and the length of the debt crisis in each EU-15-member country by developing a fiscal stress index. Empirical results also indicate, via three different models, that the debt crisis in the EU-15 is the consequence of deterioration of both financial and macroeconomic variables such as nonperforming loans over total loans, GDP growth, unemployment rates, primary balance over GDP, and cyclically adjusted balance over GDP. Besides, variables measuring governance quality, such as voice and accountability, regulatory quality, and government effectiveness, also play a significant role in the emergence and the duration of the debt crisis in the EU-15. As the econometric results clearly indicate the importance of fiscal deterioration on the occurrence of the European debt crisis, this study also aims to test the fiscal convergence among the EU member countries. The results indicate that Portugal, Ireland, Italy, Greece, and Spain diverge from other EU-15 countries in terms of public debt-to-GDP ratio. In addition, results also show that all PIIGS countries except for Greece converge to EU-10 in terms of budget deficit-to-GDP ratio.