Na Europa alguns países passaram por um processo de integração econômica, trocando suas moedas locais por uma moeda única a fim de aumentar o volume de comércio e investimento direto entre os países europeus. Em fevereiro de 1992 foi assinado o Tratado da União Européia (UE), conhecido como Tratado de Maastricht, no qual foi definida uma nova unidade monetária, conhecida como Euro, que entraria em vigor a partir de 1999 nos países integrantes da UE. O processo de ajuste experimentado por algumas economias européias para a inserção no bloco econômico europeu e para adoção do Euro pode ter afetado os fundamentos e, por conseguinte, a volatilidade do mercado acionário. O objetivo desta dissertação é analisar o impacto da introdução da moeda única no mercado acionário europeu. Para isso, será estimando um modelo GARCH com mudança de regime (SWGARCH). Mais especificamente a idéia é responder as seguintes perguntas: Será que o Euro mudou o regime da volatilidade do mercado acionário europeu? Esta possível mudança foi temporária ou permanente? Para esta análise foi utilizado um grupo de países estáveis, composto por França e Alemanha e um grupo de países instáveis, composto por Itália e Portugal. Para analisar o efeito isolado do Euro, utilizou-se a Inglaterra e a Suécia, pois são países membros da UE que não adotaram a moeda única. Para tirar o efeito dos eventos mundiais, foi incluído o mercado acionário americano como proxy do mercado mundial. Os resultados encontrados mostram que o Euro não afetou a volatilidade do mercado mundial, mas impactou temporariamente a volatilidade dos mercados locais. Para os países que não adotaram o Euro não temos como evidenciar claramente se houve algum impacto na volatilidade. / Some European countries had faced an increasing integration concerning their macroeconomic fundamentals since the mid nineties. A group of countries signed the European Union Maastricht Treaty on February 1992. This Treaty defined the creation of the European Monetary Union (EMU) and a new currency (Euro) that would be set in its members on January 1st, 1999. The European countries of UME had to adopt a lot of economics reforms in order to convert their local currencies into Euro. These changes in the macroeconomics fundamentals should have affected European stock markets. The objective of this paper is to analyze the impact of Euro on European sock markets. Has the Euro changed European stock markets volatility? Was this possible change temporary or permanent? In others words, the main goal of this paper is try to answer these questions. It will be estimated an univariate Switching GARCH model for stable and unstable European economies. The American stock market was used as a proxy to the world stock market. The results show that the Euro has not affected the world stock market, but it had a temporary impact on volatility of the European stock markets in the countries that joined EMU.

The statistical analysis of cointegration is crucial for inferring shared stochastic trends between variables and is an important area of Econometrics for analyzing long-term equilibriums in the economy. Bayesian inference of cointegration involves the identification of cointegrating vectors that are determined up to arbitrary linear combinations, for which the Gibbs sampler is often used to simulate draws from the posterior distribution. However, economic theory may not suggest linear relations and regime-switching models can be used to account for non-linearity. Modeling cointegration and regime-switching as well as the combination of them are associated with highly parameterized models that can prove to be difficult for Markov Chain Monte Carlo techniques such as the Gibbs sampler. Hamiltonian Monte Carlo, which aims at efficiently exploring the posterior distribution, may thus facilitate these difficulties. Furthermore, posterior distributions with highly varying curvature in their geometries can be adequately monitored by Hamiltonian Monte Carlo. The aim of the thesis is to analyze how Hamiltonian Monte Carlo performs in simulating draws from the posterior distributions of models accounting for cointegration and regime-switching. The results suggest that while it is not necessarily the case that regime-switching will be identified, Hamiltonian Monte Carlo performs well in exploring the posterior distribution. However, high rates of divergences from the true Hamiltonian trajectory reduce the algorithm to a Random Walk to some extent, limiting the efficiency of the sampling.

本篇論文主要在外匯市場建立市場投資組合、利差交易投資組合與動能交易投資組合，探討透過不同情境適當改變投資組合比重配置，是否能夠顯著提升交易策略的報酬表現。 以1999年1月至2015年10月為樣本期間，根據28個國家外匯市場資料建構市場投資組合、利差交易投資組合與動能交易投資組合等，之後根據三種投資組合報酬情況透過馬可夫情境轉換模型區分成三種情境。按三種情境的各種投資組合超額報酬表現，再利用馬可維茲的平均數-變異數投資組合模型配置各情境下各項交易的比重，再依據計算出的預期情境與相對應比重進行投資。其結果顯示在樣本期間內，本篇論文的交易策略相較於外匯市場投資組合、利差交易投資組合與動能交易組合有較佳的投資表現。 在樣本外測試部分，採用自2012年中開始的連續情境二資料進行分析。報酬方面，在其他交易型態呈現負報酬較多情況下，就本文交易策略而言，投資者隨時根據其各種交易平均報酬與共變異數進行交易比重配置，適時放空交易策略或投資無風險資產，產生正報酬。但從標準差可以推斷投資者面對未來的不確定，在整個樣本外期間歷時的34個月當中標準差亦無法有效降低，說明了投資者面對下一期總體環境的高不確定性。 / In this thesis, we mainly investigate whether it could improve the performance of currency portfolio by adjusting weights among carry trade, momentum and market return in foreign exchange market under different kinds of regimes. Based on a sample of 28 market currencies, we form three kinds of transactions in our portfolio, including carry trade, momentum, and market return. Under Markov switching model, we divide the sample period into three regimes, and then determine weights among carry trade, momentum and market return by parameters of each re-gime using Markowitz mean-variance analysis. Finally, we invest different weights among three transactions according to each expected regime. We find the result that although the return of the strategy is just a little higher than the carry trade, the risk is much lower compared to other transactions. In our out-of-sample testing, we analyze the performance by using the data of the regime two which begins September, 2012. With the respect to the return, most of other risky transactions have negative return, but we get positive return by adjusting the long position and short position according to the result of the mean-variance anal-ysis. However, we can not effectively reduce risk by using the strategy, and in the meantime it can explain the high uncertainty investors face toward the next period.

RESUMO No início de 1995 foi adotado no Brasil o Plano Real, tendo como um dos seus tripés de sustentação a busca pelo combate ao processo inflacionário crônico brasileiro que já se estendia por um longo período. Assim, a política monetária passou a ter um papel importante na determinação das variáveis macroeconômicas. Este trabalho busca analisar uma regra de política monetária que capte as variações ocorridas em todo o período do Plano Real, se estendendo até meados de 2005, bem como se deram as relações entre as variáveis econômicas neste período. A especificação proposta consiste na estimação de modelos não-lineares distintos dependendo do estado da economia (em crise ou fora de crise). Utilizamos um modelo com chaveamento Markoviano para a dinâmica da taxa de juros nominal onde a determinação de períodos de crise é feita por uma variável nãoobservada. Além disso, procuramos adotar dois algoritmos distintos de estimação, Expectation-Maximization (EM) e Monte Carlo Markov Chain (MCMC), concluindo que a análise para ambos é bastante próxima, sendo identificados os mesmos períodos entre regimes. Finalmente, motivamos a estimação através de modelos econômicos teóricos cujas dinâmicas são compatíveis com uma regra de fixação de juros não-linear, avaliando os padrões de resposta a impulso condicionados ao estado da economia (regimes de estabilidade e crise econômica). / ABSTRACT In the beginning of 1995, continuing the process of inflation combat, the monetary policy should have been an important role in the determinacy of macroeconomics variables. This work has a target analyzing a monetary rule that reflects the occurred variations in every Real Plan?s period. The specification proposed by the authors consists in an estimation of two independent nonlinear models for different states of the nature (crises or not crises). Here we estimate a model where the dynamic of the nominal interest rate follows a Markov Switching process and the regimes are unobservable variables. In addition, we try adopting two different algorithms to estimation; Expectation-Maximization (EM) and Monte Carlo Markov Chain (MCMC), concluded that the results are very similar. Finally, we motivate the estimations analyzing models where the theoretical dynamics of the economy are compatible with a nonlinear interest rate rule, analyzing the impulse response conditioned to state of economy (regimes of crises or not crises).

L’intérêt des modèles non-linéaires réside, d’une part, dans une meilleure prise en compte des non-linéaritéscaractérisant les séries macroéconomiques et financières et, d’autre part, dans une prévision plus riche en information.A ce niveau, l’originalité des intervalles (asymétriques et/ou discontinus) et des densités de prévision (asymétriqueset/ou multimodales) offerts par cette nouvelle forme de modélisation suggère qu’une amélioration de la prévisionrelativement aux modèles linéaires est alors possible et qu’il faut disposer de tests d’évaluation assez puissants pourvérifier cette éventuelle amélioration. Ces tests reviennent généralement à vérifier des hypothèses distributionnellessur les processus des violations et des transformées probabilistes associés respectivement à chacune de ces formes deprévision. Dans cette thèse, nous avons adapté le cadre GMM fondé sur les polynômes orthonormaux conçu parBontemps et Meddahi (2005, 2012) pour tester l’adéquation à certaines lois de probabilité, une approche déjà initiéepar Candelon et al. (2011) dans le cadre de l’évaluation de la Value-at-Risk. Outre la simplicité et la robustesse de laméthode, les tests développés présentent de bonnes propriétés en termes de tailles et de puissances. L’utilisation denotre nouvelle approche dans la comparaison de modèles linéaires et de modèles non-linéaires lors d’une analyseempirique a confirmé l’idée selon laquelle les premiers sont préférés si l’objectif est le calcul de simples prévisionsponctuelles tandis que les derniers sont les plus appropriés pour rendre compte de l'incertitude autour de celles-ci. / The interest of non-linear models is, on the one hand, to better take into account non-linearities characterizing themacroeconomic and financial series and, on the other hand, to get richer information in forecast. At this level,originality intervals (asymmetric and / or discontinuous) and forecasts densities (asymmetric and / or multimodal)offered by this new modelling form suggests that improving forecasts according to linear models is possible and thatwe should have enough powerful tests of evaluation to check this possible improvement. Such tests usually meanchecking distributional assumptions on violations and probability integral transform processes respectively associatedto each of these forms of forecast. In this thesis, we have adapted the GMM framework based on orthonormalpolynomials designed by Bontemps and Meddahi (2005, 2012) to test for some probability distributions, an approachalready adopted by Candelon et al. (2011) in the context of backtesting Value-at-Risk. In addition to the simplicity androbustness of the method, the tests we have developed have good properties in terms of size and power. The use of ournew approach in comparison of linear and non-linear models in an empirical analysis confirmed the idea according towhich the former are preferred if the goal is the calculation of simple point forecasts while the latter are moreappropriated to report the uncertainty around them.

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。

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.

Nous étudions les processus de Dirichlet dont le paramètre est une mesure proportionnelle à la loi d'un processus temporel, par exemple un mouvement Brownien ou un processus de saut Markovien. Nous les utilisons pour proposer des modèles hiérarchiques bayésiens basés sur des équations différentielles stochastiques en milieu aléatoire. Nous proposons une méthode pour estimer les paramètres de tels modèles et nous l'illustrons sur l'équation de Black-Scholes en milieu aléatoire.

This thesis, “Empirical Asset Pricing and Investment Strategies”, examines a number of topics related to portfolio choice, asset pricing, and strategic and tactical asset allocation. The first two papers treat the predictability of asset returns. Since at least the mid-1980s until quite recently, the conventional wisdom has been that it is possible to predict the return on, for example, an index of stocks. However, a series of recent papers have challenged this conventional wisdom. I answer this challenge and show that it is possible to predict returns if structural changes in the underlying economy are taken into account. The third paper examines the comovement between stocks and bonds. I show how it is possible to improve the composition of a portfolio consisting of these two asset classes by taking into account how the comovement changes over time. All three papers are self-contained and can therefore be read in any order. The first paper is entitled “Structural Breaks in Asset Return Predictability: Can They Be Explained?” Here I investigate whether predictability has changed over time and, if so, whether it is possible to tie the change to any underlying economic variables. Dividend yield and the short interest rate are often used jointly as instruments to predict the return on stocks, but several researchers present evidence that the relation has undergone a structural break. I use a model that extends the conventional structural breaks models to allow both for smooth transitions from one state to another (with a break as a special case), and for transitions that depend on a state variable other than time. The latter allows me to directly test whether, for example, the business cycle influences how the instruments predict returns. The results suggest that this is not the case. However, I do find evidence of a structural change primarily in how the instruments predict returns for large firms. The change differs from a break in that it appears to be an extended non-linear transition during the period 1993—1997. After the change, the short rate does not predict returns at all. Dividend yield, on the other hand, is strongly significant, and the return has become more sensitive to it. In the second paper, “Restoring the Predictability of Equity Returns,” I take another perspective on predictability and structural shifts. Several recent papers have questioned the predictability of equity returns, potentially implying serious negative consequences for investment decision-making. With return data including the 1990s, variables that previously predicted returns, such as the dividend yield, are no longer significant and results of out-of-sample tests are often weak. A possible reason is that the underlying structure of the economy has changed. I use an econometric model that allows for regime shifts over time as well as due to changes in a state variable, in this case the price-earnings ratio. This makes it possible to separate influences from these two sources and to determine whether one or both sources have affected return predictability. The results indicate that, first, a structural change occurred during the 1990s, and, second, that the unusually high level of price earnings in the late 1990s and early 2000s temporarily affected predictability at the 12-month horizon. In the third paper, “Coupling and Decoupling: Changing Relations between Stock and Bond Market Returns,” I investigate stock-bond comovement. The correlation between stocks and bonds has changed dramatically over the last ten years, introducing a new type of risk for portfolio managers, namely, correlation risk. I use GARCH estimates of stock volatility, simple regressions, and regime-switching econometric models to assess whether level of volatility, or changes in volatility, can be used to explain some of the changes in comovement in seven different countries. As regards volatility level, strong support is found in almost all countries to suggest that high volatility predicts lower, or negative, comovement. I argue that this can be evidence of a market-timing type of behavior. As for changes in volatility, the results are more mixed. Only for the U.S. market do I find strong support to conclude that large changes tend to coincide with lower, or negative, comovement. This could be evidence of a flight-to-quality (or cross-market hedging) type of behavior. / <p>Diss. Stockholm : Handelshögskolan, 2007</p>

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.