[pt] A formação do portfólio de uma empresa de Petróleo envolve complexas decisões devido ao ambiente de incertezas e é de extrema importância na definição do futuro estratégico da empresa. Recentemente, a otimização de um portfólio de ativos de exploração e produção de petróleo vem sendo amplamente tratada na literatura, entretanto observa-se uma escassez de trabalhos que consideram a otimização do portfólio de refino. Este trabalho tem por objetivo propor um modelo de formação de portfólio para empresas do setor de óleo e gás, que possuem atividades tanto no segmento de exploração e produção (upstream) quanto no segmento de refino (downstream), levando em conta a integração entre ambos. Assim como nos modelos tradicionais, os preços do barril de petróleo e a produtividade dos campos serão tratadas como incertezas. O modelo proposto utilizará técnicas de programação estocástica com aversão a risco, medido pelo CVaR (Conditional Value-at-Risk). A fim de validar a metodologia proposta, um estudo de caso baseado em uma empresa de óleo e gás será apresentado. A aplicação numérica indicou que o modelo que otimiza o portfólio conjunto de upstream e downstream apresenta resultado da função objetivo até 28 por cento superior ao modelo usualmente tratado na literatura que trata apenas do portfólio de upstream. / [en] The portfolio allocation of an Oil and Gas company involves complex decisions within an uncertain environment and is extremely important in defining the firm s economical and financial future behavior. Recently, the portfolio selection problem for oil exploration and production (E&P) projects has been widely treated in the literature, however, few studies consider the optimization of the combined upstream and downstream portfolio. The purpose of this work is to propose a portfolio selection model for oil and gas companies, which operates both in exploration and production (upstream) and in refining (downstream), considering the integration between them. Crude oil prices and fields performance are the main uncertainties of the problem. The proposed model makes use of risk aversion stochastic programming techniques, measured by CVaR (conditional value at risk). To validate the proposed methodology a case study based on an Oil Company will be presented. The numerical application indicates that the model considering both upstream and downstream portfolio presents objective function results 28 percent higher than the model usually used in the literature that only optimizes the upstream portfolio.

The phenomenon of financial bubbles is known to have impacted various markets since the seventeenth century. Such bubbles are known to form when the market drastically overvalues the price of an asset, causing its market value to increase hyperbolically, only to suddenly collapse once the untenable perceived future prospects of the asset are realized. Hence, it remains crucial for investors to be able to sell off assets residing within a bubble before they burst and their value is significantly diminished. Thus, portfolio optimization methods capable of accounting for financial bubbles in stock dynamics is a field of great value and interest for market participants. Portfolio optimization with respect to the mean-field is a relatively novel approach to accounting for the bubble-phenomenon. Hence, this paper investigates a previously unattempted method of portfolio optimization, providing a mean-field solution to the mean-variance trade-off problem, as well as providing new definitions of stock dynamics capable of diverting investors from bubbles. / Finansiella bubblor är ett fenomen som har påverkat marknader sedan 1600-talet. Bubblor tenderar att skapas när marknaden kraftigt övervärderar en tillgång vilket orsakar en hyperbolisk tillväxt i marknadspriset. Detta följs av en plötslig kollaps. Därför är det viktigt för investerare att kunna minska sin exponering mot aktier som befinner sig i en bubbla, så att risken för stora plötsliga förluster reduceras. Således är portföljoptimering där aktiedynamiken tar hänsyn till bubblor av högt intresse för marknadsdeltagare. Portföljoptimering med avseende på medelfältet är ett relativt nytt tillvägagångssätt för att behandla bubbelfenomen. Av denna anledning undersöks i detta arbete en hittills oprövad lösningsmetod som möjliggör en medelfältslösning till avvägningen mellan förväntad avkastning och risk. Där-utöver presenteras även ett antal nya modeller för aktier som kan bortleda investerare från bubblor.

[pt] O presente trabalho tem como objetivo final a verificação da aplicabilidade da Teoria das Opções Reais (TOR) em investimentos de papel e celulose, considerando o Movimento de Reversão à Média (MRM) nos fatores de risco, dado um modelo de gerenciamento de curto prazo, no âmbito de um estudo de caso da Fibria Celulose S.A. para o setor de papel e celulose no Brasil. Nesta dissertação, testa-se a aderência da série histórica de preços da celulose de fibra curta da Fibria, no período entre 2003 e 2013, a um modelo estocástico de reversão à média, sendo este modelo validado para o presente estudo. Uma vez o modelo validado, determinam-se os parâmetros para realização de cálculos e análises fundamentais para se chegar aos objetivos intermediários, etapa preliminar aos resultados do objetivo final. Dentre os cálculos e análises citados, ressaltam-se: determinação dos VPLs dinâmicos e os valores das Opções Reais europeias sequenciais para a Simulação de Monte Carlo com Processo Neutro ao Risco; construção e análise da Árvore Binomial com Processo Neutro ao Risco; construção e análise das Regiões de Gatilho para preços e lucros marginais em um Processo Real; comparação das Regiões de Gatilho com as determinadas pelas Árvores Binomiais. Assim, com tais análises, confirma-se, nesta dissertação, a aplicabilidade da Teoria das Opções Reais na Análise de Investimento no setor celulósico-papeleiro. / [en] The present work has the ultimate purpose of verifying the applicability of the Real Options Theory in the pulp and paper investment, considering the Mean Reversion Movement in the risk factors, given a short-term management model, within a study of Fibria Celulose S.A. for the pulp and paper industry in Brazil. This dissertation tests the adherence of Fibria s short fiber pulp historical price series, between 2003 and 2013 to a stochastic mean reversion model, being this model validated in the present study. Once the model is validated, the parameters for calculations and fundamental analyzes are determined to reach intermediate goals, preliminary step to the results of the final goal. Among the cited calculations and analyzes, it is emphasized: determination of dynamic NPVs and values of the sequential European Real Options for the Monte Carlo Simulation with Risk Neutral Process; construction and analysis of the Binomial Tree with Risk Neutral Process; construction and analysis of the Trigger Regions for prices and marginal profits in a Real Case; Comparison between Trigger Regions and those determined by the Binomial Trees. So with such analyzes, it is confirmed, in this work, the applicability of the Real Option Theory on Investment Analysis in pulp and paper industry.

[pt] Em alguns casos pode ser útil para a empresa dividir um projeto em várias subunidades independentes. Esta divisão pode ocorrer, por exemplo, em grandes projetos nos quais são identificados partes integrantes ou módulos com diferentes riscos, retornos, matérias primas, produtos, atividades e mercados. Por outro lado, na avaliação de projetos, a consideração de opções reais de adiar o investimento, investir em informação e parar temporariamente a produção é uma sofisticada e amplificada abordagem, quando comparada com o método tradicional do Valor Presente Líquido (VPL). Desta forma, o objetivo deste trabalho é apresentar os fatores econômicos de risco de um projeto dividido em várias subunidades independentes identificados como relevantes na análise da distribuição probabilística do VPL; o processo estocástico usado para simular cada um destes fatores; a distribuição probabilística deste VPL utilizando a metodologia de opções reais de adiar o investimento, investir em informação e parar temporariamente a produção, além do valor isolado e conjunto (múltiplo) destas opções para o projeto. Com esses dados, pode-se apresentar uma metodologia para achar a combinação temporal ótima para o início dos investimentos em cada uma das subunidades que constituem este tipo de projeto, aquela em que o valor do VPL deste empreendimento é maximizado. Entre outras contribuições importantes deste trabalho para a análise de risco de projetos, apresentou-se também uma modelagem inédita para a geração de cenários estocásticos apropriados para modelar a incerteza no valor do investimento, um dos principais fatores de risco em projetos. / [en] In some cases it may be advantageous for the company to divide a project into several independent subunits. This can occur, for example, on large projects, in which are identified modules with different risks, returns, raw materials, products, activities and markets. On the other hand, in the assessment of projects, the consideration of real options to postpone investment, invest in information and stop production temporarily is a sophisticated approach compared with the traditional Net Present Value (NPV). Thus, the objective of this work is to present the economic risk factors of a project divided into several independent subunits identified as relevant in the analysis of the probability distribution of NPV; the stochastic process used to simulate each of these factors; the probability distribution of NPV using the methodology of real options to postpone investment, invest in information and temporarily stop production, besides the isolated and multiple value of these options. By making use of these data, we can present a methodology for finding the optimal time combination for the investement in each of the subunits, the one in which the value of the NPV of this project is maximized. Another specific contribution of this work, refers to the generation of appropriate stochastic scenarios to model the uncertainty in the value of investment, one of the main risk factors in projects.

The most useful feature used in finance of the Ornstein-Uhlenbeck (OU) stochastic process is its mean-reverting property: the OU process tends to drift towards its long- term mean (its equilibrium state) over time. This important feature makes the OU process arguably the most popular statistical model for developing best pair-trading strategies. However, optimal strategies depend crucially on the first passage time (FPT) of the OU process to a suitably chosen boundary and its probability density is not analytically available in general. Even for crossing a simple constant boundary, the FPT of the OU process would lead to crossing a square root boundary by a Brownian motion process whose FPT density involves the complicated parabolic cylinder function. To overcome the limitations of the existing methods, we propose a novel class of non-linear boundaries for obtaining optimal decision thresholds. We prove the existence and uniqueness of the maximizer of our decision rules. We also derive simple formulas for some FPT moments without analytical expressions of its density functions. We conduct some Monte Carlo simulations and analyze several pairs of stocks including Coca-Cola and Pepsi, Target and Walmart, Chevron and Exxon Mobil. The results demonstrate that our method outperforms the existing procedures.

在過去二到三年之中，能源、金屬、軟性商品等原物料價格漲勢強勁，成為市場上最炙手可熱的商品。然而，原物料價格漲升為全球帶來了通膨隱憂，世界各國紛紛採用各種貨幣政策和財政政策試圖緩解通膨壓力。其中，利率政策即是相當重要的一環。在這樣的背景之下，是否對於能源、貴金屬和利率衍生性商品的設計和定價上產生影響，值得進一步檢視。因此，本論文選擇以中國大陸的原油與黃金連結複合式選擇權，以及利率（HIBOR）連結可贖回每日區間計息等兩種結構性存款作為研究個案，以財務工程的理論模型為中國銀行的金融創新產品作評價與分析。 在原油與黃金連結複合式選擇權部分，分別假設金價和油價服從幾何布朗運動（Geometric Brownian Motion）推導出封閉解，以及Schwartz的一因子均數回歸模型，採蒙地卡羅模擬法模擬標的資產之價格路徑並以之估算商品理論價值和發行機構利潤，之後則就避險參數和商品預期收益率作分析。在利率連結可贖回每日區間計息結構性存款部分，由於具有發行機構可提前贖回的特性，本論文採用LIBOR市場模型（BGM Model）為評價基礎，先利用市場報價資訊計算期初遠期利率及進行參數校準，再以蒙地卡羅模擬法模擬遠期利率路徑，最後以Longstaff and Schwartz（2001）提出的最小平方蒙地卡羅法（LSM）計算商品理論價值和發行機構利潤。 除估算商品理論價值以檢視中國銀行的商品定價合理性之外，本文也針對中國大陸的外匯和利率政策對金融機構在商品設計方面的影響作分析，最後則分別就財務工程與金融創新以及總體政策與金融市場兩方面提出結論與建議，以供各界參酌。 / The prices of physical commodities have risen a lot and led to pressure of inflation for several years. Many countries over the world have tried hard to tackle inflation threat with monetary and fiscal policies. Under this circumstance, the design and pricing of structured products should be affected. Therefore, the oil and gold-linked and interest rate-linked structured deposits launched by Bank of China are selected to be the case study in this thesis. Prices of the underlying assets are assumed to follow Geometric Brownian Motion, and the close-form solution of the oil and gold-linked structured deposit embedded with compound options is derived. Moreover, Schwartz’s One-Factor Mean Reversion Model is adopted to derive the fair value by simulation. In addition to the fair value and issuer’s profit, the expected rate of return, hedge parameters (Greeks) and model difference are presented in this thesis. As for the interest rate-linked Callable Daily Range Accrual Deposit, the thesis presents the steps of pricing by simulation. LIBOR Market Model (BGM Model) is adopted to derive the fair value of Callable Range Deposit with Least Squares Monte Carlo approach. Besides, the design and pricing of structured products are actually influenced by those policies in relation to interest rates and currencies adopted by government of Mainland China. The influence is discussed in the thesis as well. Eventually, the conclusions and suggestions are made with respect to macroeconomic policy and financial market as well as financial innovation.

Allocating production volumes across a portfolio of producing assets is a complex optimization problem. Each producing asset possesses different technical attributes (e.g. crude type), facility constraints, and costs. In addition, there are corporate objectives and constraints (e.g. contract delivery requirements). While complex, such a problem can be specified and solved using conventional deterministic optimization methods. However, there is often uncertainty in many of the inputs, and in these cases the appropriate approach is neither obvious nor straightforward. One of the major uncertainties in the oil and gas industry is the commodity price assumption(s). This paper investigates this problem in three major sections: (1) We specify an integrated stochastic optimization model that solves for the optimal production allocation for a portfolio of producing assets when there is uncertainty in commodity prices, (2) We then compare the solutions that result when different price models are used, and (3) We perform a value of information analysis to estimate the value of more accurate price models. The results show that the optimum production allocation is a function of the price model assumptions. However, the differences between models are minor, and thus the value of choosing the “correct” price model, or similarly of estimating a more accurate model, is small. This work falls in the emerging research area of decision-oriented assessments of information value. / text

Modern financial asset pricing theory is a broad, and at times, complex field. The literature review in this study covers many of the asset pricing techniques including factor models, random walk models, correlation models, Bayesian methods, autoregressive models, moment-matching models, stochastic jumps and mean reversion models. An important topic in finance is portfolio opti-misation with respect to risk and reward such as the mean variance optimisation introduced by Markowitz (1952). This study covers optimisation techniques such as single period mean variance optimisation, optimisation with risk aversion, multi-period stochastic programs, two-fund separa- tion theory, downside optimisation techniques and multi-period optimisation such as the Bellman dynamic programming model. The question asked in this study is, in the context of investing for South African individuals in a multi-asset portfolio, whether an active investment strategy is signi cantly di erent from a passive investment strategy. The passive strategy is built using stochastic programming with moment matching methods for non-Gaussian asset class distributions. The strategy is optimised in a framework using a downside risk metric, the conditional variance at risk. The active strategy is built with forward forecasts for asset classes using the time-varying transitional-probability Markov regime switching model. The active portfolio is finalised by a dynamic optimisation using a two-stage stochastic programme with recourse, which is solved as a large linear program. A hypothesis test is used to establish whether the results of two strategies are statistically different. The performance of the strategies are also reviewed relative to multi-asset peer rankings. Lastly, we consider whether the findings reveal information on the degree of effi ciency in the market place for multi-asset investments for the South African investor. / Operations Management / M. Sc. (Operations Research)

Le premier chapitre examine les caractéristiques statistiques à long terme des rendements financiers en France et aux USA. Les propriétés des différents actifs font apparaître qu’à long terme les actions procurent un risque sensiblement moins élevé. En outre, les propriétés de retour à la moyenne des actions justifient qu’elles soient utilisées dans une stratégie de cycle de vie comme « option par défaut » de plans d’épargne retraite. Le chapitre deux fournit une explication au débat sur l'hypothèse d’efficience des marchés. La cause du débat est souvent attribuée à la petite taille des échantillons et à la faible puissance des tests statistiques dédiés. Afin de contourner ce problème, nous utilisons l'approche développée par Campbell et Viceira (2005) qui utilisent une méthode VAR pour mettre en évidence l’existence de retour vers la moyenne dans le cours des actifs risqués.Le troisième chapitre évalue la vitesse de convergence des cours des actions. Un moyen classique pour caractériser la vitesse de retour vers la moyenne est la « demi-vie ». En comparant les indices boursiers de quatre pays développés (États-Unis, Royaume-Uni, France et Japon) sur la période 1950-2014, nous établissons une vitesse de convergence significative, avec une demi-vie entre 4,0 et 5,8 ans.Le dernier chapitre présente les résultats d'un modèle conçu pour étudier les interactions entre la démographie et les régimes de retraite. Afin d’étudier les risques inhérents à l’utilisation des revenus du capital pour financer les retraites, nous utilisons un « Trending OU process » au lieu d’un MBG classique pour modéliser les rendements. Pour un épargnant averse au risque le marché pourrait concurrencer les régimes par répartition. / Chapter one examines the long run statistical characteristics of financial returns in France and the USA for selected assets. This study clearly shows that the returns’ distributions diverge from the Gaussian strategy as regards longholding periods. Thereafter we analyze the consequences of the non-Gaussian nature of stock returns on default-option retirement plans.Chapter two provides a reasonable explanation to the strong debate on the Efficient Market Hypothesis. The cause of the debate is often attributed to small sample sizes in combination with statistical tests for mean reversion that lackpower. In order to bypass this problem, we use the approach developed by Campbell and Viceira (2005) who have settled a vectorial autoregressive methodology (VAR) to measure the mean reversion of asset returns.The third chapter evaluates the speed of convergence of stock prices. A convenient way to characterize the speed of mean reversion is the half-life. Comparing the stock indexes of four developed countries (US, UK, France and Japan) during the period 1950-2014, we establish significant mean reversion, with a half-life lying between 4,0 and 5,8 years.The final chapter provides some results from a model built in order to study the linked impacts of demography and economy on the French pension scheme. In order to reveal the risks that are contained in pension fund investment, we use a Trending Ornstein-Uhlenbeck process instead of the typical GBM for modeling stock returns. We find that funded scheme returns, net of management fees, are slightly lower thanthe PAYG internal rate of return.

本文之信用風險模型屬於簡約模型(Reduced Form Model)之範疇，以COX過程解釋違約過程，解釋為何企業會發生連帶倒閉的現象。在考慮信用風險後，各期所產生之現金流量變得具不確定性，因此在計算現金流量之現值時，折現因子就必須考慮信用風險溢酬，本文選用信用風險模型中的一大分支-約簡模型，將信用風險量化(包含系統風險及非系統風險)，進而估計出信用價差期間結構；就如同無風險利率期間結構對固定收益商品之重要性，在估計出公司之信用價差期間結構後，即可針對該公司發行之各種商品進行評價分析。本文並以花旗所羅門美邦控股公司為例進行實證，利用公司債理論價格與市價之誤差平方和，求解違約過程之參數估計值及信用價差期間結構；接著，針對花旗所羅門美邦控股公司所發行之連動債券〝TRAGETS〞，進行評價分析並比較考慮信用風險與否是否有助於理論價格與市價之配適。