Detta arbete utförs efter en förfrågan från Uddeholm Tooling om att försöka kartlägga riskerna på inköpsmarknaden för metallerna krom, molybden och vanadin. Då detta anses vara mycket svårt föreslås här istället en kartläggning av marknaden för respektive metall, detta för att ge en bild av hur marknaden ser ut och vilka aktörer som finns.Frågorna som behandlas är var bryts, förädlas, konsumeras respektive metall? Hur varierar priserna, beskrivs priserna bäst med en random walk eller med en mean reverting stokastisk process.Det visar sig relativt snart att det är mycket problematiskt att inhämta relevant data. Speciellt då dessa metaller inte handlas öppet utan där kontrakten mellan köpare och säljare är konfidentiella. Priserna som rapporteras baseras på månatliga intervjuer med köpare, säljare och traders som utförs av branschmagasin. Detta leder till att det rapporterade priset ofta är stationärt under långa tidsperioder, det kan emellertid antas att det reella priset är betydligt mer volatilt och förändras från dag till dag. Dessa metaller kan även handlas i olika typer av föreningar och med olika renhetsgrader vilket ytligare försvårar studierna. Då det inte finns en marknadsplats där metallerna kan handlas kan även antagas att priset kan skilja sig beroende på var och av vem man köper.Detta leder till att det statistiska test som genomfördes i denna studie fick ett ofullständigt resultat, med låg korrelation mellan modell och verklighet. Det gick därför inte att avgöra om priset kan beskrivas som mean reverting. Andra studier pekar dock på att mean reversion är en mer träffsäker stokastisk process för att beskriva priserna på dessa metaller än vad än random walk är.En kartläggning av marknaden för dessa metaller visar tydligt att Kina är en signifikant aktör i samtliga fall. Då alla tre metaller främst används som legeringsämne i konstruktions- och rostfrittstål har dessa marknader stor betydelse för marknaden för respektive metall. Kina är den största konsumenten och producenten av både rostfritt och konstruktionsstål, dessutom är Kina stora vid framställningen av respektive metall. Resultatet visar på tydliga kopplingar mellan priset på respektive metall och på Kinas ökande konsumtion av stål.

Yes / A key prediction of the Capital Asset Pricing Model (CAPM) is that idiosyncratic risk is not priced by investors because in the absence of frictions it can be fully diversified away. In the presence of constraints on diversification, refinements of the CAPM conclude that the part of idiosyncratic risk that is not diversified should be priced. Recent empirical studies yielded mixed evidence with some studies finding positive correlation between idiosyncratic risk and stock returns, while other studies reported none or even negative correlation. We revisit the problem whether idiosyncratic risk is priced by the stock market and what are the probable causes for the mixed evidence produced by other studies, using monthly data for the US market covering the period from 1980 until 2013. We find that one-period volatility forecasts are not significantly correlated with stock returns. The mean-reverting unconditional volatility, however, is a robust predictor of returns. Consistent with economic theory, the size of the premium depends on the degree of 'knowledge' of the security among market participants. In particular, the premium for Nasdaq-traded stocks is higher than that for NYSE and Amex stocks. We also find stronger correlation between idiosyncratic risk and returns during recessions, which may suggest interaction of risk premium with decreased risk tolerance or other investment considerations like flight to safety or liquidity requirements. The difference between the correlations of the idiosyncratic volatility estimators used by other studies and the true risk metric the mean-reverting volatility is the likely cause for the mixed evidence produced by other studies. Our results are robust with respect to liquidity, momentum, return reversals, unadjusted price, liquidity, credit quality, omitted factors, and hold at daily frequency. / National Research Foundation of Korea (2016S1A2A2912265)

The main target of this thesis is to summarize and explain the specifics of power markets and test application of models, which might be used especially in risk management area. Thesis starts with definition of market subjects, typology of traded contracts and description of market development with focus on Czech Republic. Thesis continues with development of theoretical concepts of short term/spot electricity markets and potential link between spot and forward electricity markets. After deriving of those microeconomic fundamental models we continue with stochastic models (Jump Diffusion Mean Reverting process and Extreme Value Theory) in order to depict patterns of spot and forward power contracts price volatility. Last chapter deals with credit risk specifics of power trading and develops model (using concept known as Credit Value Adjustment) to compare economic efficiency of OTC and exchange power trading. Developed and described models are tested on selected power markets, again with focus on Czech power market data set.

整體而言，會計盈餘提供財務報表使用者有關於企業獲利能力之相關資訊。然而，由於會計盈餘同時包含了雜訊 (noises) 與偏差 (biases)，因而影響到會計盈餘對公司獲利能力評價的正確性。因此，過去的會計文獻發展出不同的盈餘管理估計模型 (如: Healy 1985; DeAngelo 1986; Friedlan 1994; DeFond and Jiambalvo 1994 以及Dechow, Sloan and Sweeney 1995)，以嘗試去除這些雜訊與偏差。然而，究竟哪一個估計模型能夠提供最為純淨之非裁量性淨利 (nondiscretionary income) 的衡量指標，則並無定論。在效率市場 (market efficiency) 的假說下，本研究透過本益比 (P/E ratio) 的平均數復歸 (mean-reverting) 現象來評比五種盈餘管理估計模型。由於過去的文獻同時發現盈餘成長率與風險係數均會影響本益比的高低，因此，本研究同時將這兩個變數納入考量。 　　實證結果發現，依照上述五種盈餘管理估計模型所估計之本益比皆有平均數復歸的現象。其中Friedlan (1994) 模型在全體樣本與控制盈餘成長率之後，其本益比平均數復歸現象均較其他模型為快；次佳之盈餘管理估計模型為DeFond and Jiambalvo (1994) 與Dechow et al. (1995) 兩模型；最差的則為 Healy (1985) 模型。 / Overall speaking, accounting earnings provide financial statement users with useful information about a firm's profitability. However, because of the biases and noises included in the accounting earnings, the accuracy and reliability of accounting earnings to the evaluation of a firm's profitability may be adversely influenced. In light of this, prior earnings management studies have developed various estimation models of nondiscretionary income (e.g., Healy 1985; DeAngelo 1986; Friedlan 1994; DeFond and Jiambalvo 1994; Dechow, Sloan & Sweeney 1995) with an attempt to remove the biases and noises embedded in the accounting earnings. Nonetheless, there is no consistent empirical evidence about the relative performance of these estimation models. Assuming market efficiency, the main purpose of this study is to utilize the mean-reverting phenomenon of P/E ratios to evaluate the relative performance of these models. Since prior studies have found that earnings growth rate and risk coefficient may affect the magnitude of P/E ratios, we also control for these two variables in our analyses. 　　The empirical results reveal several findings. First, P/E ratios calculated using different earnings management estimation models exhibit the mean-reverting phenomenon. Second, the Friedlan (1994) model has the best performance among all models when we use the overall sample and three subsamples grouped based on the earnings growth rate. In addition, the DeFond and Jiambalvo (1994) and Dechow, Sloan & Sweeney (1995) models perform moderately. Finally, the Healy (1985) model shows the worst performance.

Les principaux thèmes de cette thèse sont la théorie des trajectoires rugueuses développée par T. Lyons (1998) et ses applications, notamment à l'étude des équations différentielles stochastiques (EDS) et au calcul de sensibilités. Des applications potentielles des résultats théoriques en science du vivant et en finance y sont également développés. En premier lieu, sont étendues l'existence et l'expression des grecques Delta et Véga, sensibilités bien connues en finance, pour des EDS à coefficients bornés et dirigées par un processus gaussien multidimensionnel centré, à trajectoires continues, au-dessus duquel il existe une trajectoire géométrique naturelle. Le cas du mouvement brownien fractionnaire a particulièrement été développé afin de proposer d'une part, une application du calcul de Véga dans un modèle de marché financier à volatilité stochastique fractionnaire et d'autre part, d'effectuer des simulations. En second lieu, est étudiée une généralisation d'équation mean-reverting au cas d'un signal gaussien unidimensionnel, centré et à trajectoires continues : existence globale et unicité de la solution, intégrabilité, continuité et différentiabilité de l'application d'Itô, existence d'un schéma d'approximation convergeant dans tous les Lp avec une vitesse de convergence presque-sure, un principe de grandes déviations et, l'existence d'une densité par rapport à la mesure de Lebesgue. L'étude de cette famille d'EDS a débouché sur une application en pharmacocinétique.

Multi-period portfolio optimization (MPO) has gained a lot of interest in modern portfolio theory due to its consideration for inter-temporal trading e effects, especially market impacts and transactions costs, and for its subtle reliability on return predictability. However, because of the heavy computational demand, portfolio policies based on this approach have been sparsely explored. In that regard, a tractable MPO framework proposed by N. Gârleanu & L. H. Pedersen has been investigated. Using the stochastic control framework, the authors provided a closed form expression of the optimal policy. Moreover, they used a specific, yet flexible return predictability model. Excess returns were expressed using a linear factor model, and the predicting factors were modeled as mean reverting processes. Finally, transactions costs and market impacts were incorporated in the problem formulation as a quadratic function. The elaborated methodology considered that the market returns dynamics are governed by fast and slow mean reverting factors, and that the market transactions costs are not necessarily quadratic. By controlling the exposure to the market returns predicting factors, the aim was to uncover the importance of the mean reversion speeds in the performance of the constructed trading strategies, under realistic market costs. Additionally, for the sake of comparison, trading strategies based on a single-period mean variance optimization were considered. The findings suggest an overall superiority in performance for the studied MPO approach even when the market costs are not quadratic. This was accompanied with evidence of better usability of the factors' mean reversion speed, especially fast reverting factors, and robustness in adapting to transactions costs. / Portföljoptimering över era perioder (MPO) har fått stort intresse inom modern portföljteori. Skälet till detta är att MPO tar hänsyn till inter-temporala handelseffekter, särskilt marknadseffekter och transaktionskostnader, plus dess tillförlitlighet på avkastningsförutsägbarhet. På grund av det stora beräkningsbehovet har dock portföljpolitiken baserad på denna metod inte undersökts mycket. I det avseendet, har en underskriven MPO ramverk som föreslagits av N.Gârleanu L. H. Pedersen undersökts. Med hjälp av stokastiska kontrollramen tillhandahöll författarna formuläret för sluten form av den optimala politiken. Dessutom använde de en specifik, men ändå flexibel returförutsägbarhetsmodell. Överskjutande avkastning uttrycktes med hjälp av en linjärfaktormodell och de förutsägande faktorerna modellerades som genomsnittligaåterföringsprocesser. Slutligen inkorporerades transaktionskostnader och marknadseffekter i problemformuleringen som en kvadratisk funktion. Den utarbetade metodiken ansåg att marknadens avkastningsdynamik styrs av snabba och långsammaåterhämtningsfaktorer, och att kostnaderna för marknadstransaktioner inte nödvändigtvis är kvadratiska. Genom att reglera exponeringen mot marknaden återspeglar förutsägande faktorer, var målet att avslöja vikten av de genomsnittliga omkastningshastigheterna i utförandet av de konstruerade handelsstrategierna, under realistiska marknadskostnader. Dessutom, för jämförelses skull, övervägdes handelsstrategier baserade på en enstaka genomsnittlig variansoptimering. Resultaten tyder på en överlägsen överlägsenhet i prestanda för det studerade MPO-tillvägagångssättet, även när marknadsutgifterna inte är kvadratiska. Detta åtföljdes av bevis för bättre användbarhet av faktorernas genomsnittliga återgångshastighet, särskilt snabba återställningsfaktorer och robusthet vid anpassning till transaktionskostnader

Schwarz (1997)提出均數回復過程（Mean-Reverting Process, MR）捕捉能源價格的動態過程，而Lucia and Schwarz (2002)將此模型結合確定季節性函數，並推導出期貨價格封閉解。然而，能源價格常會因為未預期事件的發生而產生大幅度的變動，為了描述價格跳躍的現象，Clewlow and Strickland (2000)延伸Schwarz的模型提出均數回復跳躍擴散模型（Mean-reverting jump diffusion process, MRJD），此模型除了保留均數回復模型對能源價格會回復至長期水準的描述外，再加上跳躍項來描述價格的異常變動。而Cartea and Figueroa (2005)則同時考慮季節性和跳躍因子，並推導出期貨價格封閉解。另外，雖然台灣目前並非京都議定書所規範的國家，但環境保護是未來的趨勢，故在衡量能源產業財務風險時，除了考慮相關原料和產品，應考慮碳權交易之影響。為了探討財務風險管理在能源產業之應用，本文以煉油廠為例，將其表示成特定期貨部位的投資組合，並透過計算投資組合風險值來衡量煉油廠的財務風險。文中使用結合季節性的均數回復過程、均數回復跳躍擴散過程進行模型配適。實證結果顯示，均數回復跳躍擴散模型在回溯測試下表現最佳；另外，考慮碳權交易後會使得煉油廠的財務風險上升。 / Schwarz (1997) proposes the mean-reverting process (MR) to model energy spot price dynamics, and Lucia and Schwarz (2002) extend this model by including mean reversion and a deterministic seasonality. This model can capture the mean-reversion of energy price, but fail to account for the huge and non-negligible price movement in the market. Clewlow and Strickland (2000) extend Schwarz’s model to mean-reverting jump diffusion process (MRJD). Cartea and Figueroa (2005) present a model which captures the most importance characteristics of energy spot prices such as mean reversion, jumps and seasonality, and provide a closed-form solution for the forward. Although Taiwan is not the member of Kyoto Protocol, but Environmental Protection is a trend in the future. In order to measure the financial risk induced by energy industries, we should consider the effect of emission trading. In this paper, we discuss the implication of financial risk management in energy industries by analyzing the exposure of refinery which represented certain energy futures portfolios. We use MR and MRJD process with seasonality to model energy spot price dynamics, and calibrate the parameters to historical data. And, we consider the interaction of all of positions and calculate the Value-at-Risk of portfolios. The results show that among various approaches the MRJD presents more efficient results in back-testing, and emission trading poses additional risk factors which will increase the financial risk for refineries.

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No. of bitstreams: 1 alexandreribeiroscarcioffolo.pdf: 4637086 bytes, checksum: cbb9a83bf6c45d454a12c1cc4deec75e (MD5) Previous issue date: 2015-05-13 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesse estudo analisamos o caso de um projeto de parque eólico participante do mercado atacadista de compra e venda de eletricidade no Estado de Ohio (EUA) em dois cenários: (1) alugando o terreno de instalação do parque (prática atual) e (2) comprando o terreno de instalação visando a operação no mercado agrícola do milhono intuito de diminuir, pelo mecanismo da diversificação, os riscos da geração de receita pelo parque eólico, com a flexibilidade de esperar o melhor momento para investir, o que só irá acontecer nos cenários em que o valor presente dos fluxos de caixa for igual ou superior ao investimento inicial. Dois horizontes de operação (20 e 30 anos) serão considerados. A avaliação financeira foi baseada na Teoria das Opções Reais, que permite a consideração das flexibilidades gerenciais no valor do projeto. Uma importante inovação do trabalho consiste na incorporação de fatores sazonais nos saltos dos preços da eletricidade no Estado de Ohio, adaptando o processo estocástico de geração de preços para a realidade do mercado. Além disso, o presente estudo analisou uma nova possibilidade para os geradores eólicos, que consiste na compra do terreno de instalação visando a operação no mercado agrícola do milho. Foram consideradas como incertezas os preços da eletricidade um dia a frente do mercado atacadista no Estado de Ohio (LMP) e o preço do grão do milho recebido pelo produtor. Para o LMP, foi adotado o Modelo Geométrico de Reversão a Média com Saltos de Clewlow, Strickland e Kaminski (2000), com as devidas modificações sazonais, e para o preço do grão de milho foi utilizado o Modelo Geométrico de Reversão a Média 1 de Schwartz. Os resultados indicam que o projeto eólico no primeiro cenárioe em ambos os horizontes de operação não apresenta viabilidade financeira, sendo exercida a opção de espera por novas informações. Tal fato pode ser explicado pelo baixo valor do preço da eletricidade no mercado atacadista e pelo perfil ineficiente de geração da região, além da recente eliminação do subsídio PTC. Em relação ao segundo cenário, houve apenas um momento na simulação na qual houve níveis de preços capazes de gerar um projeto financeiramente viável em ambos os horizontes de operação. Contudo, mesmo a regra de decisão do segundo cenário apresentando um cenário com valor positivo, a opção de espera para realizar o investimento se apresenta como a melhor escolha do investidor, pois a probabilidade de ocorrência de tais níveis de preços são ínfimas. A comparação entre os dois cenários demonstrou que a incorporação do terreno pelo investidor é melhor que o aluguel, em ambos os horizontes de operação e em todos os momentos da simulação. Entretanto, ainda assim, a instalação de parques eólicos no norte do Estado de Ohio operando no mercado atacadista é financeiramente inviável, mesmo havendo um incremento na diversificação do projeto. Tal resultado sinaliza que o setor não está preparado para operar no mercado atacadista no norte do Estado de Ohio, havendo a necessidade de novos esforços para que isso ocorra, a despeito do governo americano vir trabalhando para aumentar a participação das renováveis na matriz energética americana (o principal programa adotado pelo Estado de Ohio, Renewable Portfolio Standards - RPS, pretende aumentar a partição das renováveis em 12,5% até o ano de 2024). / In this study we analyze the case of a wind energy generator’s project, which is a wholesale market participant in the Ohio electricity market in two scenarios: 1) renting the land of the turbines installation (usual practice), and 2) buying the land in order to commercialize the corn grain productionshortening the revenue risk by diversification mechanism. Both scenarios havea flexibility to wait the right moment to invest, in which it will happen when the present value of the cash flow is greater than the initial cost of installation. Two horizons of production, 20-years and 30-years, will be considerate in this study. The financial viability was based on Real Options Theory, which allows the consideration of managerial flexibility in the project value. An important innovation of the study consists in the incorporation of a seasonal factor of the spikes of Ohio electricity prices, adapting the stochastic process of generation prices to market reality. Also, the study analyzed a new possibility to the wind energy generator’s projects, in which the investor would buy the land of turbines installation in order to operate at the corn grain market. The electricity prices at the Ohio wholesale market, LMP, and the price of corn grain received by the farmers are the uncertainties considered in this study.The stochastic process to simulate LMP was the mean-reverting jump diffusion model of Clewlow, Strickland and Kaminski (2000), with seasonal changes, and the corn price uncertainty, was based on Schwartz 1 Mean Reversion Model. The results indicate that the wind energy generator’s project at the first scenario and at both production horizons, 20-years and 30-years, does not present financial viability, in which the flexibility of waiting the right moment to invest still on. It could be explained by the lower price levels of the electricity wholesale market, and the inefficient generation profile of the project region. In addition, the PTC elimination could affect the result. The second scenario provided a slightly different result. On the second scenario, there was only one moment at the price simulation, in which there were price levels capable of generating a financially viable project in both operating horizons. Yet, even the second scenario decision rule presented a scenario with a positive value, the wait option to carry out the investment itself is the best choice of the investor, because the likelihood of such price levels are negligible. The comparison between the two scenarios demonstrated that the incorporation of land by investor generated a positive value to the project, in which those results are greater than the first scenario at both production horizons, 20-years and 30-years, and at all price simulations. Therefore, the present study demonstrated that the wind energy generator’s project in Northern Ohio operating at the wholesale electricity market is cost-prohibitive, even with the increasing of diversification.This result indicates that the wind energy generators are not prepared to just operate at the wholesale electricity market in Northern Ohio, indicating the sector needs new efforts to make this a real possibility, despite the US government has been working to increase the share of renewable energy sources in the US (the main program adopted by the State of Ohio, renewable Portfolio Standards - RPS, aims to increase renewable partition by 12.5% by the year 2024).

<p>In this thesis we investigate portfolio optimization under Value at Risk, Average Value at Risk and Limited expected loss constraints in a framework, where stocks follow a geometric Brownian motion. We solve the problem of minimizing Value at Risk and Average Value at Risk, and the problem of finding maximal expected wealth with Value at Risk, Average Value at Risk, Limited expected loss and Variance constraints. Furthermore, in a model where the stocks follow an exponential Ornstein-Uhlenbeck process, we examine portfolio selection under Value at Risk and Average Value at Risk constraints. In both geometric Brownian motion (GBM) and exponential Ornstein-Uhlenbeck (O.U) models, the risk-reward criterion is employed and the optimal strategy is found. Secondly, the Value at Risk, Average Value at Risk and Variance is minimized subject to an expected return constraint. By running numerical experiments we illustrate the effect of Value at Risk, Average Value at Risk, Limited expected loss and Variance on the optimal portfolios. Furthermore, in the exponential O.U model we study the effect of mean-reversion on the optimal strategies. Lastly we compare the leverage in a portfolio where the stocks follow a GBM model to that of a portfolio where the stocks follow the exponential O.U model.</p> / Master of Science (MSc)

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.