The use of forward-looking information from option prices attracted a lot of attention after the 2008 financial crisis, which highlighting the difficulty of using historical data to predict extreme events. Although a considerable number of papers investigate extraction of forward-information from cross-sectional option prices, Figlewski (2008) argues that it is still an open question and none of the techniques is clearly superior. This thesis focuses on getting information from option prices and investigates two broad topics: applying machine learning in extracting state price density and recovering natural probability from option prices. The estimation of state price density (often described as risk-neutral density in the option pricing litera- ture) is of considerable importance since it contains valuable information about investors' expectations and risk preferences. However, this is a non-trivial task due to data limitation and complex arbitrage-free constraints. In this thesis, I develop a more efficient linear programming support vector machine (L1-SVM) estimator for state price density which incorporates no-arbitrage restrictions and bid-ask spread. This method does not depend on a particular approximation function and framework and is, therefore, universally applicable. In a parallel empirical study, I apply the method to options on the S&P 500, showing it to be comparatively accurate and smooth. In addition, since the existing literature has no consensus about what information is recovered from The Recovery Theorem, I empirically examine this recovery problem in a continuous diffusion setting. Using the market data of S&P 500 index option and synthetic data generated by Ornstein-Uhlenbeck (OU) process, I show that the recovered probability is not the real-world probability. Finally, to further explain why The Recovery Theorem fails and show the existence of associated martingale component, I demonstrate a example bivariate recovery.

[pt] Esta pesquisa modela a estratégia exploratória sequencial de prospectos de óleo e gás em diferentes níveis de incerteza. Considera a consolidação da carteira pelo conceito de revelação da informação e as vantagens do uso da teoria do Valor da Informação para a sequência ótima de perfuração. Inclui a incerteza de preços com o Movimento Geométrico Browniano para o preço spot do barril de petróleo. Dado o tempo do contrato de concessão de exploração de petróleo, são analisados os valores das opções de investir nos ativos e no portfólio exploratório. Além dessas incertezas, o modelo considera o efeito competitivo de outra empresa em um jogo conhecido como Guerra de Atrito, examinado com uso de diversos estudos de caso. Esse jogo ocorre quando os ativos têm correlações e as empresas aguardam informação pública e gratuita de ocorrência de hidrocarboneto da perfuração do ativo pela operadora vizinha. Os resultados apontam que é melhor para a empresa analisar suas oportunidades exploratórias com a teoria das opções reais, sendo melhor a análise por portfólio exploratório, que combina o valor da espera com o valor da informação. Os efeitos da interação estratégica são relevantes, essencialmente quando os portfólios das duas empresas têm os gatilhos exploratórios similares. Em jogos assimétricos, o que define a degeneração para ação de perfurar de uma das operadoras é a relação entre os gatilhos exploratórios e os gatilhos de perfuração simultânea, efeito que também pode ser analisado na comparação do benefício da espera por informações das empresas em conflito. Caso haja perpetuação na guerra de atrito, é proposto uma mudança para o jogo de barganha cooperativa. Nessa mudança, deve haver troca de informações entre as empresas em negociação, sendo a informação privada de melhor qualidade que a informação pública, elevando a medida de aprendizado dos ativos da carteira. No caso de pequena melhora na medida de aprendizado, a mudança para a barganha cooperativa já se torna vantajosa para ambos os jogadores. / [en] This research models the sequential exploratory strategy of oil and gas prospects at different levels of uncertainty. To do so, it considers portfolio consolidation by the concept of information disclosure and the advantages of using Information Value theory for the optimal drilling sequence. The price uncertainty of the spot price of a barrel of oil is modeled as a Geometric Brownian Motion. Given the length of the oil exploration concession contract, the option values of investing in the assets and exploration portfolio are analyzed. In addition to these uncertainties, the model considers the competitive effect of another company in a game known as the War of Attrition, examined using several case studies. This game occurs when assets are correlated, and companies wait as free-riders for information of hydrocarbon occurrence from the drilling of the asset by the neighboring operator. The results point out that the firm should analyze its exploratory opportunities under the real options approach, and improves with exploratory portfolio analysis, which combines the value of waiting with the value of information. The impact of strategic interactions is relevant, especially when the two firms portfolios have similar exploratory triggers. In asymmetric games, the ratio between the exploratory triggers and the simultaneous drilling triggers defines the degeneration to drilling action of one of the operators. This effect can also be analyzed when comparing the benefit of waiting for information from the conflicting companies. If there is perpetuation in the war of attrition, agents can change to a cooperative bargaining game. In this case, there should be an information exchange between the trading firms, with private information being more relevant than public information. In the case of a marginal improvement in the learning measure, the change to cooperative bargaining already becomes advantageous for both players.