Bibliografia: p. 109-111 / Dissertação (mestrado) - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, 2014. / Estudamos a precificação de opções exóticas nos mercados de petróleo e de seus derivados. Iniciamos com uma análise exploratória dos dados, revisitando suas propriedades estatísticas e fatos estilizados relacionados às volatilidades e correlações. Subsidiados pelos resultados de tal análise, apresentamos alguns dos principais modelos forward para commodities e um vasto conjunto de estruturas determinísticas de volatilidades, bem como os respectivos métodos de calibragem, para os quais executamos testes com dados reais. Para melhorar o desempenho de tais modelos na precificação do smile de volatilidade, reformulamos o modelo de volatilidade estocástica de Heston para lidar com uma ou múltiplas curvas forward, permitindo sua utilização na precificação de contratos definidos sobre múltiplas commodities. Calibramos e testamos tais modelos a partir de dados reais dos mercados de petróleo, gasolina e gás, e comprovamos a sua superioridade frente aos modelos de volatilidade determinística. Para subsidiar a precificação de opções exóticas e contratos OTC, revisitamos dos pontos de vista teórico e prático assuntos como simulação de Monte Carlo, soluções numéricas para SDEs e exercício americano. Finalmente, por meio de uma bateria de simulações numéricas, mostramos como os modelos podem ser utilizados na precificação de opções exóticas que tipicamente ocorrem nos mercados de commodities, como as calendar spread options, crack spread options e as opções asiáticas. / We study the pricing of exotic options in the oil and its derivatives markets. We begin with a exploratory analysis of the data, revisiting statistical properties and stylized facts related to the volatilities and correlations. Based on this results, we present some of the main commodity forward models and a wide range of deterministic volatility structures, as well as its calibration methods, for which we ran tests with real market data. To improve the performance of such models in pricing the volatility smile, we reformulate the Heston stochastic volatility model to cope with one or multiple forward curves together, allowing its use for the pricing of multicommodity based contracts. We calibrate and test such models for the oil, gasoline and natural gas markets, confirming their superiority against deterministic volatility models. To support the tasks of exotic options and OTC contracts pricing, we also revisit, from the theoretical and practical points of view, tools and issues such as Monte Carlo simulation, numerical solutions to SDEs and American exercise. Finally, through a battery of numerical simulations, we show how the presented models can be used to price typical exotic options occurring in commodity markets, such as calendar spread options, crack spread options and Asian options.

M.Phil. / This research aims to establish and evaluate the main factors that influence the fuel industry in South Africa. The South African fuel industry, is influenced by different business, economical and logistical factors, which all contribute to a changing fuel environment as well as a changing fuel prices that vary on a monthly basis, as calculated by the Department of Mineral and Energy Affairs(DMEA). These factors including crude oil procurement, petroleum industry, synthetic fuel industry and geographical locations, are fundamentally important, and explained in more detail in the chapters to follow. Oil as main supply source to the fuel industry, plays a vital role to South Africa as industrial developing country. The crude oil imported from the eastern countries is refined into petroleum and alternative fuels, necessary to the economy. The oil price thus influences the petroleum price, which in turn influences the cost of food and accessories. This research will for this reason also focus on aspects such as the actual importation of crude oil, petroleum price structure, price zones, synfuels and alternative fuels, and the affect these aspects have on the fuel industry.