Preprint B76/2015
Precificação de Derivativos Exóticos no Mercado de Petróleo
Diogo Barboza Gobira
Keywords: Commodities | forward models | stochastic volatility | exotic options | heston

We study the pricing of exotic options in the oil and its derivatives markets. We begin with a data exploratory analysis, revisiting statistical properties and stylized facts related to the volatilities and correlations. Subsidized by this analysis 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 togheter, allowing its use for the pricing of multi-commodity based contracts. We calibrate and test such models for the oil, gasoline and natural gas markets, proving their superiority against deterministic volatility models. To support the tasks of exotic options and OTC contracts pricing, we also revisit, from a 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 the commodities markets, such as calendar spread options, crack spread options and asian options.