Pricing and Hedging under Processes with Conditional Independent Increments

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Olivares, Pablo PIN: 346658The general objective of the proposal is to develop techniques to price multidimensional derivative contracts and methods to obtain adaptive hedging strategies when the dynamic of the underlying assets is described by stochastic processes with conditional independent increments (PCII).The proposal is divided in four interacting components with specific objectives: asset modelling, approximating pricing methods, adaptive hedging strategies and applications to energy and environmental finance.Original contributions to scientific knowledge can be found in five main directions related with these components. Theoretical properties of new models, such as integrated characteristic functions, equivalent martingale measures, subordination, asymptotic behavior, mixed moments and first exit probability distributions will be investigated. Next, existing techniques for pricing will be adapted under the new circumstances. A combination of Fast Fourier methods, Taylor and other polynomial approximations, together with saddlepoint techniques will be taken into account. They are planned to be implemented to most common multidimensional derivatives, starting with European type contracts, and then considering Barriers and Defaultable Bonds, to Credit Derivatives Swaps (CDS), where default is given by PCII models. A novel method for hedging is proposed, where adaptive parameter estimation is studied from an optimal control perspective. Parameter estimation techniques based on approximated characteristic functions and a non parametric point of view will be developed at this stage. Finally, applications to the energy and the emerging environmental financial sectors will be explored, always under the new models in the class of PCIIs. It includes the pricing of real options with oil, heating oil and gasoline as underlying, as well as electricity prices.The relevance of this research proposal lies in the novelty of the mathematics models considered as well as in the original implementation of approximated closed pricing formulas and adaptive hedging strategies derived from them. It may have a potential impact in financial institutions, specifically in the important Canadian energy sector, as it provides practitioners with more accurate tools and faster algorithm to evaluate investment positions based on multidimensional derivative products.Results of the research will be incorporated to the existing programs in Financial Mathematics at Ryerson University, at undergraduate and graduate levels. It will be reflected in the development of our research group, the training of approximately 15 HQP, publication of 10 scientific papers in main stream journals as well as a general improvement in curricular activities.The project viability is supported by author's past experience. The author has an ample base of collaborators at Ryerson University, University of Toronto, University of Montreal, Technical University of Munich, Florida International University, Autonomous Mexican Technological Institute among others. Students will be incorporated at all stages, with special emphasis in applications to energy and environmental finance.