Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Assessing the influence of dam construction on the spatial and temporal evolution of population density across the United States of America

Finding the optimum location for placing a dam on a river is usually a complicated process which generally forces thousands of people to flee their homes because they will be inundated during the filling of the dam. Dams could also attract people living in the surrounding area after their construction. The goal of this research is to check for dam attractiveness for people by comparing growth rates of population density in surrounding areas after dam construction to those associated with the period antecedent to the dam construction. To this aim, 1859 dams across the United States of America and high-resolution population distribution from 1790 to 2010 are examined. By grouping dams as a function of their main purpose, water supply dams are found to be, as expected, the most attractive dams for people, with the biggest growth in population density. Irrigation dams are next, followed by hydroelectricity, flood control, Navigation, and finally Recreation dams. Fishery dams and dams for other uses suffered a decrease in population in the years after their construction. The regions with the greatest population growth were found approximately 40-45 km from the dam and at distances greater than 90 km, whereas the regions with the greatest population decline or only a modest gain were located within 10-15 km of the dam.

Analysis of human posterior EEG alpha frequency as a function of implicit learning of probabilistic lateralized stimuli in a visual detection task

Alpha oscillatory activity has long been associated with perceptual and cognitive processes related to attention control. The aim of this study is to explore the task-dependent role of alpha frequency in a lateralized visuo-spatial detection task. Specifically, the thesis focuses on consolidating the scientific literature's knowledge about the role of alpha frequency in perceptual accuracy, and deepening the understanding of what determines trial-by-trial fluctuations of alpha parameters and how these fluctuations influence overall task performance. The hypotheses, confirmed empirically, were that different implicit strategies are put in place based on the task context, in order to maximize performance with optimal resource distribution (namely alpha frequency, associated positively with performance): “Lateralization” of the attentive resources towards one hemifield should be associated with higher alpha frequency difference between contralateral and ipsilateral hemisphere; “Distribution” of the attentive resources across hemifields should be associated with lower alpha frequency difference between hemispheres; These strategies, used by the participants according to their brain capabilities, have proven themselves adaptive or maladaptive depending on the different tasks to which they have been set: "Distribution" of the attentive resources seemed to be the best strategy when the distribution probability between hemifields was balanced: i.e. the neutral condition task. "Lateralization" of the attentive resources seemed to be more effective when the distribution probability between hemifields was biased towards one hemifield: i.e., the biased condition task.