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.