Hedging Options in a GARCH Environment: Testing the Term Structure of Stochastic Volatility Models

This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

The topology, geometry and conformal structure of properly embedded minimal surfaces

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies, for instance, that the surface can have at most two limit ends (at the top and bottom of the ordering), which is a strong topological restriction. There are also restrictions on the asymptotic geometry and conformal structure of such a surface: for example, we prove that if the surface has exactly two limit ends (as do the classical Riemann Staircase examples), then it is recurrent (that is, almost all Brownian paths are dense in the surface, and in particular any positive harmonic function on the surface is constant). These results have played an important role in the proof of several recent advances in the theory, including the uniqueness of the helicoid, the invariance of flux for a coordinate function on a properly immersed minimal surface, and the topological classification of properly embedded minimal surfaces

Health, Climate and Development in Brazil: A Cross-Section Analysis

This study uses a cross-section of Brazilian municipal data in an attempt to estimate the impact of climate changes on the pattern of disease morbidity and infant mortality. Brazil is a country with climate conditions that range from tropical rain forest to temperate savanna regions in the southern part of the country. When one travels from north to south and west to east, and from sea level to altitudes of 1,300 meters, it is possible to examine the results of a stochastic process and a range of global warming experiences. Therefore looking at the relationship between health and climate in Brazil could help to explain the impact of climate change on the health of the population. The objective of this study is to understand the relationship between health and climate after taking into account the interaction between man and nature represented by the level of economic development and the effects of policies to create a more (or less) adequate life environment.