Valoración de opciones bajo el modelo de Kou aplicando transformada de Fourier

En esta Tesis se presenta el modelo de Kou, Difusión con saltos doble exponenciales, para la valoración de opciones Call de tipo europeo sobre los precios del petróleo como activo subyacente. Se mostrarán los cálculos numéricos para la formulación de expresiones analíticas que se resolverán mediante la implementación de algoritmos numéricos eficientes que conllevaran a los precios teóricos de las opciones evaluadas. Posteriormente se discutirán las ventajas de usar métodos como la transformada de Fourier por la sencillez relativa de su programación frente a los desarrollos de otras técnicas numéricas. Este método es usado en conjunto con el ejercicio de calibración no paramétrica de regularización, que mediante la minimización de los errores al cuadrado sujeto a una penalización fundamentada en el concepto de entropía relativa, resultaran en la obtención de precios para las opciones Call sobre el petróleo considerando una mejor capacidad del modelo de asignar precios justos frente a los transados en el mercado.

The environmental impact of civil conflict : the deforestation effect of paramilitary expansion in Colombia

Despite a growing body of literature on how environmental degradation can fuel civil war, the reverse effect, namely that of conflict on environmental outcomes, is relatively understudied. From a theoretical point of view this effect is ambiguous, with some forces pointing to pressures for environmental degradation and some pointing in the opposite direction. Hence, the overall effect of conflict on the environment is an empirical question. We study this relationship in the case of Colombia. We combine a detailed satellite-based longitudinal dataset on forest cover across municipalities over the period 1990-2010 with a comprehensive panel of conflict-related violent actions by paramilitary militias. We first provide evidence that paramilitary activity significantly reduces the share of forest cover in a panel specification that includes municipal and time fixed effects. Then we confirm these findings by taking advantage of a quasi-experiment that provides us with an exogenous source of variation for the expansion of the paramilitary. Using the distance to the region of Urab´a, the epicenter of such expansion, we instrument paramilitary activity in each cross-section for which data on forest cover is available. As a falsification exercise, we show that the instrument ceases to be relevant after the paramilitaries largely demobilized following peace negotiations with the government. Further, after the demobilization the deforestation effect of the paramilitaries disappears. We explore a number of potential mechanisms that may explain the conflict-driven deforestation, and show evidence suggesting that paramilitary violence generates large outflows of people in order to secure areas for growing illegal crops, exploit mineral resources, and engage in extensive agriculture. In turn, these activities are associated with deforestation.