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.

Gender differences in time allocation of poor children in Colombia

This paper studies the effect of credit constraints and constraints on transfers between parents and children, on differences in labor and schooling across children within the same household, with an application to gender. When families are unconstrained in these respects, differences in labor supply or education are driven by differences in wages or returns to education. If the family faces an imperfect capital market, the labor supply of each child is inefficient, but differences across children are still driven by comparative advantage. However, if interfamily transfers are constrained so that parents cannot offset inequality between their children, they will favor the human capital accumulation of the more disadvantaged child -generally the one who works more as a child. We use our theory to examine the gender gap in child labor. Using a sample of poor families in Colombia, we conform our predictions among rural households, although this is less clear for urban households. The gender gap is largely explained by the wage gap between girls and boys. Moreover, families with the potential to make capital transfers to adult children (e.g. those with large animals), can compensate adult sons for their greater child labor and reduced educational attainment. In such families, as predicted, the male/female labor gap is greater.