Essays on financial economics

Abstract

This thesis consists of three independent essays on Financial Economics. In chapter one I investigate the possible mispricing of European-style options in the Mexican Stock Exchange. The source of this problem is that when the Mexican Stock Exchange introduced options over its main index (the IPC) in 2004, it chose Heston's (1993) "square root" stochastic volatility model to price them on days when there was no trading. I investigate whether Heston's model is a good specification for the IPC and whether more elaborate models produce significantly different option prices. To do so, I use an MCMC technique to estimate four different models within the stochastic volatility family. I then present both classical and Bayesian diagnostics for the different models. Finally, I use the transform analysis proposed by Duffie, Pan and Singleton (2000) to price the options and show that the prices implied by the models with jumps are significantly different from those implied by the model currently used by the exchange. Next, I turn to a problem in behavioral portfolio choice: It has been shown that the portfolio choice problem faced by a behavioral agent that maximizes Choquet expected utility is equivalent to solving a quantile linear regression. However, if the agent faces a vast set of assets or when transaction fees are considerable, it becomes optimal for the agent to take non-zero positions on only a subset of the available assets. Thus, in chapter 2, I present a portfolio construction procedure for this context using Li penalized quantile regression methods and explore the performance of these portfolios relative to their unrestricted counterparts. In chapter three, co-authored with Victor Chernozhukov, we present the Extended Pareto Law as an alternative for modeling operational losses. Through graphical examination and formal goodness of fit tests we show that it outperforms the main parsimonious alternative, Extreme Value Theory, in terms of statistical fit. Finally, we show that using the Extended Pareto Law as a modeling technique also leads to reasonable capital requirements.