Stochastic volatility (SV) models were introduced as a refinement that tried to correct the shortcomings of the standard Black-Scholes (1973) model for asset dynamics. One of the most popular choices is Heston’s (1993) square-root model, whose popularity is largely due to a closed form equation for pricing options. Thus, when the Mexican Stock Exchange introduced options over its main index (the IPC) in 2004, it chose Heston’s model to price them on days when there was no trading. I investigate whether Heston’s captures appropriately the dynamic behavior of the IPC and whether more elaborate models produce significantly different option prices. To do so, I use an MCMC technique to estimate four different SV models. I then use both classical and Bayesian diagnostics to compare the performance of the different models and find that indeed more elaborate models outperform Heston’s model. Finally, I use the transform analysis proposed by Duffie, Pan and Singleton (2000) to price the options under the different model specifications and show that prices implied by the models with jumps are significantly different to those implied by the model currently used by the exchange.
Work in Progress
L1 restrictions in behavioral portfolio choice for vast asset sets (Joint with Victor Chernozhukov)
It has been shown that the problem of portfolio choice faced by an 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. We present a portfolio construction procedure for this context using L1 penalized quantile regression methods and we explore the performance of these portfolios relative to their unrestricted counterparts.