Abstract types and distributions in independent private value auctions

In this note, in an independent private values auction framework, I discuss the relationship between the set of types and the distribution of types. I show that any set of types, finite dimensional or not, can be extended to a larger set of types preserving incentive compatibility constraints, expected revenue and bidder’s expected utilities. Thus for example we may convexify a set of types making our model amenable to the large body of theory in economics and mathematics that relies on convexity assumptions. An interesting application of this extension procedure is to show that although revenue equivalence is not valid in general if the set of types is not convex these mechanism have underlying distinct allocation mechanism in the extension. Thus we recover in these situations the revenue equivalence.

Caracterização dos retornos e das volatilidades de ativos financeiros do mercado Brasileiro : uma abordagem baseada na volatilidade realizada

The goal of this paper is twofold. First, using five of the most actively traded stocks in the Brazilian financial market, this paper shows that the normality assumption commonly used in the risk management area to describe the distributions of returns standardized by volatilities is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when the information contained in high frequency data is used to construct the realized volatilies measures, we attain the normality of the standardized returns, giving promise of improvements in Value at Risk statistics. We also describe the distributions of volatilities of the Brazilian stocks, showing that the distributions of volatilities are nearly lognormal. Second, we estimate a simple linear model to the log of realized volatilities that differs from the ones in other studies. The main difference is that we do not find evidence of long memory. The estimated model is compared with commonly used alternatives in an out-of-sample experiment.