Bounds for the probability distribution function of the linear ACD process

This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.

Optimal auction with a general distribution: virtual valuation without densities

We characterize the optimal auction in an independent private values framework for a completely general distribution of valuations. We do this introducing a new concept: the generalized virtual valuation. To show the wider applicability of this concept we present two examples showing how to extend the classical models of Mussa and Rosen and Baron and Myerson for arbitrary distributions

Estimating Relative Risk Aversion, Risk-Neutral and Real-World Densities using Brazilian Real Currency Options

Building Risk-Neutral Densities (RND) from options data can provide market-implied expectations about the future behavior of a financial variable. And market expectations on financial variables may influence macroeconomic policy decisions. It can be useful also for corporate and financial institutions decision making. This paper uses the Liu et all (2007) approach to estimate the option-implied Risk-neutral densities from the Brazilian Real/US Dollar exchange rate distribution. We then compare the RND with actual exchange rates, on a monthly basis, in order to estimate the relative risk-aversion of investors and also obtain a Real-world density for the exchange rate. We are the first to calculate relative risk-aversion and the option-implied Real World Density for an emerging market currency. Our empirical application uses a sample of Brazilian Real/US Dollar options traded at BM&F-Bovespa from 1999 to 2011. The RND is estimated using a Mixture of Two Log-Normals distribution and then the real-world density is obtained by means of the Liu et al. (2007) parametric risktransformations. The relative risk aversion is calculated for the full sample. Our estimated value of the relative risk aversion parameter is around 2.7, which is in line with other articles that have estimated this parameter for the Brazilian Economy, such as Araújo (2005) and Issler and Piqueira (2000). Our out-of-sample evaluation results showed that the RND has some ability to forecast the Brazilian Real exchange rate. Abe et all (2007) found also mixed results in the out-of-sample analysis of the RND forecast ability for exchange rate options. However, when we incorporate the risk aversion into RND in order to obtain a Real-world density, the out-of-sample performance improves substantially, with satisfactory results in both Kolmogorov and Berkowitz tests. Therefore, we would suggest not using the “pure” RND, but rather taking into account risk aversion in order to forecast the Brazilian Real exchange rate.

Integral representation with convex capacities that are squeeze of (additive) probability measures

In this paper I will investigate the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function. Then I will present two alternatives forrnulations of the Choquet integral (and I will extend these forrnulations to the Choquet expected utility) in a parametric approach that will enable me to do comparative static exercises over the uncertainty aversion function in an easy way.

Asymmetric auctions and risk aversion within independent private valoues

We study tournaments with many ex-ante asymmetric (heterogeneous) contestants as an independent-private-values all-pay auction. The asymmetry is either with respect to the distribution of valuations for the prize or the risk preferences. By characterizing equilibria in tnonotone strategies we show that tournaments \:vith man~y heterogenous contestants are qualitatively distinct. First, with two (or many ex-ante identical) participants, a contestant always exerts some effort with positive probability. In contrast, with many asymmetric participants, one 1night not exert any effort at all, even if there is a positive probability that he has the highest valuation among ali. Second, in tournan1ents with t'wo (o r n1any ex-ante h01nogenous) contestants, equilibrium effort densities are decreasing. This prediction is at odds with experimental evidence that shows the empírica! density might be increasing at high effort levels. V\.lith rnany heterogeneous contestants, however. the increasing bid density is consistent with an equilibrium behavior.