Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model

Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulae are numerically equal to each other; an explicit derivation showing this equivalence is presented here.Comment: 4 pages, 1 figure, typeset with ReVTe

Time-Consistent No-Arbitrage Models of the Term Structure

We present an econometric procedure for calibrating no-arbitrage term structure models in a way that is time-consistent and robust to measurement errors. Typical no-arbitrage models are time-inconsistent because their parameters are assumed constant for pricing purposes despite the fact that the parameters change whenever the model is recalibrated. No-arbitrage models are also sensitive to measurement errors because they fit exactly each potentially contaminated bond price in the cross-section. We overcome both problems by evaluating bond prices using the joint dynamics of the factors and calibrated parameters and by locally averaging out the measurement errors. Our empirical application illustrates the trade-off between fitting as well as possible and overfitting the cross-section of bond prices due to measurement errors. After optimizing this trade-off, our approach fits almost exactly the cross-section of bond prices at each date and produces out-of-sample forecast errors that beat a random walk benchmark and are comparable to the results in the affine term structure literature. We find that non-linearities in the pricing kernel are important, lending support to quadratic term structure models.

Turbulent channel flow of dense suspensions of neutrally-buoyant spheres

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Phi=0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.Comment: Journal of Fluid Mechanics, 201

On the Relationship Between the Conditional Mean and Volatility of Stock Returns: A Latent VAR Approach

We model the conditional mean and volatility of stock returns as a latent vector autoregressive (VAR) process to study the contemporaneous and intertemporal relationship between expected returns and risk in a flexible statistical framework and without relying on exogenous predictors. We find a strong and robust negative correlation between the innovations to the conditional moments that leads to pronounced counter-cyclical variation in the Sharpe ratio. We document significant lead-lag correlations between the conditional moments that also appear related to business cycles. Finally, we show that although the conditional correlation between the mean and volatility is negative, the unconditional correlation is positive due to the lead-lag correlations.

Resolving Macroeconomic Uncertainty in Stock and Bond Markets

We establish an empirical link between the ex-ante uncertainty about macroeconomic fundamentals and the ex-post resolution of this uncertainty in financial markets. We measure macroeconomic uncertainty using prices of economic derivatives and relate this measure to changes in implied volatilities of stock and bond options when the economic data is released. We also examine the relationship between our measure of macroeconomic uncertainty and trading activity in stock and bond option markets before and after the announcements. Higher macroeconomic uncertainty is associated with greater reduction in implied volatilities. Higher macroeconomic uncertainty is also associated with increased volume in option markets after the release, consistent with market participants waiting to trade until economic uncertainty is resolved, and with decreased open interest in option markets after the release, consistent with market participants using financial options to hedge macroeconomic uncertainty. The empirical relationships are strongest for long-term bonds and weakest for non-cyclical stocks.