Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.Multivariate Density Forecast Evaluation, Probability Integral Transformation, Multidimensional Value at Risk, Monte Carlo Simulations

Dynamic Density Forecasts for Multivariate Asset Returns

We propose a simple and flexible framework for forecasting the joint density of asset returns. The multinormal distribution is augmented with a polynomial in (time-varying) non-central co-moments of assets. We estimate the coefficients of the polynomial via the Method of Moments for a carefully selected set of co-moments. In an extensive empirical study, we compare the proposed model with a range of other models widely used in the literature. Employing a recently proposed technique to evaluate multivariate forecasts, we conclude that the augmented joint density provides highly accurate forecasts of the negative tail of the joint distribution.Time-varying higher co-moments, Joint Density Forecasting, Method of Moments, Multivariate Value-at-Risk.

Dynamic Multilateral Markets

We study dynamic multilateral markets, in which players’ payoffs result from coalitional bargaining. In this setting, we establish payoff uniqueness of the stationary equilibria when players exhibit some degree of impatience. We focus on market games with different player types, and derive under mild conditions an explicit formula for each type’s equilibrium payoff as market frictions vanish. The limit payoff of a type depends in an intuitive way on the supply and the demand for this type in the market, adjusted by the type-specific bargaining power. Our framework may be viewed as an alternative to the Walrasian price-setting mechanism. When we apply this methodology to the analysis of labor markets, we can determine endogenously the equilibrium firm size and remuneration scheme. We find that each worker type in a stationary market equilibrium is rewarded her marginal product, i.e. we obtain a strategic underpinning of the neoclassical wage. Interestingly, we can also replicate some standardized facts from the search-theoretical literature such as positive equilibrium unemployment.Multilateral Bargaining, Dynamic Markets, Labor Markets

Extreme risk interdependence

We define tail interdependence as a situation where extreme outcomes for some variables are informative about such outcomes for other variables. We extend the concept of multiinformation to quantify tail interdependence, decompose it into systemic and residual interdependence and measure the contribution of a constituent to the interdependence of a system. Further, we devise statistical procedures to test: a) tail independence, b) whether an empirical interdependence structure is generated by a theoretical model and c) symmetry of the interdependence structure in the tails. We outline some additional extensions and illustrate this framework by applying it to several datasets

Forecasting multidimensional tail risk at short and long horizons

We define the Multidimensional Value at Risk (MVaR) as a natural generalization of VaR. This generalization makes a number of important applications possible. For example, many techniques developed for VaR can be applied to MVaR directly. As an illustration, we employ VaR forecasting and evaluation techniques. One of our forecasting models builds on the progress made in the volatility literature and decomposes MVaR into long-term trend and short-term cycle components. We compute short- and long-term MVaR forecasts for several multidimensional time series and discuss their (un)conditional accuracy

Bargaining Frictions in Trading Networks

In the canonical model of frictionless markets, arbitrage is usually taken to force all trades of homogeneous goods to occur at essentially the same price. In the real world, however, arbitrage possibilities are often severely restricted and this may lead to substantial price heterogeneity. Here we focus on frictions that can be modeled as the bargaining constraints induced by an incomplete trading network. In this context, the interplay among the architecture of the trading network, the buyers’ valuations, and the sellers’ costs shapes the effective arbitrage possibilities of the economy. We characterize the configurations that, at an intertemporal bargaining equilibrium, lead to a uniform price. Conceptually, this characterization involves studying how the network positions and valuations/costs of any given set of buyers and sellers affect their collective bargaining power relative to a notional or benchmark situation in which the connectivity is complete. Mathematically, the characterizing conditions can be understood as price-based counterparts of those identified by the celebrated Marriage Theorem in matching theory

Volatility-volume co-movements: evidence from China metal markets

This paper investigates the interactional relationship between price volatility and futures trading activity for three heavily traded metal products on the Shanghai Metal Exchange and the Shanghai Futures Exchange. Using models based on vector autoregression and generalized method of moments we show, in particular, that futures trading activity has a strong impact on both spot and futures price volatility in copper and aluminium markets. Futures trading activity leads spot market volatility in copper and aluminium markets which suggests that futures markets have a destabilizing effect. In order to disentangle the effect of different traders’ types on asset price movements, we decompose futures trading into speculators’ and hedgers’ trading and investigate their contributions to volatility. As a robustness check, we investigate the impact of endogenous structural breaks on the interactional relationship between price volatility and futures trading

Entry limiting agreements: first mover advantage, authorized generics and pay-for-delay deals

During patent litigation, pay-for-delay (P4D) deals involve a payment from a patent holder of a branded drug to a generic drug manufacturer to delay entry and withdraw the patent challenge. In return for staying out of the market, the generic firm receives a payment, and/or an authorized licensed entry at a later date, but before the patent expiration. We examine why such deals are stable when there are multiple potential entrants. We combine the first-mover advantage for the first generic with the ability of the branded manufacturer to launch an authorized generic (AG) to show when P4D deals are an equilibrium outcome. We further show that limiting a branded firm's ability to launch an AG before entry by a successful challenger will deter such deals. However, removing exclusivity period for the first generic challenger will not

Dirty neighbors — Pollution in an interlinked world

We apply a network approach to analyze individual and aggregate consumption that generates predominately local pollution (e.g., noise, water and air quality, waste disposal sites). This allows us to relate the individual pollution levels to network centralities and to determine the effects of transfers among agents on the aggregate contamination. We then apply our theoretical framework to analyze the European data on fossil fuel energy consumption and discuss the impact of EU redistributive transfer policies on the aggregate level of pollution

Telling tales from the tails: high-dimensional tail interdependence

We propose a simple and flexible framework that allows for a comprehensive analysis of tail interdependence in high dimensions. We use co-exceedances to capture the structure of the dependence in the tails and, relying on the concept of multiinformation, define the coefficient of tail interdependence. Within this framework, we develop statistical tests of (i) independence in the tails, (ii) goodness-of-fit of the tail interdependence structure of a hypothesized model with the one observed in the data, and (iii) dependence symmetry between any two tails. We present an analysis of tail interdependence among 250 constituents of the SP250 index