Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

Repeated games with present-biased preferences

We study infinitely repeated games with perfect monitoring, where players have β-δ preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in β or δ. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor.     

Excess payoff dynamics and other well-behaved evolutionary dynamics

We consider a model of evolution in games in which agents occasionally receive opportunities to switch strategies, choosing between them using a probabilistic rule. Both the rate at which revision opportunities arrive and the probabilities with which each strategy is chosen are functions of current normalized payoffs. We call the aggregate dynamics induced by this model excess payoff dynamics. We show that every excess payoff dynamic is well-behaved: regardless of the underlying game, each excess payoff dynamic admits unique solution trajectories that vary continuously with the initial state, identifies rest points with Nash equilibria, and respects a basic payoff monotonicity property. We show how excess payoff dynamics can be used to construct well-behaved modifications of imitative dynamics, and relate them to two other well-behaved dynamics based on projections.     

Risk-dominance and perfect foresight dynamics in N-player games

In perfect foresight dynamics, an action is linearly stable if expectation that people will always choose the action is self-fulfilling. A symmetric game is a PIM game if an opponent's particular action maximizes the incentive of an action, independently of the rest of the players. This class includes supermodular games, games with linear incentives and so forth. We show that, in PIM games, linear stability is equivalent to u-dominance, a generalization of risk-dominance, and that there is no path escaping a u-dominant equilibrium. Existing results on N-player coordination games, games with linear incentives and two-player games are obtained as corollaries.     

The rate of convergence to perfect competition of matching and bargaining mechanisms

We study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information. A friction parameter is τ, the length of the time period until the next meeting. We provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in τ, which is shown to be the fastest possible among all bargaining mechanisms. The condition requires that buyers and sellers always retain some bargaining power. The bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power (NBP) mechanisms. Simple random proposer take-it-or-leave-it protocols are NBP, while k-double auctions (k-DA) are not. We find that k-DAs have equilibria that converge to perfect competition at a linear rate, converge at a slower rate or even do not converge at all.     

Stable games and their dynamics

We study a class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising agents are switching are always exceeded by the improvements in the payoffs of strategies which revising agents are abandoning. We prove that the set of Nash equilibria of a stable game is globally asymptotically stable under a wide range of evolutionary dynamics. Convergence results for stable games are not as general as those for potential games: in addition to monotonicity of the dynamics, integrability of the agents' revision protocols plays a key role.     

Coase theorem, complexity and transaction costs

This paper, by introducing complexity considerations, provides a dynamic foundation for the Coase theorem and highlights the role of transaction costs in generating inefficient bargaining/negotiation outcomes. We show, when the players have a preference for less complex strategies, the Coase theorem holds in negotiation models with repeated surplus and endogenous disagreement payoffs if and only if there are no transaction costs. Specifically, complexity considerations select only efficient equilibria in these models without transaction costs while every equilibrium induces perpetual disagreement and inefficiency with transaction costs. We also show the latter is true in the Rubinstein bargaining model with transaction costs.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Decentralized learning from failure

We study decentralized learning in organizations. Decentralization is captured through Crawford and Haller's [Learning how to cooperate: optimal play in repeated coordination games, Econometrica 58 (1990) 571-595] attainability constraints on strategies. We analyze a repeated game with imperfectly observable actions. A fixed subset of action profiles are successes and all others are failures. The location of successes is unknown. The game is played until either there is a success or the time horizon is reached. We partially characterize optimal attainable strategies in the infinite horizon game by showing that after any fixed time, agents will occasionally randomize while at the same time mixing probabilities cannot be uniformly bounded away from zero.     

Uniform payoff security and Nash equilibrium in compact games

We introduce a condition, uniform payoff security, for games with compact Hausdorff strategy spaces and payoffs bounded and measurable in players’ strategies. We show that if any such compact game G is uniformly payoff secure, then its mixed extension is payoff secure. We also establish that if a uniformly payoff secure compact game G has a mixed extension with reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of compact games satisfying uniform payoff security.     

On general periodic time-varying bilinear processes

We study in this note the class of bilinear processes with periodic time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of strict and second order stationary solutions (in periodic sense) and for the existence of higher order moments. The given conditions can be applied to periodic ARMA or periodic GARCH models. The central limit theorem and the law of iterated logarithm (LIL) for higher order sample moments are showed.     

Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics

This note shows, by means of two simple, three-strategy games, the existence of stable periodic orbits and of multiple, interior steady states in a smooth version of the Best-Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three-strategy games. We also show that the Logit Dynamics displays another bifurcation which cannot occur under the Replicator Dynamics: the fold bifurcation, with non-monotonic creation and disappearance of steady states.     

Proper belief revision and equilibrium in dynamic games

We present a theory of rationality in dynamic games in which players, during the course of the game, may revise their beliefs about the opponents’ utility functions. The theory is based upon the following three principles: (1) the players’ initial beliefs about the opponents’ utilities should agree on some profile u of utility functions, (2) every player should believe, at each of his information sets, that his opponents are carrying out optimal strategies and (3) a player at information set h should not change his belief about an opponent's ranking of strategies a and b if both a and b could have led to h. Scenarios with these properties are called preference conjecture equilibria for the profile u of utility functions. We show that every normal form proper equilibrium for u induces a preference conjecture equilibrium for u, thus implying existence of preference conjecture equilibrium.     

Modeling volatility with time-varying FIGARCH models

This paper puts the light on a new class of time-varying FIGARCH or TV-FIGARCH processes to model the volatility. This new model has the feature to account for the long memory and the structural change in the conditional variance process. The structural change is modeled by a logistic function allowing the intercept to vary over time. We also implement a modeling strategy for our TV-FIGARCH specification whose performance is examined by a Monte Carlo study. An empirical application to the crude oil price and the S&P 500 index is carried out to illustrate the usefulness of our techniques. The main result of this paper is that the long memory behavior of the absolute returns is not only explained by the existence of the long memory in the volatility but also by deterministic changes in the unconditional variance.     

The strategic value of recall

This work studies the value of two-person zero-sum repeated games in which at least one of the players is restricted to (mixtures of) bounded recall strategies. A (pure) k-recall strategy is a strategy that relies only on the last k periods of history. This work improves previous results ( [Lehrer, 1988] and [Neyman and Okada, 2009]) on repeated games with bounded recall. We provide an explicit formula for the asymptotic value of the repeated game as a function of the one-stage game, the duration of the repeated game, and the recall of the agents.     

On efficiency of the English auction

We study efficiency properties of the irrevocable exit English auction in a setting with interdependent values. Maskin (1992) [1] shows that the pairwise single-crossing condition is sufficient for efficiency of the English auction with two bidders and suggests that it is also a necessary condition. This paper clarifies and extends Maskin?s results to the case of N bidders. We introduce the generalized single-crossing condition—a fairly intuitive extension of the pairwise single-crossing condition—and prove that it is essentially a necessary and sufficient condition for the existence of an efficient equilibrium of the N-bidder English auction.     

Von Neumann-Morgenstern stable sets, discounting, and Nash bargaining

We establish a link between von Neumann-Morgenstern stable set and the Nash solution in a general n-player utility set. The stable set-solution is defined with respect to a dominance relation: payoff vector u dominates v if one player prefers u even with one period delay. We show that a stable set exists and, if the utility set has a smooth surface, any stable set converges to the Nash bargaining solution when the length of the period goes to zero.     

Fair imposition

We introduce a new mechanism-design problem called fair imposition. In this setting a center wishes to fairly allocate tasks among a set of agents whose cost structures are known only to them, and thus will not reveal their true costs without appropriate incentives. The center, with the power to impose arbitrary tasks and payments on the agents, has the additional goal that his net payment to these agents is never positive (or, that it is tightly bounded if a loss is unavoidable). We consider two different notions of fairness that the center may wish to achieve. The central notion, which we call k-fairness, is in the spirit of max-min fairness. We present both positive results (in the form of concrete mechanisms) and negative results (in the form of impossibility theorems) concerning these criteria. We also briefly discuss an alternative, more traditional interpretation of our setting and results, in the context of auctions.     

Randomization and simplification in dynamic decision-making

Randomization adds beneficial flexibility to the construction of optimal simple plans in dynamic environments. A decision-maker, restricted to the use of simple plans, may find a stochastic plan that strictly outperforms all deterministic ones. This is true even in noninteractive deterministic environments where the decision-maker's choices have no influence on his signals nor on the future evolution of the system. We describe a natural decomposition of simple plans into two components: an action selection rule and a behavior modification rule. In noninteractive environments optimal simple plans do not require randomization in the action selection rule. Only randomization in the behavior modification rule may be necessary.     

Unmediated communication in games with complete and incomplete information

We study the effects of adding unmediated communication to static, finite games of complete and incomplete information. We characterize S^U(G), the set of outcomes of a game G, that are induced by sequential equilibria of cheap talk extensions. A cheap talk extension of G is an extensive-form game in which players communicate before playing G. A reliable mediator is not available and players exchange private or public messages that do not affect directly their payoffs. We first show that if G is a game of complete information with five or more players and rational parameters, then S^U(G) coincides with the set of correlated equilibria of G. Next, we demonstrate that if G is a game of incomplete information with at least five players, rational parameters and full support (i.e., all profiles of types have positive probability), then S^U(G) is equal to the set of communication equilibria of G.