Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models

A new LM specification procedure to choose between Logistic and Exponential Smooth Transition Autoregressive (STAR) models is introduced. The new decision rule has better properties than those previously available in the literature when the model is ESTAR and similar properties when the model is LSTAR. A simple natural extension of the usual LM-test for linearity is introduced and evaluated in terms of power. Monte-Carlo simulations and empirical evidence are provided in support of our claims.     

Commitment and choice of partner in a negotiation with a deadline

This paper analyses the effects of partially revocable endogenous commitments of a seller in a negotiation with a deadline. In particular, we examine when commitment is a source of strength, a source of inefficiency and when it does not affect the bargaining outcome at all. We show that when commitment possesses a minimum amount of irrevocability this crucially determines the bargaining outcome. In the bilateral bargaining case, commitment becomes a source of inefficiency since it causes a deadline effect. In the choice of partner framework, however, the deadline effect disappears and there is an immediate agreement and, moreover, commitment becomes a source of strength since it increases the seller's equilibrium payoff by triggering off competition between the buyers.     

Aggregation, efficiency and mutual fund separation in incomplete markets

Summary. This paper studies the conditions for aggregation, portfolio separation and effective completeness of competitive allocations in general equilibrium models with incomplete markets where agents have general preference and endowment distributions. We show that these properties are distinct. Demands may aggregate yet may fail to exhibit fund separation and conversely. Fund separation implies effective completeness while aggregation does not. The implications of these properties for the structure of equilibria are discussed, and generalizations of the CAPM, the consumption CAPM and the CAPM with nonmarketed wealth emerge from the analysis. Received: September 12, 1996; revised version: November 7, 1996     

Matching and bargaining models of markets: approximating small markets by large markets

Summary. We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.Received: January 22, 1996; revised version: September 24, 1996This revised version was published online in February 2005 with corrections to the cover date.     

A note on the “size” of determinacy and indeterminacy

Summary. It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies may have “typically” determinate equilibria – even though uncountably many of them – as would have been desirable for comparative statics exercises. Received: May 19, 1995; revised version: March 24, 1997     

Incomplete markets, continuum of states and default

Summary. We show that when bankruptcy, subject to penalties, is allowed, it is possible to prove the existence of equilibrium in a model with a continuum of states without imposing any assumptions on ex-post endowments.Received: November 20, 1995; revised version: September 16, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Randomly available outside options in bargaining

We consider an extension of the standard Rubinstein model where both players are randomly allowed to leave the negotiation after a rejection, in which case they obtain a payoff of known value. We show that, when the value of the outside opportunities is of intermediate size, there exist a continuum of subgame-perfect equilibrium outcomes, including some with delayed agreements. Considering outside opportunities of significant value, we prove that efficient delays arise caused by the bargainers' aspirations, in waiting for their outside, option rather than by threats. Moreover, if taking the outside option decreases the probability that the opponent receives an outside option in the future, then it is possible that exactly two equilibrium payoffs coexist. In this latter case, inefficiencies may be created by agreeing too early.     

Constrained suboptimality in incomplete markets: a general approach and two applications

Summary. In this paper we re-examine generic constrained suboptimality of equilibrium allocations with incomplete numeraire asset markets. We provide a general framework which is capable of resolving some issues left open by the previous literature, and encompasses many kinds of intervention in partially controlled market economies. In particular, we establish generic constrained suboptimality, as studied by Geanakoplos and Polemarchakis, even without an upper bound on the number of households. Moreover, we consider the case where asset markets are left open, and the planner can make lump-sum transfers in a limited number of goods. We show that such a perfectly anticipated wealth redistribution policy, though consistent with the assumed incomplete financial structure, is typically effective. Received: August 14, 1995; revised version: April 11, 1997     

A semiparametric estimation of liquidity effects on option pricing

Abstract. This paper proposes a semiparametric option pricing model with liquidity, as proxied by the relative bid-ask spread. A nonparametric volatility function with liquidity costs as an explanatory variable is estimated using the Symmetrized Nearest Neighbors (SNN) estimator rather than the traditional kernel estimator. The SNN estimator is particularly suitable for the characteristics of option data in financial markets. Moreover, we propose a natural extension of the univariate bandwidth parameter optimal estimation to the multivariate case. A statistical design to test competing option pricing models which takes into account the lack of independence between them is also presented. The in-sample performance of the model turns out to be statistically favorable relative to the competing model without liquidity. Also, an additional experiment is performed within sample, but with just a subsample of options not employed in the nonparametric estimation of the implied volatility function being priced. The results are also favorable to our semiparametic theoretical option pricing model with liquidity. However, the out-of-sample performance is quite disappointing regardless of what option pricing model is employed in the estimation. Eva Ferreira and Gonzalo Rubio acknowledge the financial support provided by Dirección Interministerial Científica y Técnica (DGICYT) grants PB98-0149 and PB97-0621 respectively. All three authors aknowledge the financial support provided by Universidad del País Vasco (UPV/EHU) grant UPV 038.321-HA129/99, and the BSI Gamma Foundation. We appreciate the helpful comments of two anonymous referees, ángel León, José M. Campa, Fernando Tusell and Javier Fernández Navas, seminar participants at the Bank of Spain and the European Financial Management Association (Athens), and the computational assistance of Gregorio Serna. We thank Juan Ayuso and MEFF for providing the data used in this article. The contents of this paper are the sole responsability of the authors.     

Intraday return and volatility relationships between the Ibex 35 spot and futures markets

This paper analyses the intraday lead-lag relationships between returns and volatilities in the Ibex 35 spot and futures markets. Using hourly data, we jointly analyze the interactions between markets, estimating a bivariate error correction model with GARCH perturbations which captures stochastically the presence of an intraday U-shaped curve for both spot and futures market volatility. Our findings show a bidirectional causal relationship between market volatilities, with a positive feedback. This two-way transmission of volatility is consistent with market prices evolving according to a long-run equilibrium relationship, and shocks affecting both markets in the same direction. Our empirical results also support a unidirectional cross interaction from futures to spot market returns. This pattern suggests that the futures market leads the spot market in order to incorporate the arrival of new information.     

Strategic bargaining in the variable threat game

Summary. In this paper the alternating offer model with an exogenous risk of breakdown is taken to explicitly model the bargaining process underlying the variable threat game (Nash, Econometrica, 1953). A modified version of the variable threat game without commitment is also analysed within a dynamic context. The limit set of subgame perfect equilibria is characterized in both dynamic versions. The analysis gives rise to different results than in the two standard models. By making additional assumptions the original results can be regained, indicating that these are implicitly present in the standard analysis.Received: August 29, 1995; revised version: November 11, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Uniqueness of asset prices in an exchange economy with unbounded utility

Summary. This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value – i.e., no bubbles can arise – in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example. Received: January 22, 1996; revised version: February 18, 1997     

Generalized assignment models: with an applicationto technology transfer

Summary.  We consider a generalized assignment model where the payoffs depend on the number of matchings that take place. We formulate a simple non-cooperative game and look for subgame perfect equilibrium of this model. Existence is established for a wide class of games. We also look at a refinement criterion which, for the standard assignment model, selects the -optimal outcome as the unique equilibrium. We then apply these concepts to a model of technology transfer between domestic and foreign firms. Received: June 24, 1994; revised version October 12, 1995     

Risk preference and productivity measurement under output price uncertainty

This paper deals with joint estimation of production and risk preference functions in the presence of output price uncertainty. We use quadratic production and utility functions under the assumption that producers maximize expected utility of anticipated profit. A panel data on Norwegian salmon farms is used for this purpose. Empirical results show that all salmon farmers are risk averse. Relative risk premium (the implicit cost of private risk bearing) is found to be about 15% of mean profit. We also find rapid technological change taking place (3.75% per year) in the salmon farming industry. First version received: February 2000/Final version received: February 2001     

Pareto improving financial innovation in incomplete markets

Summary. In this paper we develop a differential technique for investigating the welfare effects of financial innovation in incomplete markets. Utilizing this technique, and after parametrizing the standard competitive, pure-exchange economy by both endowments and utility functions, we establish the following (weakly) generic property: Let S be the number of states, I be the number of assets and H be the number of households, and consider a particular financial equilibrium. Then, provided that the degree of market incompleteness is sufficiently larger than the extent of household heterogeneity, S−I≥2H−1 [resp. S−I≥H+1], there is an open set of single assets [resp. pairs of assets] whose introduction can make every household better off (and, symmetrically, an open set of single assets [resp. pairs of assets] whose introduction can make them all worse off ). We also devise a very simple nonparametric procedure for reducing extensive household heterogeneity to manageable size, a procedure which not only makes our restrictions on market incompleteness more palatable, but could also prove to be quite useful in other applications involving smooth analysis. Received: August 14, 1995; revised version: April 14, 1997     

Which improves welfare more: A nominal or an indexed bond?

Summary. Economists have long argued that loan contracts should be indexed to remove the risks arising from fluctuations in the purchasing power of money: indexation however while eliminating one risk, substitutes another, arising from fluctuations in relative prices of goods. We present a theoretical framework which permits the relative merits of a nominal versus an indexed bond to be assessed in a general equilibrium setting. Received: July 31, 1995; revised version August 7, 1996     

Unemployment duration and workers' wage aspirations in Spain

This paper examines unemployed workers' declared willingness to work for wages lower than the one adequate for their qualification. We analyze which personal and economic characteristics determine this willingness and how it changes along the individuals' unemployment spells. The main results are: (i) Young workers, less educated and those living in regions or times of high unemployment are more willing to accept reduced wages while married women with a working husband are much less willing to do so; (ii) Once the individual fixed effect is controlled for, the willingness to work for reduced wages increases with the duration of unemployment; (iii) Not having access to unemployment benefits increases the probability that initially unwilling workers become willing to accept reduced wages.     

Sequential equilibria of asymmetric ascending auctions: The case of log-normal distributions

Summary. The sequential equilibrium of an ascending-price auction of a single item is derived explicitly for the case of log-normal distributions and a multiplicative valuation model comprising both common and private factors, and allowing asymmetries. If the prior distribution on the common factors is diffuse, or of the form obtained by Bayesian updating from a diffuse prior distribution, then the equilibrium strategies are log-linear with coefficients obtained by solving a set of linear equations. A similar construction applies to normal distributions and additive terms in the valuation model. An example illustrates the predictions derived from the model. Received: December 11, 1996; revised version: July 15, 1997     

Cooperative games in permutational structure

Summary. By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition being a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. In this paper we consider non-transferable utility games in which for any coalition the set of payoffs depends on a permutation or ordering upon any partition of the coalition into subcoalitions. We call such a game a cooperative game in permutational structure or shortly permutational game. Doing so we extend the scope of the standard cooperative game theory in dealing with economic or political problems. Next we define the concept of core for such games. By introducing balancedness for ordered partitions of coalitions, we prove the nonemptiness of the core of a balanced non-transferable utility permutational game. Moreover we show that the core of a permutational game coincides with the core of an induced game in coalitional structure, but that balancedness of the permutational game need not imply balancedness of the corresponding coalitional game. This leads to a weakening of the conditions for the existence of a nonempty core of a game in coalitional structure, induced by a game in permutational structure. Furthermore, we refine the concept of core for the class of permutational games. We call this refinement the balanced-core of the game and show that the balanced-core of a balanced permutational game is a nonempty subset of the core. The proof of the nonemptiness of the core of a permutational game is based on a new intersection theorem on the unit simplex, which generalizes the well-known intersection theorem of Shapley. Received: October 31, 1995; revised version: February 5, 1997