Contributions published at Financial Economics (Felix Kübler)

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In Arrow’s seminal analysis of optimal risk bearing in which he introduced contingent claim securities, he assumed preferences were representable by a state independent Expected Utility function. Although the classic contingent claim setting assumes agents choose over contingent consumption vectors conditioned on a fixed set of probabilities, later work on information economics suggested that allowing probabilities to change across contingent claim spaces could be an interesting extension. However the set of axioms that are necessary and sufficient for the existence of an Expected Utility representation for the classic contingent claim space with a fixed set of probabilities does not ensure that this form utility extends across multiple contingent claim spaces. In this paper, we derive a set of axioms on preferences which are necessary and sufficient for the existence of an Expected Utility representation when probabilities change. We also consider the incremental axioms which are necessary and sufficient for Expected Utility preferences to extend to the classic lottery setting of von Neumann and Morgenstern, where agents choose not only over consumption vectors but also over probabilities vectors.

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This study uses the price reaction after matches of the stocks of ten European football clubs to test stock market efficiency. This approach has several advantages over other studies using e.g. income data or mergers and acquisition announcements as matches are played more often and on a regular basis, betting odds can be used to control for the expectations and insider trading is a problem that can be neglected. The results show that the main explanatory factor for football stock returns after matches is the number of unexpected points. This leads to significant price reactions also after expected outcomes because some points are always unexpected. The analysis also shows significantly positive stock price reactions when the team won more points than expected and significantly negative stock price movements when it won fewer points than expected. The magnitudes of the returns also show that the bigger the difference between the expectation and the realiza-tion, the bigger the impact on the stock price. But the differences are only significant after wins. The study fails to show that the impact of European Competition matches is bigger than that of National League matches. The regression models show that match-outcomes on average explain 8.4% of the returns on trading days following a match, combined with a country-index and the STOXX Europe Football index on average another 7.5%, meaning 15.9% of the returns on trading days fol-lowing a match are explained. Extending the model to all trading-days and adding some lagged variables it can explain on average 8.0% of all the returns of a team. Further research shows that the constellation in the table and the results of direct opponents, especially when competing for the qualification for the European Competitions, have a great impact on the stock prices whereas the influence of transfers is limited.

We generalize the Kou (2002) double exponential jump-diusion model in two directions. First, we independently displace the two tails of the jump size distribution away from the origin. Second, we allow for each of the displaced tails to follow a gamma distribution with an integer-valued shape parameter. Both extensions introduce additional exibility in the tails of the corresponding return distribution. Our model is supported by an equilibrium economy and we obtain closed-form solutions for European plain vanilla options. Our valuation function is computationally fast to evaluate and robust across the full parameter space. We estimate the physical model parameters through maximum likelihood and for a diverse sample of equities, commodities and exchange rates. For all assets under consideration, the original Kou (2002) model can be rejected in favor of our newly introduced asymmetrically displaced double gamma dynamics.

We propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce non-differentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the non-differentiabilities and adds interpolation nodes there. To handle this flexible grid, it uses Delaunay interpolation, a simplicial interpolation technique. Hence, we call this method Adaptive Simplicial Interpolation (ASI). We embed ASI into a time iteration algorithm to compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. We show that this method computes equilibria accurately and outperforms other grid schemes by far.

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In this paper we develop a Negishi approach to characterize recursive equilibria in stochastic models with overlapping generations. When competitive equilibria are Pareto-optimal, using Negishi-weights as a co-state variable has three major computational advantages over the standard approach of using the natural state: First, the endogenous state space is a unit simplex and thus easy to handle. Second, the number of unknown functions characterizing equilibrium dynamics is orders of magnitude smaller. Third, approximation errors have a compelling economic interpretation. Our main contribution is to show that the Negishi approach extends naturally to models with borrowing-constraints and incomplete financial markets where the welfare theorems fail. Many of the computational advantages carry over to this setting. We derive sufficient conditions for the existence of Markov equilibria in the complete markets model as well as for models with incomplete markets and borrowing constraints.

In this paper we develop a Negishi approach to characterize recursive equilibria in stochastic models with overlapping generations. When competitive equilibria are Pareto-optimal, using Negishi-weights as a co-state variable has three major computational advantages over the standard approach of using the natural state: First, the endogenous state space is a unit simplex and thus easy to handle. Second, the number of unknown functions characterizing equilibrium dynamics is orders of magnitude smaller. Third, approximation errors have a compelling economic interpretation. Our main contribution is to show that the Negishi approach extends naturally to models with borrowing-constraints and incomplete financial markets where the welfare theorems fail. Many of the computational advantages carry over to this setting. We derive sufficient conditions for the existence of Markov equilibria in the complete markets model as well as for models with incomplete markets and borrowing constraints.

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