Complete market

Abstract: This paper investigates the informational role of transactions volume in options markets. We develop an asymmetric information model in which informed traders may trade in option or equity markets. We show conditions under which informed traders trade options, and we investigate the implications of this for the linkage between markets. Our model predicts an important informational role for the volume of particular types of option trades. We empirically test our model's hypotheses with intraday option data. Our main empirical result is that negative and positive option volumes contain information about future stock prices. THE INFORMATION CONTENT of trading activity is a subject of widespread interest. If trades are correlated with private information, then the outcome of the transaction process may portend future movements in price. The extension of trading to different venues or to derivative instruments, however, means that this link between transactions and information need not be easily discernible. If there are alternative markets in which informed traders can profit from their information, then where informed traders choose to trade may have important implications not only for security p:rice movements, but for the behavior of related prices as well. This suggests that transactions in derivative markets may be an important predictor of future security price movements. In this paper we investigate the informational role of transactions volume in options markets. For some readers, this focus may seem puzzling; an option is a derivative security so its price should be dictated unilaterally by the behavior of the stock price. This unidirectional linkage is only true, however, in complete markets; if information is impounded into prices by trading, then the ability of informed traders to transact in options markets mearns

Abstract: Can extrinsic uncertainty ("animal spirits," "market psychology," "sunspots,"...) play a significant role in rational expectations equilibrium models? We establish that extrinsic uncertainty cannot matter in the static Arrow-Debreu economy with complete markets. But we also establish that extrinsic uncertainty can matter in the overlapping-generations economy with complete markets but where market participation is limited to those consumers alive when the markets are open. Equilibrium allocations in which extrinsic uncertainty plays no role are Pareto optimal in the traditional sense. Equilibrium allocations in which extrinsic uncertainty does play a role are Pareto optimal in a (weaker) sense which is appropriate to dynamic analysis.

Abstract: Since the primary role of international financial linkages is to facilitate consumption smoothing in the face of country-specific shocks, the degree of international financial integration should play an important role in the international transmission of business cycles. This paper therefore studies the business cycle implications of restricting international trade in financial assets. The key restriction is that domestic residents must hold all risky claims to domestic output, trading only noncontingent bonds on the international asset markets. We find that restricting asset trade may or may not change the business cycle implications of the model relative to complete markets, depending on the parameterization of the stochastic process for productivity. When there are important differences, these stem largely from differential wealth effects. We also find that restricting asset trade can resolve the chief problem inherent in complete markets models, which is their predictions of too-high consumption correlations and too-low output correlations. When technology follows a random walk process, the restricted asset markets model predicts that cross-country output correlations are positive, and cross-country consumption correlations are smaller than the output correlations, as is typically observed in the data.

Abstract: The use of the risk-neutral probability measure has proved to be very powerful for computing the prices of contingent claims in the context of complete markets, or the prices of redundant securities when the assumption of complete markets is relaxed. We show here that many other probability measures can be defined in the same way to solve different asset-pricing problems, in particular option pricing. Moreover, these probability measure changes are in fact associated with numeraire changes, this feature, besides providing a financial interpretation, permits efficient selection of the numeraire appropriate for the pricing of a given contingent claim and also permits exhibition of the hedging portfolio, which is in many respects more important than the valuation itself. The key theorem of general numeraire change is illustrated by many examples, among which the extension to a stochastic interest rates framework of the Margrabe formula, Geske formula, etc.