Imperfect Knowledge and Asset Price Dynamics: Modeling the Forecasting of Rational Agents, Dynamic Prospect Theory and Uncertainty Premia on Foreign Exchange

Abstract

Models using the Rational Expectations Hypothesis (REH) are widely recognized to be inconsistent with the observed behavior of premia in financial markets, as well as other features of asset price dynamics. Moreover, many reasons have been advanced as to why the REH cannot generally represent, even approximately, the expectations behavior of individually rational agents. In this paper, we develop a new model of the equilibrium premium in the foreign exchange market that replaces the REH with the Imperfect Knowledge Forecasting (IKF) framework. Because we maintain that agents must cope with imperfect knowledge and that they are not grossly irrational, our IKF approach imposes only qualitative conditions on the formation of individual forecasting models and their updating. We also develop a dynamic extension of the original formulation of Kahneman and Tversky’s prospect theory. We find that under IKF and dynamic prospect theory, the equilibrium premium on foreign exchange is positively related to the gap between the aggregate forecast of the exchange rate and its historical benchmark level. We test this implication, using survey data on the German mark-U.S. dollar exchange rate, and find that the behavior of the ex ante premium on foreign exchange is consistent with our model of the premium.