Economic Foundations of Finance

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Virtually all of the work in continuous-time finance assumes that the prices of securities follow an exogenously specified process. However, the prices of securities are in fact determined day-by-day and minute-by-minute by the balancing of supply and demand. A complete economic model of continuous-time trading requires the derivation of the pricing process as an equilibrium determined by more primitive data of the economy, in particular the agents' information, utility functions, and endowments. The known results on existence of equilibrium in multi-agent continuous-time financial markets are limited to the case in which markets are dynamically complete, i.e. the available securities either include a complete set of Arrow-Debreu contingent claims, or it is possible to construct a complete set of Arrow-Debreu contingent claims from the available securities. The assumption that the available securities include a complete set of Arrow-Debreu contingent claims is highly implausible; the assumption that one can construct a complete set of Arrow-Debreu contingent claims from the available securities is highly endogenous, since dynamic completeness is a property of the prices of the securities, not the underlying data of the economy. Without equilibrium underpinnings, the economic foundations of finance models are seriously in question. The main goal of the project is to prove the existence of equilibrium prices in continuous-time finance models with dynamically incomplete markets. The second goal is to explore the implications of equilibrium for the nature of securities price processes. This research is intended to provide solid economic foundations for continuous-time finance. In particular, it will provide alternative pricing processes to those which are currently studied in continuous-time finance; these alternative pricing processes may provide a better fit to actual stock market data than those currently in use. This research has the potential to benefit society by improving the accuracy of pricing in securities markets. First, because the research leads to specific predictions about the interaction of prices for different types of assets, it should lead to more accurate pricing across markets, such as housing, mortgages, stocks and bonds, which currently function largely independently. Second, it should lead to more accurate pricing of options in the situation where the exercise price of the option differs significantly the current price of the underlying stock.