13 - The hidden binomial economy and the role of forecasts in determining prices

Abstract

The chapter investigates the many possible versions of underlying economies that are consistent with the usual binomial structure central to option pricing. These economies are used to model explicitly a number of interesting problems that are usually intractable in more complex frameworks. In particular, equilibria is considered where agents have subjective expected utility and heterogeneous utility functions without satisfying standard aggregation conditions. The chapter looks at an economy that underpins the binomial option pricing model, generalizing considerably the setting of Johnstone (2006). In this model the focus is always on the price of the redundant asset (the derivative) and not the price of the traded asset (the stock). The outline of the chapter includes the general structure of the models, cases of power utility, mixed equilibria, and others. Further, it shows that in such a one-period world, price is driven entirely by forecasts and has no connection with true probability. It concludes with deriving formulae for equilibrium equity prices in a number of novel cases.