Derivative Finance and Complete Markets
The fundamental theory of finance. Spurred by seminal contributions by Kenneth Arrow, Gerard Debreu, Robert Lucas, Paul Samuelson, Robert Merton, Fischer Black, and many other economists and financial theorists has provided applied and theoretical finance an extraordinary boost. Under certain well-defined conditions it has made it possible to price derivatives of various sorts and augmented importantly the observable information regarding market price processes. Unlike the utility approach, based on a personal valuation of real financial states, fundamental theory is utility free and has replaced real states with implied market states priced by bets of buyers and sellers. In the fundamental finance approach, market states (specific and well-defined gains or losses) are priced by the bets made by buyers and sellers, resulting in state prices that define the market equilibrium. When such equilibrium exists fueled by information, market liquidity, and the many economic and noneconomic factors that determine the financial market environment, markets are said to be complete; when it does not exist, markets are said to be incomplete.
When markets are in equilibrium, defined by a single price, a current price implies future state prices. Inversely, future states and their prices imply a current price. For example, the current price of an option implies a belief about future option prices (and thereby the underlying ...