The preceding chapter on the economic functions of derivatives mentioned the concept of ‘market completion’ as a possible socially useful economic function of derivatives. A detailed examination of the Nobel Prize winning Arrow–Debreu theorem on which the market completion concept is based, would be beyond the scope of this book. However, the implications of market completion theory for derivatives, especially for regulation, are substantial. Therefore, this chapter explores this issue in greater detail. The Arrow-Debreu theorem and the various arguments it involves are extremely complex and abstruse, so (in the interest of the non-specialist reader) this chapter takes a highly simplified approach in order to enable the reader to grasp the essentials.

Kenneth Arrow and Gerard Debreu postulated that under certain conditions a welfare-maximizing general equilibrium could be attained. This would be a welfare maximizing equilibrium in the sense that it would be Pareto-optimal, i.e., no change could be made to this equilibrium made without making at least one person worse off. This theoretical conclusion rests on a number of assumptions that do not obtain in real life. Two of the conditions required for this general equilibrium, and the most difficult to attain in practice, are the presence of perfect competition and the existence of complete markets. The Arrow-Debreu theorem has for many years been used as a philosophical basis for advocating free markets and laissez faire on the grounds that a perfectly competitive system will maximize welfare.

Apart from perfect competition, the utopian situation of the Arrow–Debreu equilibrium requires ‘complete markets’. The term ‘complete markets’ or ‘complete market’ is used as a short form for the more accurate term a ‘complete system of markets’. A complete system of markets is one where there is a market for every good.