Chapter 9. Complete Markets


Principal, Cove Island Ventures

Abstract: A financial market is complete if there exist contracts to insure against all possible eventualities. First, complete markets are desirable because they enable producers, consumers, and investors to allocate scarce resources, invest capital, and share financial risks in a Pareto-efficient way. For example, calls options, put options, and other derivatives are socially beneficial because they enhance completeness. Second, complete markets in the Arrow-Debreu space provide state-of-the-art analysis of capital markets and capital structures. For example, arbitrage-free pricing is feasible only in a complete market; and investor expectations are easy to infer from complete market prices. Finally, the complete market theory offers guidance to financial entrepreneurs regarding new securities, investment strategies and capital market architecture.

Keywords: complete market, Pareto-efficient allocation, optimal allocation of risk, Arrow-Debreu space, Arrow-Debreu prices, risk-neutral probabilities, arbitrage-free preference-free pricing, decoding market prices, missing markets, financial innovation, mean-variance theory

The two main models of securities markets are the mean-variance model, the subject of Chapter 9, and the complete market model, the subject of this chapter. A securities market is said to be complete if for every future state of the world there is a state security (or a portfolio of securities) ...

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