[The role of ordinary options in facilitating the completion of securities markets is examined in the context of a model of contingent claims sufficiently general to accommodate the continuous distributions of asset pricing theory and option pricing theory. In this context, it is shown that call options written on a single security approximately span all contingent claims written on this security and that call options written on portfolios of call options on individual primitive securities approximately span all contingent claims that can be written on these primitive securities. In the case of simple options, explicit formulas are given for the approximating options and portfolios of options. These results are applied to the pricing of contingent claims by arbitrage and to irrelevance propositions in corporate finance.]

The role of ordinary options in facilitating the completion of securities markets is examined in the context of a model of contingent claims sufficiently general to accommodate the continuous distributions of asset pricing theory and option pricing theory. In this context, it is shown that call options written on a single security approximately span all contingent claims written on this security and that call options written on portfolios of call options on individual primitive securities approximately span all contingent claims that can be written on these primitive securities. In the case of simple options, explicit formulas are given for the approximating options and portfolios of options. These results are applied to the pricing of contingent claims by arbitrage and to irrelevance propositions in corporate finance. The role of complete contingent-claims markets in the optimal allocation of risk bearing is well known [Arrow (1964) and Debreu (1959)] and is the cornerstone of the economic theory of financial markets [Mossin (1977)]. As a consequence, it becomes important from a practical as well as a scholarly perspective to determine how complex the securities markets must be in order to achieve the allocational efficiencies of complete markets. The literature on this question has grown to be sizable. Much of this literature has been reviewed in John (1981, 1984) and Amershi (1985). A seminal contribution concerning the complexity of complete securities markets was made by Ross (1976) in analyzing the role of conventional options in com-

[A firm must decide what security to sell to raise external capital to finance a profitable investment opportunity. There is ex ante asymmetry of information regarding the probability distribution of cash flow generated by the investment. In this setting, we derive necessary and sufficient conditions for a security to be optimal (uniquely optimal), that is, for pooling at this security to be an (the unique) equilibrium outcome. Using these conditions we show that the debt contract is (uniquely) optimal if and only if cash flows are ordered by (strict) conditional stochastic dominance. Finally, we derive an equivalence relationship between optimal security designs and designs that minimize mispricing.]

A firm must decide what security to sell to raise external capital to finance a profitable investment opportunity. There is ex ante asymmetry of information regarding the probability distribution of cash flow generated by the investment. In this setting, we derive necessary and sufficient conditions for a security to be optimal (uniquely optimal), that is, for pooling at this security to be an (the unique) equilibrium outcome. Using these conditions we show that the debt contract is (uniquely) optimal if and only if cash flows are ordered by (strict) conditional stochastic dominance. Finally, we derive an equivalence relationship between optimal security designs and designs that minimize mispricing.

The agency relationship of corporate insiders and bondholders is modeled as a dynamic game with asymmetric information. The incentive effect of risky debt on the investment policy of a levered firm is studied in this context. In a sequential equilibrium of the model, a concept of reputation arises endogenously resulting in a partial resolution of the classic agency problem of underinvestment. The incentive of the firm to underinvest is curtailed by anticipation of favorable rating of its bonds by the market. This anticipated pricing of debt is consistent with rational expectations pricing by a competitive bond market and is realized in equilibrium. Some empirical implications of the model for bond rating, debt covenants, and bond price response to investment announcements are explored.

The agency relationship of corporate insiders and bondholders is modeled as a dynamic game with asymmetric information. The incentive effect of risky debt on the investment policy of a levered firm is studied in this context. In a sequential equilibrium of the model, a concept of reputation arises endogenously resulting in a partial resolution of the classic agency problem of underinvestment. The incentive of the firm to underinvest is curtailed by anticipation of favorable rating of its bonds by the market. This anticipated pricing of debt is consistent with rational expectations pricing by a competitive bond market and is realized in equilibrium. Some empirical implications of the model for bond rating, debt covenants, and bond price response to investment announcements are explored.