Spanning and Completeness with Options (1988)
| Venue: | Review of Financial Studies |
| Citations: | 14 - 0 self |
BibTeX
@ARTICLE{Nachman88spanningand,
author = {David C. Nachman},
title = {Spanning and Completeness with Options},
journal = {Review of Financial Studies},
year = {1988},
pages = {311--328}
}
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Abstract
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-
