On the Non-Existence of Redundant Options |
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Authors: | Alexandre M Baptista |
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Institution: | (1) Department of Finance, School of Business, The George Washington University, 2201 G Street NW, Funger Hall, Suite 501, DC 20052 Washington, USA |
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Abstract: | In a seminal paper, Ross (Q J Econ 90:75–89, 1976) shows that if security markets are resolving, then there exist (non-redundant)
options that generate complete security markets. Complementing his work, Aliprantis and Tourky (2002) show that if security
markets are strongly resolving and the number of primitive securities is less than half the number of states, then every option is non-redundant. Our paper extends Aliprantis and Tourky’s result to the case when
their condition on the number of primitive securities is not imposed. Specifically, we show that if there exists no binary
payoff vector in the asset span, then for each portfolio there exists a set of exercise prices of full measure such that any
option on the portfolio with an exercise price in this set is non-redundant. Since the condition that there exists no binary
payoff vector in the asset span holds generically, redundant options are thus rare.
I am grateful to an anonymous referee for very helpful comments. Research support from the School of Business at The George
Washington University is gratefully acknowledged |
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Keywords: | Options Redundant securities Incomplete markets |
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