# The financial market: not as big as you think

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## Abstract

In a general multiperiod financial market, we show that the market trading prices at intermediate dates of some securities with simple specifications, either compound call option or portfolios of index options, reveal sufficient information from the terminal date to intermediate dates; therefore, these simple securities dynamically span and complete the entire space of all state-contingent claims. We further demonstrate that those specifications of state-contingent claims are the simplest ones to dynamically span all state-contingent claims. Our results do not depend on agents’ risk-preference and basic asset’s stochastic price process. Therefore, the financial market might be not as big as we think.

## Keywords

Dynamic spanning Index option Compound option## JEL Classification

G12 G13## Notes

### Acknowledgements

The author would like to thank the editor, the associate editor and an anonymous referee for their constructive comments and insightful suggestions that improved the paper.

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