Arbitrage, Continuous Trading, and Margin Requirements

Authors

  • DAVID C. HEATH,

  • ROBERT A. JARROW

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    • Heath is from the Department of Operations Research and Industrial Engineering, Cornell University; Jarrow is from the Johnson Graduate School of Management, Cornell University. Research supported by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell University and by a grant from the AT&T Foundation. Helpful comments from the Finance Workshops at Cornell University, the University of Minnesota, Northwestern University, Ohio State University, and the University of Wisconsin are gratefully acknowledged.

ABSTRACT

This paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options. In the context of the Black-Scholes economy, margin restrictions are shown to exclude continuous-trading arbitrage opportunities and, with two additional hypotheses, still to allow the Black-Scholes call model to apply. The Black-Scholes economy consists of a continuously traded stock with a price process that follows a geometric Brownian motion and a continuously traded bond with a price process that is deterministic.

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