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Arbitrage, Continuous Trading, and Margin Requirements

In: Financial Derivatives Pricing Selected Works of Robert Jarrow

Author

Listed:
  • DAVID C. HEATH

    (Department of Operations Research and Industrial Engineering, Cornell University, USA)

  • ROBERT A. JARROW

    (Johnson Graduate School of Management, Cornell University, USA)

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.

Suggested Citation

  • David C. Heath & Robert A. Jarrow, 2008. "Arbitrage, Continuous Trading, and Margin Requirements," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 2, pages 33-46, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812819222_0002
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    Cited by:

    1. Santa-Clara, Pedro & Saretto, Alessio, 2009. "Option strategies: Good deals and margin calls," Journal of Financial Markets, Elsevier, vol. 12(3), pages 391-417, August.
    2. Feyzullah Egriboyun & H. Soner, 2010. "Optimal investment strategies with a reallocation constraint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 551-585, June.
    3. A. Fiori Maccioni, 2011. "The risk neutral valuation paradox," Working Paper CRENoS 201112, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    4. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    5. Chin‐Ho Chen, 2021. "Investor sentiment, misreaction, and the skewness‐return relationship," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(9), pages 1427-1455, September.
    6. Alessandro Fiori Maccioni, 2011. "Endogenous Bubbles in Derivatives Markets: The Risk Neutral Valuation Paradox," Papers 1106.5274, arXiv.org, revised Sep 2011.
    7. Yuan Zhou & Zhe Wu, 2013. "Mean-Variance Portfolio Selection with Margin Requirements," Journal of Mathematics, Hindawi, vol. 2013, pages 1-9, April.

    More about this item

    Keywords

    Derivatives; Options; Hedging; HJM; Black–Scholes; Forwards; Futures; Martingale Measure; Calls; Puts; Market Manipulation; Margin Requirements;
    All these keywords.

    JEL classification:

    • B26 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Financial Economics
    • O16 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Financial Markets; Saving and Capital Investment; Corporate Finance and Governance
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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