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Instantaneous Arbitrage and the CAPM

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  • Lars Tyge Nielsen

Abstract

This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrage argument and the CAPM argument in Black and Scholes (1973) is this: the arbitrage argument assumes that there exists some portfolio satisfying the capm equation, whereas the CAPM argument assumes, in addition, that this portfolio is the market portfolio.

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  • Lars Tyge Nielsen, 2019. "Instantaneous Arbitrage and the CAPM," Papers 1901.05113, arXiv.org.
    • Handle: RePEc:arx:papers:1901.05113
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. Schaefer, Stephen M, 1998. " Robert Merton, Myron Scholes and the Development of Derivative Pricing," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(2), pages 425-445, June.
    4. Stephen M. Schaefer, 1998. "Robert Merton, Myron Scholes and the Development of Derivative Pricing," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(2), pages 425-445, June.
    5. Darrell Duffie, 1998. "Black, Merton and Scholes — Their Central Contributions to Economics," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(2), pages 411-424, June.
    6. Lars Nielsen, 2007. "Dividends in the theory of derivative securities pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 447-471, June.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    8. Nielsen, Lars Tyge, 1999. "Pricing and Hedging of Derivative Securities," OUP Catalogue, Oxford University Press, number 9780198776192.
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