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Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate

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  • Martin Gremm

Abstract

We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diversified portfolio rather than as an arbitrary external parameter. The risk-free rate measures the rate of global price rescaling, which is a gauge symmetry of economies. We explore the properties of risk-free rates, rederive the Black Scholes equation with a new interpretation of the risk-free rate parameter as a that background gauge field, and discuss gauge invariant discounting of cash flows.

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  • Martin Gremm, 2016. "Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate," Papers 1605.03551, arXiv.org.
    • Handle: RePEc:arx:papers:1605.03551
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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. Lee Smolin, 2009. "Time and symmetry in models of economic markets," Papers 0902.4274, arXiv.org.
    3. Martin Gremm, 2015. "The Stress-Dependent Random Walk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-16, December.
    4. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    5. 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.
    6. J. K. Hoogland & C. D. D. Neumann, 2001. "Local Scale Invariance And Contingent Claim Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-21.
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    Cited by:

    1. Magomet Yandiev, 2021. "Risk-Free Rate in the Covid-19 Pandemic: Application Mistakes and Conclusions for Traders," Papers 2111.07075, arXiv.org.

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