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Relativistic Black-Scholes model

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  • Maciej Trzetrzelewski

Abstract

Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclidean version of the Dirac equation. Therefore the relativistic extension of the Black-Scholes model follows from relativistic quantum mechanics quite naturally. We investigate this particular model for the case of European vanilla options. Due to the notion of locality incorporated in this way one finds that the volatility frown-like effect appears when comparing to the original Black-Scholes model.

Suggested Citation

  • Maciej Trzetrzelewski, 2013. "Relativistic Black-Scholes model," Papers 1307.5122, arXiv.org, revised Feb 2018.
  • Handle: RePEc:arx:papers:1307.5122
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    1. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. 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.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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