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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.

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  • 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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