The relativistic Black-Scholes model
M. Smoluchowski Institute of Physics, Jagiellonian University - Łojasiewicza, St. 11, 30-348 Kraków, Poland
Received: 21 January 2017
Accepted: 8 March 2017
The 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.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 87.10.Mn – Stochastic modeling / 02.50.Fz – Stochastic analysis
© EPLA, 2017