  Drawing insights from the triumph of relativistic over classical mechanics
when velocities approach the speed of light, we explore a similar improvement
to the seminal Black-Scholes (Black and Scholes (1973)) option pricing formula
by considering a relativist version of it, and then finding a respective
solution. We show that our solution offers a significant improvement over
competing solutions (e.g., Romero and Zubieta-Martinez (2016)), and obtain a
new closed-form option pricing formula, containing the speed limit of
information transfer c as a new parameter. The new formula is rigorously shown
to converge to the Black-Scholes formula as c goes to infinity. When c is
finite, the new formula can flatten the standard volatility smile which is more
consistent with empirical observations. In addition, an alternative family of
distributions for stock prices arises from our new formula, which offer a
better fit, are shown to converge to lognormal, and help to better explain the
volatility skew.
