2017/11/12 by Yanlin Qu, Qu, Yanlin, Randall R. Rojas +1
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Statistical Mechanics and Entropy #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1711.04219
arxiv created 2017/11/12 · openalex publication_date 2017/11/12 · arxiv updated 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.