English

Statistical Arbitrage in the Black-Scholes Framework

Mathematical Finance 2014-09-02 v4 Pricing of Securities

Abstract

In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expected value, variance, and probability of loss for the discounted cumulative trading profits. No-statistical arbitrage condition is derived for the Black-Scholes framework, which imposes a constraint on the Sharpe ratio of the stock. Furthermore, we verify our theoretical results via extensive Monte Carlo simulations.

Keywords

Cite

@article{arxiv.1406.5646,
  title  = {Statistical Arbitrage in the Black-Scholes Framework},
  author = {Ahmet Goncu},
  journal= {arXiv preprint arXiv:1406.5646},
  year   = {2014}
}
R2 v1 2026-06-22T04:44:04.418Z