Statistical arbitrage in the Black–Scholes framework

Ahmet Göncü*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


In this study, we prove the existence of statistical arbitrage opportunities in the Black–Scholes framework by considering trading strategies that consist of borrowing at 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. The statistical arbitrage condition is derived in 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.

Original languageEnglish
Pages (from-to)1489-1499
Number of pages11
JournalQuantitative Finance
Issue number9
Publication statusPublished - 2 Sept 2015


  • Black–Scholes model
  • Geometric Brownian motion
  • Monte Carlo simulation
  • Statistical arbitrage


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