Journal
QUANTITATIVE FINANCE
Volume 15, Issue 9, Pages 1489-1499Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/14697688.2014.961531
Keywords
Statistical arbitrage; Black-Scholes model; Geometric Brownian motion; Monte Carlo simulation
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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.
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