2014/06/21 by Goncu, Ahmet
#FOS: Economics and business #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR)
paper · doi:10.48550/arxiv.1406.5646
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.