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Statistical Arbitrage in the Black-Scholes Framework

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  • Ahmet Goncu

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.

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  • Ahmet Goncu, 2014. "Statistical Arbitrage in the Black-Scholes Framework," Papers 1406.5646, arXiv.org, revised Aug 2014.
    • Handle: RePEc:arx:papers:1406.5646
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    1. Mark Cummins & Andrea Bucca, 2012. "Quantitative spread trading on crude oil and refined products markets," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1857-1875, December.
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    6. Hogan, Steve & Jarrow, Robert & Teo, Melvyn & Warachka, Mitch, 2004. "Testing market efficiency using statistical arbitrage with applications to momentum and value strategies," Journal of Financial Economics, Elsevier, vol. 73(3), pages 525-565, September.
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    Cited by:

    1. Erdinc Akyildirim & Ahmet Goncu & Alper Hekimoglu & Duc Khuong Nguyen & Ahmet Sensoy, 2023. "Statistical arbitrage: factor investing approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(4), pages 1295-1331, December.

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