Statistical Arbitrage in the Black-Scholes Framework

Ahmet Goncu

Papers from arXiv.org

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.

Date: 2014-06, Revised 2014-08
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Citations: View citations in EconPapers (1)

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Journal Article: Statistical arbitrage in the Black-Scholes framework (2015)
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