Statistical Arbitrage in the Black-Scholes Framework
Mathematical Finance
2014-09-02 v4 Pricing of Securities
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.
Keywords
Cite
@article{arxiv.1406.5646,
title = {Statistical Arbitrage in the Black-Scholes Framework},
author = {Ahmet Goncu},
journal= {arXiv preprint arXiv:1406.5646},
year = {2014}
}