Real-Time Detection of Local No-Arbitrage Violations

TL;DR

This paper develops real-time sequential detectors for identifying local violations of the Itô semimartingale assumption in high-frequency financial data, enabling immediate detection of potential arbitrage opportunities.

Contribution

It introduces new stopping rules for real-time detection of local no-arbitrage violations, with proven asymptotic properties and demonstrated effectiveness on empirical data.

Findings

Detectors are asymptotically exponentially distributed under no violation.

Immediate detection is possible when violations occur.

Empirical tests on S&P 500 futures data confirm detector effectiveness.

Abstract

This paper focuses on the task of detecting local episodes involving violation of the standard It\^o semimartingale assumption for financial asset prices in real time that might induce arbitrage opportunities. Our proposed detectors, defined as stopping rules, are applied sequentially to continually incoming high-frequency data. We show that they are asymptotically exponentially distributed in the absence of Ito semimartingale violations. On the other hand, when a violation occurs, we can achieve immediate detection under infill asymptotics. A Monte Carlo study demonstrates that the asymptotic results provide a good approximation to the finite-sample behavior of the sequential detectors. An empirical application to S&P 500 index futures data corroborates the effectiveness of our detectors in swiftly identifying the emergence of an extreme return persistence episode in real time.