On the existence of sure profits via flash strategies

TL;DR

This paper characterizes the absence of sure profits via flash strategies in financial markets, showing it is equivalent to the absence of predictable jumps in asset prices, under very general conditions.

Contribution

It provides the most general conditions under which sure profits via flash strategies cannot exist, without assuming semimartingale properties.

Findings

Sure profits via flash strategies exist iff asset prices have predictable jumps.

Asset prices are right-continuous if no sure profits exist.

Results hold under small transaction costs and minimal assumptions.

Abstract

We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there are no sure profits via flash strategies if and only if asset prices do not exhibit predictable jumps. This result relies on the general theory of processes and provides the most general formulation of the well-known fact that, in an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable direction or magnitude at predictable times. We furthermore show that any price process is always right-continuous in the absence of sure profits. Our results are robust under small transaction costs and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.