On the existence of sure profits via flash strategies

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 arbitragefree 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.According to the efficient market hypothesis, asset prices should fully reflect all available information (see [Fam70]). In particular, if asset prices suddenly change at scheduled or predictable dates, then this can only be due to the release of unanticipated information. Indeed, under market Date: July 31, 2019.2010 Mathematics Subject Classification. 60G07, 60G17, 60G44, 91G99.

Term structure modeling with overnight rates beyond stochastic continuity

“…More specifically, condition (iii) relates the stochastic discontinuities  in the numéraire to the short end of the forward rate, while condition (iv) concerns the stochastic discontinuities  in the forward term rate. Taken together, conditions (iii) and (iv) exclude the possibility of predicting the size (or the direction) of the jump occurring at any discontinuity date, as this would be incompatible with absence of arbitrage (see Fontana et al (2019) for an analysis of the arbitrage possibilities arising with predictable jumps).…”

“…Taken together, conditions (iii) and (iv) exclude the possibility of predicting the size (or the direction) of the jump occurring at any discontinuity date, as this would be incompatible with absence of arbitrage (see Fontana et al. (2019) for an analysis of the arbitrage possibilities arising with predictable jumps).…”

Term structure modelling with overnight rates beyond stochastic continuity

“…More specifically, condition (iii) relates the stochastic discontinuities T in the numéraire to the short end of the forward rate, while condition (iv) concerns the stochastic discontinuities S in the forward term rate. Taken together, conditions (iii)-(iv) exclude the possibility of predicting the size (or the direction) of the jump occurring at any discontinuity date, as this would be incompatible with absence of arbitrage (see Fontana et al (2019) for an analysis of arbitrages possibilities arising with predictable jumps).…”

Term structure modelling for multiple curves with stochastic discontinuities

“…Together, they correspond to excluding the possibility that, at some predetermined date T n , discounted assets exhibit jumps whose size can be predicted on the basis of the information contained in F Tn´. Indeed, such a possibility would violate absence of arbitrage (compare with Fontana et al (2019)).…”