Arbitrage-free Models In Markets With Transaction Costs

The existence of time-lagged cross-correlations between the returns of a pair of assets, which is known as the lead-lag relationship, is a well-known stylized fact in financial econometrics. Recently some continuous-time models have been proposed to take account of the lead-lag relationship. Such a model does not follow a semimartingale as long as the lead-lag relationship is present, so it admits an arbitrage without market frictions. In this paper we show that they are free of arbitrage if we take account of market frictions such as the presence of minimal waiting time on subsequent transactions or transaction costs.

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“…Noting the above results, we obtain the following result from Proposition 1 of Sayit and Viens [48]:…”

Section: Trading Under Transaction Costsmentioning

confidence: 59%

“…The above definition of the stickiness is due to Definition 2.2 of Bender et al [3]. However, as is pointed out in Remark 2.1 of [3], this definition turns out to be equivalent to the notion of joint stickiness in Sayit and Viens [48]. More precisely, we have the following result:…”

Section: Trading Under Transaction Costsmentioning

confidence: 79%

No arbitrage and lead–lag relationships

Hayashi

Koike

2019

Statistics & Probability Letters

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“…To show the second claim in the Lemma it is sufficient to show that X t , Y t are sticky for H. The stickiness of X t ±Y t with respect to H then follows from Proposition 1 of Sayit and Viens [24] (continuous functions of sticky processes are sticky). We only show that X is sticky for H, the argument for Y being identical.…”

Section: Resultsmentioning

confidence: 98%

“…Let X satisfy CFS and let L be a sticky Lévy process such that they are independent. Then S t := f (X t , L t ) is also sticky for any continuous function f : R d+1 → R, by Proposition 1 of Sayit and Viens [24]. For example, one can replace the Brownian motion B t in (4) by a fractional Brownian motion B H t that is independent from N t , and obtain a sticky process which is not a semi-martingale.…”

Section: Examplesmentioning

confidence: 93%

Sticky processes, local and true martingales

Rásonyi¹,

Sayit²

2018

Bernoulli

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We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingaleS that is arbitrarily close to S in L p (Q) norm. For continuous S,S can be chosen arbitrarily close to S in supremum norm. In the case where S is a local martingale we may choose Q arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present an application in mathematical finance. * The first author was supported by the "Lendület" Grant LP2015-6 of the Hungarian Academy of Sciences. Discussions with Martin Keller-Ressel led to formulating the main results of the present paper, we sincerely thank him. We also thank Eberhard Mayerhofer for spotting an error and two anonymous referees for helpful reports which revealed, in particular, another problem in a previous version of this paper. † MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15,

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“…One well‐known example is the conditional full support condition proposed by Guasoni, Rásonyi, and Schachermayer (). Other related sufficient conditions are discussed in Bayraktar and Sayit (), Maris, Mbakop, and Sayit (), and Sayit and Viens (). Recently, for continuous price processes, Rásonyi and Schachermayer () built the equivalence between the absence of arbitrage with general strategies for any small constant transaction cost

λ > 0

and the existence of a CPS for any small transaction cost

λ > 0

.…”

Section: Introductionmentioning

confidence: 99%

On the market viability under proportional transaction costs

Bayraktar

2017

Mathematical Finance

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Abstract. This paper studies the market viability with proportional transaction costs. Instead of requiring the existence of strictly consistent price systems (SCPS) as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABP). In particular, we show that the NUPBR and NLABP conditions in the robust sense for the smaller bid-ask spreads is the equivalent characterization of the existence of SCLMS for general market models. We also discuss the implications for the utility maximization problem.

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Arbitrage-free Models In Markets With Transaction Costs

Cited by 11 publications

References 19 publications

No arbitrage and lead–lag relationships

No arbitrage and lead–lag relationships

Sticky processes, local and true martingales

On the market viability under proportional transaction costs

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