On the Microstructural Hedging Error

Robert, Christian; Rosenbaum, Mathieu

doi:10.1137/090764578

Cited by 14 publications

(4 citation statements)

References 32 publications

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“…It is shown in [34] that this model indeed reproduces (almost) all the main stylized facts of prices and durations at any frequency (from low frequency data to ultra high frequency data). In practice, this model is particularly convenient in order to estimate relevant parameters such as the volatility or the covariation at the ultra high frequency level, see [35], or when one wants to hedge a derivative in an intraday manner, see [33].…”

Section: Statistical Modelmentioning

confidence: 99%

Large Tick Assets: Implicit Spread and Optimal Tick Size

Dayri¹,

Rosenbaum²

2015

Mark. Microstructure Liq.

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In this work, we provide a framework linking microstructural properties of an asset to the tick value of the exchange. In particular, we bring to light a quantity, referred to as implicit spread, playing the role of spread for large tick assets, for which the effective spread is almost always equal to one tick. The relevance of this new parameter is shown both empirically and theoretically. This implicit spread allows us to quantify the tick sizes of large tick assets and to define a notion of optimal tick size. Moreover, our results open the possibility of forecasting the behavior of relevant market quantities after a change in the tick value and to give a way to modify it in order to reach an optimal tick size. arXiv:1207.6325v2 [q-fin.TR]

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Section: Statistical Modelmentioning

confidence: 99%

Large Tick Assets: Implicit Spread and Optimal Tick Size

Dayri¹,

Rosenbaum²

2015

Mark. Microstructure Liq.

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“…This asymptotic approach has also been recently used in the context where the rebalancing times are random stopping times. Some specific hitting times based schemes derived from a microstructure model are investigated in [12]. In [4], the author works with quite general sampling schemes based on stopping times.…”

Section: Introductionmentioning

confidence: 99%

Optimal Discretization of Hedging Strategies with Directional Views

Cai¹,

Fukasawa²,

Rosenbaum³

et al. 2016

SIAM J. Finan. Math.

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We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him to keep the discretization error small while taking advantage of market trends. Assuming that the portfolio is readjusted at high frequency, we introduce an asymptotic framework in order to derive optimal discretization strategies. More precisely, we formulate the optimization problem in terms of an asymptotic expectation-error criterion. In this setting, the optimal rebalancing times are given by the hitting times of two barriers whose values can be obtained by solving a linear-quadratic optimal control problem. In specific contexts such as in the Black-Scholes model, explicit expressions for the optimal rebalancing times can be derived.

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“…[18,35] for relevant examples in the setting of continuous processes) and for approximating the solutions of stochastic differential equations by Euler-type schemes with random discretization dates (see e.g., [26,39]). …”

Section: Introductionmentioning

confidence: 99%

Asymptotic results for time-changed Lévy processes sampled at hitting times

Rosenbaum

Tankov

2011

Stochastic Processes and their Applications

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We provide asymptotic results for time-changed Lévy processes sampled at random instants. The sampling times are given by the first hitting times of symmetric barriers, whose distance with respect to the starting point is equal to ε. For a wide class of Lévy processes, we introduce a renormalization depending on ε, under which the Lévy process converges in law to an α-stable process as ε goes to 0. The convergence is extended to moments of hitting times and overshoots. These results can be used to build high frequency statistical procedures. As examples, we construct consistent estimators of the time change and, in the case of the CGMY process, of the Blumenthal-Getoor index. Convergence rates and a central limit theorem for suitable functionals of the increments of the observed process are established under additional assumptions.

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On the Microstructural Hedging Error

Cited by 14 publications

References 32 publications

Large Tick Assets: Implicit Spread and Optimal Tick Size

Large Tick Assets: Implicit Spread and Optimal Tick Size

Optimal Discretization of Hedging Strategies with Directional Views

Asymptotic results for time-changed Lévy processes sampled at hitting times

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