Optimal Hedge Tracking Portfolios in a Limit Order Book

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Standard

Optimal Hedge Tracking Portfolios in a Limit Order Book. / Ellersgaard, Simon; Tegner, Martin.

I: Market Microstructure and Liquidity, Bind 3, Nr. 2, 1850003, 06.2017.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Ellersgaard, S & Tegner, M 2017, 'Optimal Hedge Tracking Portfolios in a Limit Order Book', Market Microstructure and Liquidity, bind 3, nr. 2, 1850003. https://doi.org/10.1142/S238262661850003X

APA

Ellersgaard, S., & Tegner, M. (2017). Optimal Hedge Tracking Portfolios in a Limit Order Book. Market Microstructure and Liquidity, 3(2), [1850003]. https://doi.org/10.1142/S238262661850003X

Vancouver

Ellersgaard S, Tegner M. Optimal Hedge Tracking Portfolios in a Limit Order Book. Market Microstructure and Liquidity. 2017 jun.;3(2). 1850003. https://doi.org/10.1142/S238262661850003X

Author

Ellersgaard, Simon ; Tegner, Martin. / Optimal Hedge Tracking Portfolios in a Limit Order Book. I: Market Microstructure and Liquidity. 2017 ; Bind 3, Nr. 2.

Bibtex

@article{a81ed50759b1422ba025b9d678e10d37,
title = "Optimal Hedge Tracking Portfolios in a Limit Order Book",
abstract = "Derivative hedging under transaction costs has attracted considerable attention over the past three decades. Yet comparatively little effort has been made towards integrating this problem in the context of trading through a limit order book. In this paper, we propose a simple model for a wealth-optimizing option seller, who hedges his position using a combination of limit and market orders, while facing certain constraints as to how far he can deviate from a targeted (Bachelierian) delta strategy. By translating the control problem into a three-dimensional Hamilton–Jacobi–Bellman quasi-variational inequality (HJB QVI) and solving numerically, we are able to deduce optimal limit order quotes alongside the regions surrounding the targeted delta surface in which the option seller must place limit orders vis-{\`a}-vis the more aggressive market orders. Our scheme is shown to be monotone, stable, and consistent and thence, modulo a comparison principle, convergent in the viscosity sense.",
keywords = "Delta hedging and limit order book, HJB QVI",
author = "Simon Ellersgaard and Martin Tegner",
year = "2017",
month = jun,
doi = "10.1142/S238262661850003X",
language = "English",
volume = "3",
journal = "Market Microstructure and Liquidity",
issn = "2382-6266",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - Optimal Hedge Tracking Portfolios in a Limit Order Book

AU - Ellersgaard, Simon

AU - Tegner, Martin

PY - 2017/6

Y1 - 2017/6

N2 - Derivative hedging under transaction costs has attracted considerable attention over the past three decades. Yet comparatively little effort has been made towards integrating this problem in the context of trading through a limit order book. In this paper, we propose a simple model for a wealth-optimizing option seller, who hedges his position using a combination of limit and market orders, while facing certain constraints as to how far he can deviate from a targeted (Bachelierian) delta strategy. By translating the control problem into a three-dimensional Hamilton–Jacobi–Bellman quasi-variational inequality (HJB QVI) and solving numerically, we are able to deduce optimal limit order quotes alongside the regions surrounding the targeted delta surface in which the option seller must place limit orders vis-à-vis the more aggressive market orders. Our scheme is shown to be monotone, stable, and consistent and thence, modulo a comparison principle, convergent in the viscosity sense.

AB - Derivative hedging under transaction costs has attracted considerable attention over the past three decades. Yet comparatively little effort has been made towards integrating this problem in the context of trading through a limit order book. In this paper, we propose a simple model for a wealth-optimizing option seller, who hedges his position using a combination of limit and market orders, while facing certain constraints as to how far he can deviate from a targeted (Bachelierian) delta strategy. By translating the control problem into a three-dimensional Hamilton–Jacobi–Bellman quasi-variational inequality (HJB QVI) and solving numerically, we are able to deduce optimal limit order quotes alongside the regions surrounding the targeted delta surface in which the option seller must place limit orders vis-à-vis the more aggressive market orders. Our scheme is shown to be monotone, stable, and consistent and thence, modulo a comparison principle, convergent in the viscosity sense.

KW - Delta hedging and limit order book

KW - HJB QVI

U2 - 10.1142/S238262661850003X

DO - 10.1142/S238262661850003X

M3 - Journal article

VL - 3

JO - Market Microstructure and Liquidity

JF - Market Microstructure and Liquidity

SN - 2382-6266

IS - 2

M1 - 1850003

ER -

ID: 197769238