Optimal Hedge Tracking Portfolios in a Limit Order Book
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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
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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