Algorithmic Trading with Model Uncertainty

Forthcoming: SIAM Journal on Financial Mathematics

47 Pages Posted: 15 Aug 2013 Last revised: 5 Apr 2017

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Ryan Francis Donnelly

University of Washington - Department of Applied Mathematics

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: April 4, 2017

Abstract

Algorithmic traders acknowledge that their models are incorrectly specified, thus we allow for ambiguity in their choices to make their models robust to misspecification in: (i) the arrival rate of market orders (MOs), (ii) the fill probability of limit orders, and (iii) the dynamics of the midprice of the asset they deal. In the context of market making, we demonstrate that market makers (MMs) adjust their quotes to reduce inventory risk and adverse selection costs. Moreover, robust market making increases the strategies Sharpe ratio and allows the MM to fine tune the tradeoff between the mean and the standard deviation of profits. We provide analytical solutions for the robust optimal strategies, show that the resulting dynamic programming equations have classical solutions and provide a proof of verification. The behavior of the ambiguity averse MM are found to generalize those of a risk averse MM, and coincide in a limiting case.

Keywords: market making, algorithmic trading, high frequency trading, robust optimization, ambiguity aversion, Knightian uncertainty, Poisson random measures, short term alpha, adverse selection

JEL Classification: C6, C61, C73, G12

Suggested Citation

Cartea, Álvaro and Donnelly, Ryan Francis and Jaimungal, Sebastian, Algorithmic Trading with Model Uncertainty (April 4, 2017). Forthcoming: SIAM Journal on Financial Mathematics. Available at SSRN: https://ssrn.com/abstract=2310645 or http://dx.doi.org/10.2139/ssrn.2310645

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Ryan Francis Donnelly

University of Washington - Department of Applied Mathematics ( email )

Box 352420
Seattle, WA 98195-2420
United States

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://www.utstat.utoronto.ca/sjaimung

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