Algorithmic Trading with Model Uncertainty

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