Ambiguity Aversion in Algorithmic and High Frequency Trading

Abstract

The concept of model uncertainty is one of increasing importance in the field of Mathematical Finance. The main goal of this work is to explore model uncertainty in the specific area of algorithmic and high frequency trading. From a behavioural perspective, model uncertainty naturally leads to the notion of ambiguity aversion - a person's tendency to avoid situations in which randomness plays a role, but the type of randomness itself is uncertain.

Electronic trading algorithms rely heavily on stochastic models of relevant variables, and the act of postulating a specific model creates vulnerabilities and risks due to model misspecification. Within the setting of a commonly used model for limit order and market order dynamics, the effects of protecting oneself against such misspecification in both high frequency market making and liquidation scenarios are investigated. In this case, different types of ambiguity aversion are shown to have different effects on optimal behaviour.

Further in this work, a new reference model is introduced in order to alleviate some practical issues with the original model. This model results in a highly simplified set of allowable trading behaviours, but introduces powerful predictive elements. This work concludes with another investigation of the effects of ambiguity aversion in the context of this new model.

Keywords: algorithmic trading, ambiguity aversion, stochastic control

JEL Classification: C61, C73, D81