Risk Metrics and Fine Tuning of High Frequency Trading Strategies

We propose risk metrics to assess the performance of High Frequency (HF) trading strategies that seek to maximize profits from making the realized spread where the holding period is extremely short (fractions of a second, seconds or at most minutes). The HF trader maximizes expected terminal wealth and is constrained by both capital and the amount of inventory that she can hold at any time. The risk metrics enable the HF trader to fine tune her strategies by trading off different metrics of inventory risk, which also proxy for capital risk, against expected profits. The dynamics of the midprice of the asset are driven by information flows which are impounded in the midprice by market participants who update their quotes in the limit order book. Furthermore, the midprice also exhibits stochastic jumps as a consequence of the arrival of market orders that have an impact on prices which can give rise to market momentum (expected prices to trend up or down). The HF trader's optimal strategy incorporates a buffer to cover adverse selection costs and manages inventories to maximize the expected gains from market momentum