Need for Speed? Exchange Latency and Liquidity

Speeding up the exchange has a non-trivial effect on liquidity. On the one hand, more speed enables high-frequency market makers (HFMs) to update their quotes more quickly on incoming news. This reduces adverse-selection cost and lowers the competitive bid-ask spread. On the other hand, HFM price quotes are more likely to meet speculative high-frequency “bandits,” thus less likely to meet liquidity traders. This raises the spread. The net effect depends on a security’s news-to-liquidity-trader ratio. Empirical analysis of a NASDAQ-OMX speed upgrade shows that a faster market can indeed raise the spread and thus lower liquidity.


Topology of modern exchanges
HFTs choose between two strategies: 1.1 High-frequency market maker (HFM) 1.2 High-frequency bandit (HFB) HFTs have an inventory constraint of one unit (long/short).

Primitives
HFTs choose between two strategies: HFTs choose between two strategies: HFTs have an inventory constraint of one unit (long/short).

Uninformed and slow: Liquidity traders (LT
HFTs choose between two strategies: 1.1 High-frequency market maker (HFM) 1.2 High-frequency bandit (HFB) HFTs have an inventory constraint of one unit (long/short).

Uninformed and slow: Liquidity traders (LT).
Exchange 1. News arrives with probability ατ in a period of length τ . Common value jumps by ±σ.
3. Either zero or one event possible in a latency interval δ. The probability of two or more events is ignored.
Common value v t can change in an interval δ: Timing Timing of the model is as follows: and HFBs send quote-snipe order at matcher 1. At t ∈ {−1, 0}, HFTs decide whether to submit a market order, cancel limit orders, or both.
Let U HFB (s|trade) be the expected HFB profit conditional on a trade (s is half-spread, referred to as spread throughout): No event during latency delay News arrives during latency delay

HFB profit
Let U HFB (s|trade) be the expected HFB profit conditional on a trade (s is half-spread, referred to as spread throughout): No event during latency delay

News arrives during latency delay
Each HFT is first to the market with probability 1 H .

HFB profit
Let U HFB (s|trade) be the expected HFB profit conditional on a trade (s is half-spread, referred to as spread throughout): No event during latency delay

News arrives during latency delay
Each HFT is first to the market with probability 1 H . The HFB expected profit is:

HFM profit
The HFM expected profit, U HFB (s), is:

HFM profit
The HFM expected profit, U HFB (s), is: No event/LT on same side + µδ 2 2s LT on opposite side

HFM profit
The HFM expected profit, U HFB (s), is:

HFM profit
The HFM expected profit, U HFB (s), is: No event/LT on same side + µδ 2 2s LT on opposite side µδ (s − σ) γ LT on news side LT on no-news side News arrives during latency delay No event during latency delay The following strategies for HFM and HFB constitute a unique equilibrium for γ <γ.
1. At t = −1, all HFTs submit one buy limit order at v 0 − s * and one sell limit order at v 0 + s * . The first arriving HFT (picked randomly) fills the order book; we refer to this HFT as the HFM and to the other HFTs as HFBs.
2. A trigger event occurs at time t = 0. If the trigger event is a news arrival (i.e., if v 0 = v −1 ), then the HFM submits a quote-cancel order and, at the same time, all HFBs submit a market order aimed at the stale quote on the news side of the book (i.e., the ask side if news was good or the bid side when news was bad).