Trades Beget Trades: Cartea, Jaimungal and Ricci on High-Frequency Market Making

Watch a live order feed for five minutes and you will notice something that no textbook random-walk model captures: trades cluster. Nothing happens for twenty seconds, then eleven buy orders land in half a second, then quiet again. The market breathes in gasps.

Most market making models pretend otherwise. They assume orders arrive like raindrops, independently, at a steady average rate. Alvaro Cartea, Sebastian Jaimungal and Jason Ricci built a market making model that takes the clustering seriously, and the strategy that falls out of it is meaningfully smarter than the strategies that ignore it.

The problem: independence is a lie

The standard high-frequency market making setup, running from Ho and Stoll through Avellaneda and Stoikov, has a market maker posting a bid and an ask, with buy and sell orders arriving as independent random events. The market maker's only real worry is inventory.

That framework misses two things that any high-frequency trader will tell you are the entire game.

Order flow is self-exciting. A buy market order makes another buy market order more likely in the next few moments. Traders split large orders into pieces, other participants detect the buying and pile in, momentum algorithms wake up. Buying begets buying.

Order flow predicts price. A burst of aggressive buying is not noise. It is information. It tells you the price is more likely to go up than down over the next few seconds. Any market maker who ignores this will happily sell into a buying stampede and get run over, over and over again.

The key idea via analogy: earthquakes, not raindrops

Raindrops fall independently. One raindrop tells you nothing about the next.

Earthquakes do not work like that. A big earthquake dramatically raises the probability of another quake in the same place soon. Aftershocks cluster. The world has a memory, and recent events make near-future events more likely.

The mathematical object for describing earthquakes is a Hawkes process, a self-exciting process where each event temporarily bumps up the arrival rate of future events, and that bump then decays away. Cartea, Jaimungal and Ricci model order flow as exactly this, and they use a mutually exciting version, which means buy orders can excite sell orders and vice versa, not just their own kind.

Now the market maker has something genuinely new to work with: a live, decaying estimate of how hot the market currently is, and in which direction. And this changes the optimal quotes in ways that make immediate intuitive sense.

• When buying is hot, the model says the price is likely drifting up. So the market maker should be reluctant to sell. They pull their ask higher, out of harm's way, and they lower their bid too, because they would quite like to accumulate a long position ahead of an anticipated rise. They skew with the flow.
• When flow is balanced, the market maker quotes symmetrically and simply harvests the spread.
• When inventory piles up, the old inventory-management skew kicks in and pulls in the opposite direction.

So the optimal strategy is a tug of war between two forces: the short-term directional signal coming from the flow, which says lean into the move, and inventory risk, which says get flat. The paper solves that tug of war properly, delivering quoting rules that balance the two.

There is a further wrinkle the paper handles that most models ignore: the market maker's own trades feed the excitement. When you get filled, that is itself an event in the flow, which raises the intensity of subsequent orders. You are not an outside observer of the earthquake, you are standing on the fault line.

Why it mattered

• It made "alpha" and "inventory" coexist in one framework. Before this, the market making literature was mostly about inventory control, and the signal literature was mostly about prediction. This paper puts a genuine short-horizon price forecast inside a market making control problem and works out how the two interact. That is what real high-frequency trading desks actually do.
• It brought Hawkes processes into mainstream execution research. Clustering in order flow was well documented empirically. This paper showed you could put it inside a tractable control problem and get usable answers, which opened the floodgates for a wave of Hawkes-based execution and market making work.
• It formalises what "speed" is actually worth. The whole edge in the model comes from being able to observe the flow and react to it before it fully plays out. That is a precise, model-based statement of why low latency is valuable, and it is more honest than vague appeals to "being fast."
• It won recognition as a standout contribution, receiving SIAM's SIGEST award for its journal, which is a fair signal of how the mathematical finance community rated it.

The honest limitations

• Estimating a mutually exciting process is genuinely hard. You are fitting decay rates and cross-excitation parameters from noisy tick data. Those parameters are unstable, they shift across the trading day, and a strategy tuned to yesterday's parameters may be badly calibrated today.
• Everybody else in the market is a robot following fixed rules. The flow excites itself according to a mechanical law. Nobody adapts to you, nobody detects that you are systematically leaning into their flow and changes their behaviour to punish you. In a real market populated by other clever high-frequency firms, this is a strong assumption.
• Latency is assumed to be zero. The market maker sees the flow and instantly repositions their quotes. In practice, by the time you have observed the burst, decided, and got your cancel to the exchange, the informed traders have already taken your stale quote. The model's edge lives entirely in a window that real-world latency partially eats.
• Being filled is not the same as being right. The model's fills are essentially mechanical consequences of the intensity process. It does not really model the asymmetry that the trades you get filled on are disproportionately the ones you should not have wanted.
• It is a single-venue, single-asset world. Modern high-frequency trading is a cross-venue, cross-asset arbitrage business, and none of that is here.

The one-line takeaway

Cartea, Jaimungal and Ricci replaced the fiction that orders arrive independently with a model where trades excite more trades, like earthquakes and aftershocks, and showed that the optimal market maker must constantly balance two competing pulls: lean into the direction the flow is predicting, while never letting inventory build up enough to hurt.