Where Should a Market Maker Set Its Prices? Avellaneda-Stoikov

Imagine you run a little booth at a busy market where your job is to always be willing to both buy and sell the same item. You shout out two prices at once: "I'll buy at $99, I'll sell at $101." People walk up and take whichever side they like. You earn the $2 gap when a buyer and a seller show up in roughly equal numbers.

Simple, until the crowd gets lopsided. Suppose sellers keep coming and buyers vanish. You keep buying and buying, and now you're sitting on a mountain of the item. If its value suddenly drops, you're in serious trouble. This pile you've involuntarily accumulated is your inventory, and managing the risk of it is the market maker's central headache.

In 2008, Marco Avellaneda and Sasha Stoikov wrote the paper that finally answered, with clear math, the two questions every market maker faces every instant: where exactly should I set my two prices, and how should I shift them as my inventory piles up? It became the go-to recipe for automated market making.

The two jobs pulling against each other

A market maker is trying to do two things at once, and they fight each other:

• Earn the spread. You want to quote a wide gap between your buy and sell prices, because that gap is your profit on every round-trip trade. Wider is more profitable per trade.
• Actually get trades. But quote too wide and nobody uses your booth, they'll go to a competitor with tighter prices. Quote narrow and you get lots of business but earn little per trade, and you accumulate inventory fast.

On top of that tug-of-war sits the inventory danger. Every trade you do leaves you holding more or less of the item than you'd like, and holding a big pile, long or short, is risky, because the price could move against you before you can offload it.

The core trick: lean your prices to shed inventory

Here's the paper's central and most intuitive idea. Your two quotes shouldn't just sit symmetrically around the market price. They should lean depending on what you're holding.

• Holding too much (you've been buying too much and are sitting on a big long pile)? Shift both your prices down. By lowering your sell price you become eager to offload, and by lowering your buy price you discourage buying even more. You're nudging the crowd to take inventory off your hands.
• Holding too little / short (you've sold more than you've bought)? Shift both prices up. Now you're eager to buy back and reluctant to sell more, pulling your position back toward neutral.

This leaning is the whole game. The market maker uses their prices like a steering wheel, constantly nudging themselves back toward a comfortable, balanced inventory. When you're overloaded, you make it attractive for others to relieve you, even at a slightly worse price, because dumping the risk is worth more than squeezing out the last bit of spread.

The "fair price" versus the "quotes"

Avellaneda and Stoikov split the problem into two clean pieces, and the split is genuinely clarifying.

First, they define a reservation price, think of it as your personal fair value for the item, adjusted for the risk you're carrying. It is not the same as the market's mid-price. If you're holding a big long inventory, your personal fair value sits below the market price, because you're anxious to sell and would accept a bit less. Your inventory literally tilts your sense of what the thing is worth to you.

Second, they place your two quotes at a comfortable distance on either side of that personal fair value. How wide to space them depends on:

• How nervous you are (risk aversion). More cautious market makers quote wider and steer their inventory back to neutral more aggressively.
• How bouncy the item is (volatility). More volatile means more danger in holding inventory, so you quote wider to compensate.
• How much time is left. Near the end of the trading day, you get more anxious to flatten out your inventory, so you steer harder, nobody wants to be stuck holding a big risky pile overnight.

That two-step structure, first figure out your inventory-adjusted fair value, then set a spread around it, is the paper's lasting contribution. It cleanly separates "what's it worth to me right now?" from "how wide should I quote?"

Why it mattered

This paper landed right as electronic and high-frequency trading were exploding, and it hit a sweet spot: rigorous enough to be trustworthy, simple enough to actually run on a computer thousands of times a second.

• It became the standard baseline for automated market making. If you want to build a market-making bot, in stocks, crypto, futures, anywhere with an order book, the Avellaneda-Stoikov model is very often where you start. It's the "hello world" of quote-setting.
• It made inventory risk the star. Earlier microstructure work (like Glosten-Milgrom) focused on the adverse selection reason for spreads, fear of informed traders. Avellaneda-Stoikov shone the light on the other big reason: the plain risk of getting stuck holding too much. Together, those two ideas explain most of why spreads exist.
• It's endlessly extended. Countless research papers and trading systems have taken this skeleton and added realism, competition, informed traders, richer order books, but the core steering logic remains recognizably theirs.

The honest limitations

It's a foundational model, which means it trades realism for clarity:

• It largely ignores adverse selection. The basic model treats incoming orders as essentially random, saying little about the danger that whoever's trading with you knows something. In reality that fear is huge, and it's exactly what Glosten-Milgrom focused on. A real market maker must worry about both inventory and informed traders.
• It assumes a fairly simple, well-behaved market. Real order books are chaotic, orders cancel, queues form, competitors react to you, liquidity vanishes in a flash crash. The clean model doesn't capture that turbulence.
• The parameters are hard to pin down. Just like the other models here, the "right" settings for risk aversion and order arrival rates must be estimated from messy data, and getting them wrong degrades the strategy.
• It's a starting point, not a finished trading system. Anyone deploying real money layers on many practical safeguards the paper never mentions.

The one-line takeaway

Avellaneda and Stoikov showed that a market maker should set its two prices around an inventory-adjusted fair value and lean those prices to steer its stockpile back to neutral, earning the spread while never letting the pile of stock it accidentally accumulates grow dangerous, which is why it remains the go-to recipe for automated market-making bots today.