Market Making

Market making is the process of providing liquidity to a financial market by simultaneously quoting both a buy (bid) and a sell (ask) price for an asset. Market makers profit from the bid-ask spread while managing the risks associated with price movements and inventory accumulation.

I. Core Mechanics: The Limit Order Book (LOB)

Most modern electronic markets operate via a Limit Order Book, which aggregates all outstanding buy and sell orders.

Bid-Ask Spread: The difference between the lowest sell price (Best Ask) and the highest buy price (Best Bid).
Mid-Price: The average of the best bid and best ask: $S_{mid} = \frac{P_{ask} + P_{bid}}{2}$ .
Market Depth: The volume of orders available at different price levels. A "deep" market can absorb large trades without significant price changes.
Adverse Selection: The risk that a market maker trades with someone who has superior information (e.g., an institutional trader or an insider), leading to a loss as the price moves against the market maker's position.

II. Inventory Risk Management

The primary challenge for a market maker is Inventory Risk—the risk that the value of the assets they hold (their inventory) will decrease before they can sell them.

Inventory Skew: When a market maker accumulates a large long or short position. To manage this, they adjust their quotes:
- Long Position ( $q > 0$ ): Lower both bid and ask prices to discourage further buys and encourage sells.
- Short Position ( $q < 0$ ): Raise both bid and ask prices to encourage buys and discourage further sells.
Reservation Price ( $r$ ): The "indifference" price at which a market maker is neutral to their current inventory. It is typically shifted away from the mid-price based on the current inventory $q$ and risk aversion $\gamma$ .

III. Mathematical Models: Avellaneda-Stoikov

The Avellaneda-Stoikov (2008) model is the classic framework for optimal market making, balancing the tradeoff between the spread (profit per trade) and the probability of execution.

1. The Reservation Price ( $r$ )

The model calculates a reference price that accounts for inventory risk:

r(s, t, q) = s - q \gamma \sigma^2 (T - t)

$s$ : Current market mid-price.
$q$ : Current inventory (number of units).
$\gamma$ : Risk aversion parameter.
$\sigma$ : Market volatility.
$T - t$ : Remaining time in the trading session.

2. The Optimal Spread ( $\delta$ )

The optimal distance from the reservation price for the bid and ask quotes is:

\delta = \frac{2}{\gamma} \ln\left(1 + \frac{\gamma}{\kappa}\right) + \gamma \sigma^2 (T - t)

$\kappa$ : Order book liquidity parameter (measures how quickly the probability of execution drops as the price moves away from the mid-price).

3. Quote Placement

The final bid and ask prices are placed symmetrically around the reservation price, not the mid-price:

Ask Price: $P_{ask} = r + \frac{\delta}{2}$
Bid Price: $P_{bid} = r - \frac{\delta}{2}$

IV. Key Performance Metrics

Metric	Description	Importance
Sharpe Ratio	Risk-adjusted return of the market-making strategy.	Measures if the spread profit compensates for the inventory risk.
Inventory Turnover	How quickly the market maker cycles through their inventory.	High turnover reduces exposure to long-term price trends.
Maximum Drawdown	The largest peak-to-trough decline in the portfolio value.	Critical for managing capital requirements and avoiding ruin.
Fill Rate	The percentage of quotes that are actually executed.	Measures the competitiveness of the quotes.