做市 / Market Making

本页结构

核心概念

限价订单簿机制与买卖价差 Limit order book mechanics and bid-ask spread
库存风险与保留价格 Inventory risk and reservation price
报价位置与做市绩效指标 Quote placement and market-making performance metrics

学习顺序

把逆向选择风险和库存风险分开讨论。 Discuss adverse selection separately from inventory risk.
更宽价差降低成交概率，但提高单笔补偿。 A wider spread reduces fill rate but improves per-trade compensation.
把模型参数和波动率、风险厌恶、订单到达率联系起来。 Relate model parameters to volatility, risk aversion and order arrival.

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.

做市是通过同时报价资产的买入（买入）和卖出（卖出）价格来向金融市场提供流动性的过程。做市商从买卖价差中获利，同时管理与价格变动和库存积累相关的风险。

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

大多数现代电子市场通过限价订单簿运作，该订单簿汇总了所有未完成的买卖订单。

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.

买卖价差：最低卖出价（最佳卖出价）和最高买入价（最佳买入价）之间的差额。
中间价格：最佳出价和最佳要价的平均值： $S_{mid} = \frac{P_{ask} + P_{bid}}{2}$ 。
市场深度：不同价格水平下的可用订单量。 “深度”市场可以吸收大量交易，而无需发生重大价格变化。
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.

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.

做市商面临的主要挑战是库存风险——他们持有的资产（库存）的价值在出售之前就会下降的风险。

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 $\gamma$ .

库存偏斜：当做市商积累大量多头或空头头寸时。为了管理这一点，他们调整报价： 多头头寸 ( $q > 0$ )：降低买入价和卖出价以阻止进一步买入并鼓励卖出。 空头头寸 ( $q < 0$ )：提高买入价和卖出价以鼓励买入并阻止进一步卖出。
保留价格 ( $r$ )：做市商对其当前库存保持中立的“无差异”价格。它通常会根据当前库存 $q$ 和风险规避 $\gamma$ 偏离中间价格。

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.

Avellaneda-Stoikov (2008) 模型是最佳做市的经典框架，平衡点差（每笔交易的利润）和执行概率之间的权衡。

1. The Reservation Price (rr)

1. 预订价格（rr）

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

该模型计算考虑库存风险的参考价格：

$s$ : 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.

$s$ : 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 (δ\delta)

2. 最佳价差 (δ\delta)

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

买入价和卖出价与保留价的最佳距离是：

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

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

3. Quote Placement

3. 报价放置

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

最终买入价和卖出价围绕保留价对称放置，而不是中间价：

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

要价： $P_{ask} = r + \frac{\delta}{2}$
投标价格： $P_{bid} = r - \frac{\delta}{2}$

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.

公制	描述	重要性
夏普比率	做市策略的风险调整回报。	衡量价差利润是否补偿库存风险。
库存周转率	做市商循环库存的速度有多快。	高周转率减少了对长期价格趋势的影响。
最大回撤	投资组合价值从峰到谷的最大跌幅。	对于管理资本需求和避免破产至关重要。
填充率	实际执行的报价百分比。	衡量报价的竞争力。

补充讲解

价差补偿多种风险

Spread compensates several risks

买卖价差补偿库存风险、逆向选择、延迟和运营成本。价差更窄不一定意味着策略更好。

The bid-ask spread compensates inventory risk, adverse selection, latency, and operational costs. A narrow spread is not automatically better.

库存会改变报价

Inventory changes quotes

做市商通常根据库存偏移报价：多头库存过高时降低买价或提高卖出积极性；空头库存过高时反向处理。

A market maker usually skews quotes based on inventory: lower bids or more aggressive asks reduce long inventory, and the reverse reduces short inventory.

成交质量比成交数量更重要

Fill quality matters

高成交率并不一定好；如果成交主要发生在知情交易者预期价格将朝不利方向移动时，策略反而受损。

High fill rates can be bad if fills occur mainly when informed traders know the price is about to move against you.

做市