market-microstructure

# Market Microstructure

## Overview

Study the micro-level mechanisms of price formation: who is trading, how they are trading, and how trades affect prices. For quantitative strategies, this matters because it improves transaction-cost estimation, identifies informed trading, and optimizes execution.

Applicable scenarios:
- Precise estimation of strategy trading costs (instead of simply assuming a flat 0.1% fee)
- Designing large-order execution strategies (`TWAP / VWAP / IS`)
- Detecting order-flow toxicity (avoid time windows dominated by informed traders)
- Quantifying liquidity risk (flash-crash warning)
- Capturing China A-share-specific microstructure features (call auction / closing auction / block trades)

## Core Concepts

### Bid-Ask Spread

**Three measurements:**
| Metric | Formula | Meaning |
|------|------|------|
| Quoted spread | `Ask - Bid` | Best spread shown in the limit order book |
| Effective spread | `2 × |trade price - mid price|` | Actual spread paid by the trader |
| Realized spread | `2 × direction × (trade price - mid price 5min later)` | True market-maker profit |

```
China A-share example:
  Instrument: 600519.SH Kweichow Moutai
  Best bid: 1680.00  Best ask: 1680.50
  Quoted spread: 0.50 RMB = 0.03%

  Instrument: 000001.SZ Ping An Bank
  Best bid: 11.05  Best ask: 11.06
  Quoted spread: 0.01 RMB = 0.09%

Spread decomposition (Roll):
  Spread = adverse-selection cost + inventory cost + order-processing cost
  In China A-shares: adverse selection accounts for 60-70% (mixture of retail and informed traders)

Spread drivers:
  - Larger market cap -> smaller spread (Moutai 0.03% vs small-cap 0.5%)
  - Higher volatility -> wider spread (market-maker risk premium)
  - Higher volume -> narrower spread (greater competition)
  - Higher information asymmetry -> wider spread (adverse selection)
```

### Order-Flow Toxicity Metrics

**VPIN (Volume-Synchronized Probability of Informed Trading):**
```
Principle: replace clock time with volume time to measure the probability of informed trading

Calculation steps:
  1. Bucket trades by fixed volume (Volume Bucket)
     Bucket size V = average daily volume / 50 (about 5-10 minutes per bucket)

  2. Classify buy and sell volume in each bucket (Bulk Volume Classification):
     buy_volume = V × Φ(ΔP / σ)  (standard normal CDF)
     sell_volume = V - buy_volume

  3. Compute order-flow imbalance:
     OI_i = |buy_volume_i - sell_volume_i|

  4. VPIN = Σ(OI_i) / (n × V)  (n=50-bucket rolling window)

Interpretation:
  VPIN < 0.3 -> normal, low informed-trading share
  VPIN 0.3-0.5 -> caution, informed trading rising
  VPIN > 0.5 -> dangerous, high probability that major information is about to be released

China A-share usage:
  A sudden VPIN spike in a stock may foreshadow:
  - insider trading ahead of a major announcement
  - institutional position building / distribution
  Before the 2015 China A-share flash crashes, VPIN stayed above 0.6 for a prolonged period
```

**Kyle's Lambda (price impact coefficient)**:
```
Model: ΔP = λ × OrderFlow + ε
  where OrderFlow = buy volume - sell volume

Estimation method:
  1. Compute ΔP and OrderFlow in 5-minute windows
  2. Regress ΔP = α + λ × OrderFlow
  3. λ = price change caused by one unit of order flow

Interpretation:
  Large λ -> poor liquidity, high impact
  Small λ -> good liquidity, large orders can be executed cheaply

Typical China A-share values:
  Large cap (CSI 300): λ ≈ 0.001-0.005
  Mid cap (CSI 500): λ ≈ 0.005-0.02
  Small cap (CSI 1000): λ ≈ 0.02-0.1
```

### Liquidity Measures

| Metric | Formula | Advantages | Disadvantages |
|------|------|------|------|
| Amihud illiquidity | `|R_t| / Volume_t` | Requires only daily data | Sensitive to extreme returns |
| Roll implied spread | `2√(-Cov(R_t, R_{t-1}))` | Requires only daily data | Fails when covariance is positive |
| LOT zero-return ratio | zero-return days / total days | Intuitive | Too coarse |
| Turnover ratio | volume / free float | Simple and intuitive | Does not reflect price impact |
| Traded value | average daily notional | Absolute liquidity | Does not reflect relative impact |

```
Amihud calculation (China A-shares):
  ILLIQ = (1/D) × Σ(|R_d| / VOL_d)  (D=trading days, monthly)

  Normalization: ILLIQ × 10^6 (for readability)

  Screening rules:
    ILLIQ < 0.5 -> high liquidity (large-cap blue chips)
    ILLIQ 0.5-5 -> medium liquidity
    ILLIQ > 5 -> low liquidity (trade cautiously)

  Strategy application:
    - Liquidity factor: low-liquidity stocks tend to earn long-run excess return (liquidity premium)
    - Liquidity monitor: sudden rise in ILLIQ -> warning of liquidity drying up
```

## Analysis Framework

### 1. Price-Impact Models

**Linear impact (Almgren-Chriss)**:
```
Model: impact = η × σ × (Q / V)^0.6
  η: impact coefficient, about 0.5-1.5 for China A-shares
  σ: daily volatility
  Q: traded quantity (shares)
  V: average daily volume (shares)

Example:
  Sell 100,000 shares of Kweichow Moutai
  Average daily volume 5,000,000 shares, daily volatility 1.8%
  impact = 1.0 × 0.018 × (100000/5000000)^0.6
         = 0.018 × 0.0085
         = 0.015% (1.5bp, acceptable)

  Sell 100,000 shares of a small-cap stock
  Average daily volume 500,000 shares, daily volatility 3.0%
  impact = 1.0 × 0.03 × (100000/500000)^0.6
         = 0.03 × 0.076
         = 0.23% (23bp, should be executed in slices)

Execution-splitting methods:
  TWAP: uniform in clock time -> simple but ignores market state
  VWAP: volume-profile execution -> better matches market rhythm
  IS: minimize Implementation Shortfall -> optimal but requires real-time optimization
```

**Nonlinear impact (square-root model)**:
```
impact = σ × √(Q / (ADV × T))
  σ: daily volatility
  Q: total trade size
  ADV: average daily traded value
  T: execution days

Applicable to: large trades (Q/ADV > 5%)
```

### 2. Limit Order Book Analysis

```
Depth metrics:
  Level 1 depth: queue size at the best bid and best ask
  Level 5 depth: total