Supply and Demand Elasticity in Market Microstructure

Understanding elasticity in market microstructure

Supply and demand elasticity in market microstructure differs from traditional economic elasticity by focusing on the immediate price response to order flow in financial markets. The concept helps explain how liquidity is provided and consumed in electronic markets.

The elasticity of supply (ES) and elasticity of demand (ED) in market microstructure can be expressed as:

$ES = \frac{\Delta Q_s/Q_s}{\Delta P/P}$

$ED = -\frac{\Delta Q_d/Q_d}{\Delta P/P}$

Where:

• $\Delta Q_s$ and $\Delta Q_d$ represent changes in supplied and demanded quantities
• $\Delta P$ represents price changes
• $Q_s$, $Q_d$, and $P$ are initial quantities and price

Role in price formation

Price formation in electronic markets is heavily influenced by the elasticity of supply and demand in the limit order book. Market makers adjust their quotes based on these elasticities:

The speed and magnitude of price adjustments depend on:

• Market maker inventory positions
• Order flow toxicity levels
• Current market volatility
• Trading volume

Impact on market making strategies

Market making algorithms must account for supply and demand elasticity when:

1. Setting bid-ask spreads
2. Determining quote sizes
3. Managing inventory risk
4. Responding to order flow imbalances

The optimal quote placement can be modeled as:

$P_{opt} = P_{mid} \pm \frac{\sigma}{2\sqrt{\kappa}}$

Where:

• $P_{opt}$ is the optimal quote price
• $P_{mid}$ is the mid-price
• $\sigma$ is volatility
• $\kappa$ is the elasticity parameter

Applications in algorithmic trading

Algorithmic trading strategies utilize elasticity measurements to:

1. Predict short-term price movements
2. Optimize execution timing
3. Detect market regime changes
4. Assess market impact costs

The market impact function incorporating elasticity can be expressed as:

$MI(q) = \sigma \cdot \left(\frac{q}{V}\right)^{\frac{1}{\epsilon}}$

Where:

• $MI(q)$ is the market impact for order size $q$
• $V$ is daily volume
• $\epsilon$ is the elasticity coefficient
• $\sigma$ is volatility

Relationship with market stability

Market elasticity plays a crucial role in:

1. Price discovery efficiency
2. Market resilience during stress
3. Liquidity formation dynamics
4. Flash crash prevention

Higher elasticity generally indicates:

• More resilient markets
• Better price discovery
• Lower transaction costs
• Reduced market impact

Measuring market elasticity

Market elasticity can be estimated using:

1. Order book pressure metrics
2. Volume-price relationships
3. Trade flow analysis
4. Quote revision patterns

The empirical estimation often uses regression models:

$\Delta P_t = \alpha + \beta \cdot OFI_t + \gamma \cdot \epsilon_t$

Where:

• $\Delta P_t$ is price change
• $OFI_t$ is order flow imbalance
• $\epsilon_t$ is the elasticity term
• $\alpha$, $\beta$, $\gamma$ are model parameters

Regulatory implications

Understanding supply and demand elasticity helps regulators:

1. Design effective circuit breakers
2. Set appropriate tick sizes
3. Evaluate market making obligations
4. Monitor market quality

This knowledge informs policy decisions about:

• Market access rules
• Trading halts
• Market maker requirements
• Risk controls