---
title: Optimal Tick Size Selection
url: https://www.emergentmind.com/topics/optimal-tick-size-selection
type: topic
---

# Optimal Tick Size Selection

The optimal tick size is a central design parameter in limit order markets, delineating the finest price granularity at which participants can quote or transact. A suitably chosen tick size promotes liquidity by encouraging limit order provision and maintaining reasonable bid-ask spreads, but excessive coarseness or fineness can result in widened effective spreads, liquidity fragmentation, increased volatility, or adverse selection. This entry synthesizes recent advances in optimal tick-size selection, emphasizing microstructure models, empirical criteria, and exchange-level optimization, with focus on large-tick and small-tick regimes, side-specific tick sizes, and regulatory implications as established in multiple empirical and theoretical studies [2005.14126], [2410.08744], [1507.07052], [1207.6325], [1602.00839].

## 1. Microstructure Foundations: Tick Size and Liquidity Metrics

The tick size, denoted $\delta$ or $\alpha$, determines the discrete set of allowable price levels. Microstructure models categorize stocks by the interaction between the tick and endogenous microstructure metrics:

- **Quoted Spread ($\Delta_q$):** $\Delta_{q}=\text{Ask}_{t}-\text{Bid}_{t}$
- **Effective Spread ($\Delta_e$):** $\Delta_{e}=2(P_{\mathrm{trade}} - \frac{1}{2}(\text{Bid}_{t} + \text{Ask}_{t}))$
- **Implicit Spread ($2\eta\alpha$):** “Uncertainty zone” width for large-tick assets, where $\eta$ is the microstructure parameter estimated by $\widehat{\eta} = N^{(c)}/(2N^{(a)})$—i.e., the ratio of continuation to alternation one-tick moves [1207.6325].
- **Relative Tick Size ($\epsilon$):** $\epsilon = \delta/\langle P_{\mathrm{mid}}\rangle \times 10^4$ (bps) [2410.08744]
- **Volume and Trade Count ($M$):** Number of daily trades and total volume, entering the volatility-per-trade $\sigma/\sqrt{M}$ relation.

In large-tick assets, the spread is often fixed at a single tick, and microstructure equilibrium is established between market-makers' profit and takers’ cost, where tick size acts as a lower bound for the spread and effective spread dynamics are captured by the implicit spread metric [1207.6325].

## 2. Theoretical Models for Optimal Tick Selection

Optimal tick-size selection is framed by analytic and simulation-based methodologies:

### 2.1 Model with Uncertainty Zones

- **Efficient price process:** $dY_t = a_t\,dt + \sigma_{t^-}\,dW_t$ with $a_t \equiv 0$ in calibration.
- **Discrete price grids:** Separate bid $(\alpha^b)$ and ask $(\alpha^a)$ ticks allow for asymmetric granularity.
- **Tick-size-dependent order arrival:** $\lambda^i = \lambda/(1 + (\kappa\,\alpha^i)^2)$, where $\kappa$ modulates sensitivity [2005.14126].
- **Exchange revenue maximization:** Maximizing $v(\alpha^a, \alpha^b) = E^{\ell^*}[c(N_T^a + N_T^b)]$ over bid/ask tick sizes, with optimal pairs $(\alpha^{a*}, \alpha^{b*})$ determined numerically due to non-smooth control boundaries.

### 2.2 Implicit Spread and Volatility Per Trade

- **Large-tick equilibrium:** $\eta\alpha \simeq \sigma/\sqrt{M}$, reflecting the efficient price’s volatility per trade [1207.6325], [1507.07052].
- **Market order cost:** $C_{\mathrm{mkt}}(\alpha) = \alpha/2 - \eta \alpha$
- **Limit order profit:** $G_{\mathrm{lim}}(\alpha) = \alpha/2 - \eta\alpha$
- **Forecasting parameter shift:** After a tick change $\alpha_0 \to \alpha$, $\eta(\alpha) \simeq (\eta_0+\delta)(\alpha_0/\alpha)^{1/2} - \delta$, $\delta \approx 0.1$ empirically [1507.07052].
- **Criterion for optimal tick:** Choose $\alpha^*$ such that $\eta(\alpha^*) = 1/2$, enforcing zero expected market-order cost and balanced liquidity provision [1207.6325].

### 2.3 Simulation-Based Approach for Arbitrary Tick Regimes

- **Stylized fact metrics:** Average spread in ticks ($\overline{s}$), coefficient of variation of spread ($CV_s$), average mid-price move $\langle |r_{\mathrm{mid}}|\rangle$, and book shape features (mode $x^*$) are synthesized to diagnose current regime (“large-tick,” “medium-tick,” or “small-tick”) and guide target selection [2410.08744].
- **Wide-Queue Hawkes Model:** Multi-type Hawkes processes drive LOB events, with parameters $(\alpha, \beta, \hat{\eta})$ controlling in-spread activity and sparsity, supporting transition and calibration across tick regimes using empirical data.

## 3. Practical Procedures for Tick Size Calibration

### 3.1 Closed-Form Procedure for Large-Tick Assets

For assets with a one-tick spread:

1. **Estimate pre-change $\eta_0$ and $\alpha_0$** from high-frequency data; compute $(N^{(c)}, N^{(a)})$, $\sigma$, $M$ [1207.6325], [1507.07052].
2. **Compute optimal tick:**
   - $\alpha^* = \left(\frac{\eta_0 + 0.1}{0.6}\right)^2 \alpha_0$ [1507.07052], or
   - $\delta^* \simeq \delta_0 (2\eta_0)^{1/(1-\beta/2)}$ with latent liquidity exponent $\beta$ [1207.6325].
3. **Forecast post-change microstructure:** Predict $\eta(\alpha^*)$, confirm $\eta(\alpha^*) \approx 1/2$ ensures optimality.

### 3.2 Simulation-Based Multi-Regime Approach

For both large- and small-tick stocks [2410.08744]:

1. **Empirical diagnosis:** Compute all stylized-fact metrics for current $\delta_0$.
2. **Set target regime:** E.g., $\overline{s}_{\text{target}} = 2\!\sim\!3$ ticks, $CV_s \approx 0.5$–1, $x^*\approx2$–5 ticks.
3. **Grid search:** Use the Hawkes-LOB model to simulate order-flow and book shape as $\delta$ varies; adjust $(\alpha, \beta, \hat{\eta}, \delta)$ to achieve target metrics.
4. **Validation:** Cross-check execution costs, price move tails, depth, and event endogeneity against empirical benchmarks.

### 3.3 Empirical Trade-Off Guidelines

Empirical studies of real-world tick-size changes, e.g., the Tokyo Stock Exchange pilot [1602.00839], establish actionable guidelines:

- Require quoted spread reduction of at least 20% post-change to justify reduction.
- Impose a maximum acceptable drop in average trade size (e.g., $\leq 15\%$) to preserve large-order liquidity.
- Use regression-based rules to ensure changes balance benefits to small traders (spread improvements) against potential costs to large traders (impact, depth decreases).

| Approach                 | Regime focus         | Required inputs                  |
|--------------------------|---------------------|----------------------------------|
| Uncertainty zone model   | Large-tick assets   | $\eta_0$, $\alpha_0$, volatility/trades |
| Hawkes simulation        | All regimes         | LOB event time series, calibrable model parameters |
| Empirical trade-off      | Ex-post/pre-change  | Order-level data, time series of spreads/depth |

## 4. Side-Specific Tick Sizes and Asymmetric Optimization

Permitting distinct tick sizes on bid and ask sides, as analyzed in the uncertainty-zone/HJB framework [2005.14126], enhances exchange control over liquidity and market-maker incentives:

- **Bid/ask-specific grids:** Price levels defined by $\{k\alpha^b : k\}$ for bids, $\{k\alpha^a : k\}$ for asks.
- **Optimization problem:** Maximize expected fee flow $v(\alpha^a, \alpha^b)$ across $(\alpha^a, \alpha^b)$ space; numerical grid search preferred due to non-smooth optimal controls.
- **Inventory penalty asymmetry:** High penalty for short positions ($\phi_-\gg0$) justifies $\alpha^b > \alpha^a$, aligning maker incentives with exchange revenue.
- **Arbitrage window dynamics:** With $\alpha^a\ne\alpha^b$, temporary windows where both buy and sell are profitable for the market maker increase alternations, reduce inventory drift, and facilitate spread compression.

Practical implementation requires real-time monitoring to ensure continued “large-tick” status ($\eta^i\leq1/2$) on both sides, and may encounter challenges from non-Poisson order flow, strategic adaptation of liquidity takers, and inter-venue effects [2005.14126].

## 5. Empirical Findings and Exchange Policy Implications

Analysis of major tick-size experiments substantiates both intended and unintended microstructural outcomes [1602.00839]:

- **Key empirical results:**
  - Tighter spreads and increased trade counts observed post-reduction.
  - Displayed depth and average trade size decrease, raising costs/uncertainty for large orders.
  - Volatility of execution costs and message traffic increase.
- **Optimal tick policy recommendations:**
  - Phase-in via pilots, calibrate by monitoring intraday depth and execution-size distribution.
  - Employ tiered tick schedules: finer ticks for liquid/high-priced issues; coarser for illiquid stocks.
  - Enforce revertive criteria (e.g., threshold breaches in depth or cost-volatility).
  - Weight welfare of small- versus large-order traders in optimization rules.

A plausible implication is that exchanges seeking to optimize tick size must continuously trade off small-order execution gains against potential harm to institutional liquidity and operational stability.

## 6. Limitations and Future Research Directions

Closed-form optimal tick rules are applicable primarily to large-tick assets with persistent one-tick spreads. Models based on Poisson arrivals and linear latent liquidity may not capture feedback loops, strategic order-splitting, or volatility-tail dependencies. Simulation-based and hybrid approaches are required for assets transitioning between small- and large-tick regimes, or where tick-induced regime boundaries are approached [2410.08744].

Challenges remain in universalizing “optimal” tick prescriptions across heterogeneous assets, in modeling cross-venue interactions, and in operationalizing dynamic tick adaptation frameworks responsive to evolving volume, volatility, and liquidity conditions.

## 7. Summary Table of Optimal Tick-Size Approaches

| Methodology            | Primary Scope       | Key Formula/Rule                             | Reference         |
|------------------------|--------------------|----------------------------------------------|-------------------|
| Uncertainty zone model | Large-tick assets  | $\alpha^* = [(\eta_0+0.1)/0.6]^2 \alpha_0$  | [1507.07052], [1207.6325] |
| Hawkes simulation      | All regimes        | Grid search for $\delta$ with target metrics | [2410.08744]      |
| Empirical regression   | Ex-post impact     | Spread and trade-size thresholds ($>20\%$, $<15\%$) | [1602.00839]      |
| Side-specific optimization | Order-book asymmetry | Maximize $v(\alpha^a, \alpha^b)$ numerically | [2005.14126]      |

The selection of an optimal tick size is thus both a theoretically tractable and empirically contingent problem, requiring the interplay of high-frequency data calibration, analytic microstructure models, and simulation-based robustness checks to address the diversity of market microstructure landscapes.

Source: https://www.emergentmind.com/topics/optimal-tick-size-selection