Liquidity Stability Impact Score (LSIS)
- Liquidity Stability Impact Score (LSIS) is a family of liquidity-sensitive metrics that quantify how market stability shifts with liquidity changes, supply variations, and trading behavior.
- It integrates diverse methodologies—from elasticity in cryptocurrency valuation to spread–impact in order-book analysis and wallet reputations in DeFi—to offer context-specific insights.
- LSIS enables practitioners to assess liquidity roles, stress-test market conditions, and calibrate trading strategies using normalized, model-dependent score constructions.
Searching arXiv for the cited papers to ground the article and confirm identifiers. Liquidity Stability Impact Score (LSIS) denotes a family of liquidity-sensitive scoring constructions that quantify how market stability changes with liquidity conditions, liquidity provision or withdrawal, and liquidity-dependent trading behavior. In the literature represented here, LSIS is not a single canonical formula but a context-specific object: it appears as an elasticity-based stability score in liquidity-value models of cryptocurrencies, as a spread–impact and order-book fragility construct in market microstructure, as a signed and normalized liquidity-demand statistic for algorithmic strategies, as a counterfactual degradation metric for concentrated-liquidity market makers, and as a context-aware wallet score in DeFi reputation systems (Caginalp et al., 2018, Jaisson, 2015, Corradi et al., 2015, Aldridge, 27 Jun 2026, RajabiNekoo et al., 25 Jul 2025, Kandaswamy et al., 28 Jul 2025).
1. Conceptual scope and taxonomy
Across the cited works, LSIS is best understood as a stability-impact functional whose meaning depends on the market model, observables, and unit of analysis. Some formulations score an asset or market state, some score a trading strategy, some score an individual liquidity provider, and some score a wallet. The common element is that liquidity is treated not as a passive stock but as a determinant of price impact, resilience, and instability.
| Context | Core LSIS object | Primary interpretation |
|---|---|---|
| Cryptocurrencies | Elasticity and volatility around | Sensitivity of price stability to cash and supply |
| Fair markets and LOBs | Spread, impact, depletion, resilience | Microstructure-based liquidity quality and fragility |
| Algorithmic trading | Normalized covariance plus corrections | Net liquidity consumption or provision |
| CLMMs | Counterfactual change in average price impact | Functional importance of an LP |
| DeFi wallet scoring | Composite stability, impact, and risk score | Context-aware liquidity reputation |
This taxonomy also distinguishes explicit from retrospective uses of the acronym. In "SILS: Strategic Influence on Liquidity Stability and Whale Detection in Concentrated-Liquidity DEXs" (RajabiNekoo et al., 25 Jul 2025), LSIS is defined directly. In several earlier or adjacent works, LSIS is constructed from the paper’s formal objects and empirical findings rather than named in the original source, which makes the term partly synthetic and partly native to the later literature.
2. Liquidity-value LSIS in cryptocurrencies
In Carey Caginalp and Gunduz Caginalp’s framework for cryptocurrency valuation, the central quantity is the liquidity value,
or, in the cryptocurrency specialization,
Here is the trading price per unit, the total number of units, the total cash devoted to purchasing the asset, the total dollars owned by the group of potential users who want to bypass the traditional financial system, and the share of that pool actually committed to the cryptocurrency at time (Caginalp et al., 2018).
The paper’s equilibrium intuition is that in the absence of clear information and attention to value, price gravitates toward the liquidity value. In this setting, the equilibrium price is
and for the cryptocurrency specialization,
0
The LSIS constructions derived from this framework therefore treat stability as a function of comparative statics around a liquidity-driven equilibrium rather than from a formal Jacobian analysis, which the paper does not provide (Caginalp et al., 2018).
The local sensitivity form is built from the log-elasticity of price with respect to liquidity. Under 1, the score
2
equals 3. The supply-inclusive form adds the absolute cash and supply elasticities,
4
The volatility-coupled variants,
5
treat realized instability as a product of structural sensitivity and volatility (Caginalp et al., 2018).
The empirical anchor comes from both cryptocurrency observation and experimental asset markets. For Bitcoin on October 13, 2017, the paper reports 66{,}0007N\approx 168PN\approx \$L(t)=\frac{C(t)}{N(t)},$9 billion, from which it infers $L(t)=\frac{p_c(t)\,M}{N(t)}.$096%%%%2$L(t)=\frac{C(t)}{N(t)},$2$L(t)=\frac{p_c(t)\,M}{N(t)}.$2%%%%31 per share. The corresponding empirical bubble-slope score,
$L(t)=\frac{p_c(t)\,M}{N(t)}.$4
is therefore approximately $L(t)=\frac{p_c(t)\,M}{N(t)}.$5 (Caginalp et al., 2018).
The significance of this formulation is that it treats instability as endogenous to liquidity and supply when there is no tangible value anchor. The paper explicitly argues that momentum becomes destabilizing under such conditions, because rising prices attract more cash and falling prices reverse the process, while valuation-focused buyers do not step in to stabilize prices. It also argues that uncertainty in $L(t)=\frac{p_c(t)\,M}{N(t)}.$6, including forks and competition from other cryptocurrencies, adds a supply-side instability channel (Caginalp et al., 2018).
3. Fair-price, spread–impact, and order-book formulations
In high-frequency microstructure, the LSIS idea is grounded in the fair market assumption and in the distinction between static depletion and dynamic resilience. Under the fair market assumption of zero expected profit for infinitesimal market-making strategies, there exists a martingale fair price
$L(t)=\frac{p_c(t)\,M}{N(t)}.$7
with respect to the left-continuous filtration $L(t)=\frac{p_c(t)\,M}{N(t)}.$8. The bid and ask can be written as fair price plus conditional impact,
$L(t)=\frac{p_c(t)\,M}{N(t)}.$9
so that the spread–impact identity is
$P(t)$0
In a symmetric setting, $P(t)$1, where buy orders impact up by $P(t)$2 and sell orders impact down by $P(t)$3 (Jaisson, 2015).
A microstructure-oriented LSIS built from this framework uses three components. The liquidity component rewards tight spreads, ample top-of-book depth, favorable queue positions, and high fill probabilities. The impact component penalizes instantaneous expected fair-price change per unit volume, using the size-dependent variant
$P(t)$4
The stability component measures resilience of impact and liquidity, using fair-price volatility $P(t)$5, impact resilience $P(t)$6, and spread stability $P(t)$7. The paper-specific additive and multiplicative LSIS aggregations are
$P(t)$8
and
$P(t)$9
with the caveat that $N(t)$0 and $N(t)$1 should be harmonized to avoid double-counting because of the spread–impact identity (Jaisson, 2015).
A second line of microstructure work introduces an explicitly time-scale-dependent liquidity crisis view. On the 30-second horizon, the relevant object is static depletion of the limit order book. The exponential liquidity on one side is
$N(t)$2
with $N(t)$3 ticks, and the liquidity imbalance is
$N(t)$4
The paper reports that the coefficient of determination for the liquidity–return relation peaks around $N(t)$5–$N(t)$6 ticks, and for positive returns fits
$N(t)$7
with $N(t)$8 and $N(t)$9 (Corradi et al., 2015).
On the 15-minute horizon, the relevant object is failure of the compensation mechanism between market orders and limit orders. The relative flow of sell limit orders at the best ask during large positive events is defined as
$C(t)$0
and the paper documents a near-linear relationship
$C(t)$1
whose slope is reduced during large positive events on the ask side, indicating a resilience shortfall (Corradi et al., 2015).
The LSIS mapping proposed from these findings separates short-horizon static fragility from long-horizon compensation failure:
$C(t)$2
$C(t)$3
and then combines them as
$C(t)$4
with the normalized form
$C(t)$5
This makes explicit that “liquidity stability” is not a single-horizon property: near-best depth governs very short-run fragility, while resilience of order replenishment governs larger jumps (Corradi et al., 2015).
4. Observable-strategy LSIS and systemic liquidity balance
In the audit literature for algorithmic trading strategies, LSIS is a signed and scale-normalized stress score that uses only observable trade or position history and price or return history. Let $C(t)$6 denote the observable per-period cost vector and $C(t)$7 the observable decision. Under the linear policy approximation
$C(t)$8
the core statistic is the covariance between costs and decisions,
$C(t)$9
which, for linear policies, satisfies
$M$0
where $M$1 (Aldridge, 27 Jun 2026).
The sign of this statistic classifies liquidity role. Positive covariance indicates a net liquidity consumer, negative covariance a net liquidity provider, and zero covariance a liquidity-neutral strategy. Under i.i.d. costs and the mean-unbiased policy condition, total regret equals the sum of per-period covariances,
$M$2
Under non-stationary martingale-difference costs,
$M$3
with $M$4 vanishing when the conditional mean-unbiased policy holds (Aldridge, 27 Jun 2026).
The proposed score is
$M$5
where $M$6 is a capital or exposure scaling. Its magnitude measures stability impact, and its sign measures liquidity role. Positive LSIS means a strategy earns its PnL by leaning with price moves and potentially increasing instability during stress; negative LSIS means market-making or contrarian behavior (Aldridge, 27 Jun 2026).
With an AR(1) cost process,
$M$7
the multi-period regret becomes
$M$8
In scalar form, the paper links the correction to Roll’s implied spread. If
$M$9
and the strategy is contrarian,
$p_c(t)$0
then the per-period correction is
$p_c(t)$1
This identifies the AR(1) correction as strategy size times squared Roll spread, and therefore as a proxy for prevailing illiquidity (Aldridge, 27 Jun 2026).
The framework also incorporates endogenous price impact. Under linear temporary impact with effective unit cost $p_c(t)$2, the per-period impact correction is
$p_c(t)$3
For $p_c(t)$4 correlated strategies, the liquidity-balance condition is
$p_c(t)$5
Violation produces welfare loss, and under common-factor costs and symmetric agents aggregate regret is
$p_c(t)$6
which converges to $p_c(t)$7 under perfect correlation. Including price impact yields
$p_c(t)$8
a closed-form fire-sale externality (Aldridge, 27 Jun 2026).
Operationally, the estimator is computable in $p_c(t)$9 time. The paper’s CRSP calibration over 2016–2025 reports typical normal-year daily $t$0–$t$1, $t$2/day in COVID crisis Q2 2020, and $t$3/day in the 2022 rate-shock episode. It also proposes daily per-unit-capital interpretation bands: LSIS $t$4 for provision/stability, between $t$5 and $t$6 for neutral, $t$7 for consumption/instability, and severe stress when $t$8 (Aldridge, 27 Jun 2026).
5. Counterfactual LSIS in concentrated-liquidity DEXs
In concentrated-liquidity automated market makers, especially Uniswap v3–style CLMMs, LSIS is a counterfactual score for the functional importance of an individual liquidity provider. The market is indexed by integer ticks $t$9, with spot price
$P^{*}=L=\frac{C}{N},$0
and square-root price represented on chain by
$P^{*}=L=\frac{C}{N},$1
Each position with liquidity $P^{*}=L=\frac{C}{N},$2 and tick bounds $P^{*}=L=\frac{C}{N},$3 contributes to the liquidity ledger via
$P^{*}=L=\frac{C}{N},$4
and the active liquidity at tick $P^{*}=L=\frac{C}{N},$5 is
$P^{*}=L=\frac{C}{N},$6
Let $P^{*}=L=\frac{C}{N},$7 denote the baseline liquidity state and $P^{*}=L=\frac{C}{N},$8 the state obtained by removing all contributions of LP $P^{*}=L=\frac{C}{N},$9 (RajabiNekoo et al., 25 Jul 2025).
Stability is operationalized through average price impact across a fixed synthetic swap battery $L(t)=\frac{C(t)}{N(t)},$00:
$L(t)=\frac{C(t)}{N(t)},$01
Lower $L(t)=\frac{C(t)}{N(t)},$02 means higher stability, and one may equivalently define $L(t)=\frac{C(t)}{N(t)},$03. The core score is the normalized counterfactual degradation,
$L(t)=\frac{C(t)}{N(t)},$04
The absolute form is
$L(t)=\frac{C(t)}{N(t)},$05
A positive value means that removing LP $L(t)=\frac{C(t)}{N(t)},$06 increases average price impact and therefore degrades stability (RajabiNekoo et al., 25 Jul 2025).
Price impact is computed using single-tick approximations. For token0 in,
$L(t)=\frac{C(t)}{N(t)},$07
For token1 in,
$L(t)=\frac{C(t)}{N(t)},$08
The same synthetic swap set $L(t)=\frac{C(t)}{N(t)},$09 is reused in the baseline and counterfactual states so that any difference in average price impact is attributable to the excluded LP (RajabiNekoo et al., 25 Jul 2025).
The SILS framework supplements LSIS with Exponential Time-Weighted Liquidity (ETWL), which characterizes temporal behavior rather than stability directly. In continuous time,
$L(t)=\frac{C(t)}{N(t)},$10
and in the discrete implementation,
$L(t)=\frac{C(t)}{N(t)},$11
ETWL is used for ranking and anomaly detection, whereas LSIS measures counterfactual degradation under withdrawal (RajabiNekoo et al., 25 Jul 2025).
This distinction supports a central empirical claim of the paper: nominal capital size is not sufficient to identify systemic importance. The reported dataset is USDC/WETH, 0.05% fee tier, Ethereum mainnet, from block 12,376,729 on May 5, 2021 to 21,001,766 on October 19, 2024, with ETWL decay $L(t)=\frac{C(t)}{N(t)},$12. The findings distinguish “active, critical whales,” “dormant-but-critical whales,” and “false positives” of size-based baselines with LSIS $L(t)=\frac{C(t)}{N(t)},$13. The two-axis view of LSIS versus ETWL rank is used to identify “linchpins” whose removal would massively increase average price impact (RajabiNekoo et al., 25 Jul 2025).
The production interpretation given in the paper is explicitly operational. A protective oracle layer can intercept burn requests, simulate $L(t)=\frac{C(t)}{N(t)},$14, compute $L(t)=\frac{C(t)}{N(t)},$15 in real time, and then hard block, rate-limit, or allow withdrawals depending on whether the score exceeds a threshold or the post-withdrawal average price impact breaches a slippage budget. For practical interpretation, the paper suggests that $L(t)=\frac{C(t)}{N(t)},$16 in the range $L(t)=\frac{C(t)}{N(t)},$17–$L(t)=\frac{C(t)}{N(t)},$18 is marginal, $L(t)=\frac{C(t)}{N(t)},$19–$L(t)=\frac{C(t)}{N(t)},$20 material, and above $L(t)=\frac{C(t)}{N(t)},$21 critical, while also emphasizing dependence on the synthetic swap design $L(t)=\frac{C(t)}{N(t)},$22 and on the single-tick approximation (RajabiNekoo et al., 25 Jul 2025).
6. Wallet-level LSIS, LPS, and SBS in DeFi reputation systems
A further use of LSIS appears in wallet scoring for Uniswap v3 data, where it is formulated as a context-aware reputation-style metric that combines stability, impact, and risk adjustment. The paper defines two role-specific blueprint scores, Liquidity Provision Score (LPS) and Swap Behavior Score (SBS), and then maps the feature set onto an LSIS:
$L(t)=\frac{C(t)}{N(t)},$23
with $L(t)=\frac{C(t)}{N(t)},$24 and $L(t)=\frac{C(t)}{N(t)},$25 (Kandaswamy et al., 28 Jul 2025).
The stability term is
$L(t)=\frac{C(t)}{N(t)},$26
where $L(t)=\frac{C(t)}{N(t)},$27 is size-weighted holding time, $L(t)=\frac{C(t)}{N(t)},$28 size-weighted time-in-range, $L(t)=\frac{C(t)}{N(t)},$29 liquidity retention, $L(t)=\frac{C(t)}{N(t)},$30 withdrawal frequency, and $L(t)=\frac{C(t)}{N(t)},$31 position churn. The impact term is the time-weighted context-relative contribution,
$L(t)=\frac{C(t)}{N(t)},$32
and is converted to a z-score across wallets. The risk-adjustment term penalizes volatility exposure, erratic liquidity provision, and suspicious swap patterns:
$L(t)=\frac{C(t)}{N(t)},$33
Optional additions include narrow-range exposure and adverse-selection proxies (Kandaswamy et al., 28 Jul 2025).
This LSIS sits inside a broader blueprint-plus-learning paradigm. LPS and SBS are first built from rule-based feature aggregations with soft caps and penalties. The learned outputs
$L(t)=\frac{C(t)}{N(t)},$34
are then trained to approximate noisy blueprint targets on a 0–1000 scale. The architecture is a deep residual multilayer perceptron with four residual blocks and U-Net-inspired skip logic, optimized with AdamW at learning rate $L(t)=\frac{C(t)}{N(t)},$35 and weight decay $L(t)=\frac{C(t)}{N(t)},$36 for up to 500 epochs with early stopping (Kandaswamy et al., 28 Jul 2025).
The paper is explicit that its “zScore” is not the standard statistical z-score but the output of a supervised regression head. This is important because LSIS here is not a direct market-stability observable; it is a calibrated score synthesized from interpretable features, cohort normalization, and pool-level context such as TVL, fee tier, and realized volatility. The reported dataset uses Uniswap v3 subgraph data and Ethereum logs, with more than 50,000 wallets in external validation, 44,975 wallets in LP bin analyses, and 33,491 wallets in swap bin analyses. Reported alignment with blueprint targets is 91.79% within $L(t)=\frac{C(t)}{N(t)},$37 for LP predictions and 90.83% within $L(t)=\frac{C(t)}{N(t)},$38 for swap predictions (Kandaswamy et al., 28 Jul 2025).
A notable implication is that LSIS can be made comparable across heterogeneous pools only by conditioning on pool context. The paper therefore uses $L(t)=\frac{C(t)}{N(t)},$39 normalization, fee-tier coefficients $L(t)=\frac{C(t)}{N(t)},$40, and volatility factors $L(t)=\frac{C(t)}{N(t)},$41 so that similar wallet behaviors can score differently across pools with different sizes and risk profiles. This suggests a shift from purely transaction-counting reputation to structural liquidity-role scoring (Kandaswamy et al., 28 Jul 2025).
7. Interpretation, normalization, and recurring limitations
Several recurring themes constrain interpretation of LSIS across domains. First, sign conventions are model-dependent. In the strategy-audit framework, positive LSIS indicates net liquidity consumption and negative LSIS net liquidity provision (Aldridge, 27 Jun 2026). In the CLMM framework, LSIS is typically nonnegative in practice because it measures degradation under removal, though the formal definition is a relative change in average price impact (RajabiNekoo et al., 25 Jul 2025). In the cryptocurrency and order-book formulations, LSIS is often an unsigned sensitivity or risk score (Caginalp et al., 2018, Corradi et al., 2015).
Second, the object being scored differs materially across uses. Some versions score a market state, some an agent, some a wallet, and some a hypothetical counterfactual intervention. A common misconception is therefore to treat LSIS as if it were directly comparable across centralized order books, cryptoasset valuation models, algorithmic execution audits, and DeFi LP analysis. The literature summarized here does not support such a universal comparison. At most, it supports a family resemblance: LSIS captures the extent to which liquidity conditions shape price impact and stability.
Third, normalization is essential. The cryptocurrency formulations prefer log-elasticities because they are dimensionless and comparable across assets and time windows (Caginalp et al., 2018). The strategy-audit formulation normalizes by horizon and capital (Aldridge, 27 Jun 2026). The fair-market and LOB formulations rely on rolling medians, cross-sectional benchmarks, or exponential mappings to 0–100 (Jaisson, 2015, Corradi et al., 2015). The wallet-scoring literature maps raw scores to 0–1000 after feature z-scoring (Kandaswamy et al., 28 Jul 2025). The choice of normalization therefore determines whether LSIS is primarily descriptive, diagnostic, or rank-ordering.
Finally, all versions carry domain-specific limitations. The cryptocurrency framework does not reproduce formal asset-flow differential equations or a Jacobian, so LSIS is derived from static comparative statics and experimental evidence (Caginalp et al., 2018). Fair-price approaches assume infinitesimal quantities, negligible fees and order-processing costs, and work best for small-tick assets; large-tick assets can exhibit 42 deviations (Jaisson, 2015). Order-book crisis measures depend strongly on time scale, event selection, and depth truncation at 43 ticks (Corradi et al., 2015). Strategy-audit LSIS depends on a linear policy approximation, stationarity over the estimation window, and a temporary linear impact model (Aldridge, 27 Jun 2026). CLMM LSIS depends on single-tick approximations, synthetic swap design, event attribution, and sensitivity of ETWL to the decay parameter 44 (RajabiNekoo et al., 25 Jul 2025). Wallet-level LSIS depends on blueprint targets, cohort normalization, and the absence of hard ground-truth labels (Kandaswamy et al., 28 Jul 2025).
Taken together, these limitations show that LSIS is not a universal law of liquidity stability but a structured family of scores. What unifies the family is a shared premise: liquidity is measurable through its effect on price impact, resilience, and counterfactual degradation, and stability can therefore be scored by tracing how prices, spreads, or slippage respond when liquidity conditions, supply, strategy behavior, or provider participation change.