Intrinsic Liquidity: An Internal Market Measure

• Intrinsic liquidity is defined as an endogenously generated capacity embedded within assets, contracts, or trading mechanisms rather than solely external market statistics.
• Researchers quantify it using diverse methodologies including event-time decomposition, geometric projections in order books, and liquidity-adjusted models in FX, crypto, and fixed-income contexts.
• The concept informs practical strategies in risk management, optimal execution, and decentralized finance by linking internal liquidity to market stability and execution quality.

Intrinsic liquidity denotes a family of concepts that place liquidity inside the asset, book, contract, balance sheet, or trading mechanism itself, rather than treating liquidity only as an exogenous spread, volume, or funding statistic. In recent work, the term has been used for the unlikeliness of price paths in intrinsic event time, the static fragility of a limit order book, a latent asset-level property decomposed into liquidity jump and liquidity diffusion, a projected density in pregeometric order-book models, the marketability value embedded in bonds, the self-generated liquidation capacity of banks, and the local depth coordinate of constant-function market makers [(Golub et al., 2014); (Corradi et al., 2015); (Deng et al., 2024); (Cruz, 24 Jan 2026); (Barik et al., 2023); (Brody et al., 2009); (Risk et al., 2 Mar 2026)]. The literature therefore does not present a single universal definition; instead, it develops several domain-specific notions that share the idea that liquidity is an internal structural property rather than a purely external market condition.

1. Conceptual scope and recurrent distinctions

Across the literature, intrinsic liquidity is best understood as a contrast term. It is contrasted with clock-time activity, with purely dynamic resilience, with nominal capital size, with primitive supply-and-demand curves, with external emergency funding, and with protocol-specific reserve invariants. The common move is to identify a deeper state variable, geometry, or mechanism that governs realized trading capacity or price impact.

Domain	Intrinsic liquidity as	Representative object
Event-time FX microstructure	Unlikeliness of price trajectories	$\mathcal{L}$
Short-horizon LOB analysis	Static book depletion and imbalance	$L(\delta),\,L_{imb}(\delta)$
Crypto assets	Latent asset-level liquidity split into two components	liquidity jump, liquidity diffusion
Pregeometric order books	Projected density around a mid price	$\rho(p),\,q(x)$
Bonds	Survival/marketability value	$P_{tT},\,\gamma$
Banking	Internal liquidation and collateral capacity	haircut-constrained liquidation
CFMMs	Local geometric liquidity coordinate	$\ell,\;L(q)$

A recurrent distinction is between static and dynamic liquidity. On 30-second windows, intrinsic liquidity can mean the static depth and breadth of the limit order book near the best quotes; on 15-minute windows, the relevant object becomes effective liquidity, namely resilience and the ability of limit-order flow to compensate market-order pressure (Corradi et al., 2015). Another distinction is between primitive and emergent liquidity. In the pregeometric order-book framework, liquidity is not assumed at the microscopic level at all; it is measured only after projection from a relational graph (Cruz, 24 Jan 2026). A further distinction is between nominal and functional liquidity. In concentrated-liquidity DEXs, nominal capital, raw volume, and turnover are explicitly rejected as sufficient proxies for the liquidity that actually stabilizes execution at the active price range (RajabiNekoo et al., 25 Jul 2025).

Several papers also redefine intrinsic liquidity as internally generated liquidity. In bank portfolio models, it is the bank’s own ability to meet withdrawals by liquidating assets (Barik et al., 2023). In blockchain protocol design, it is liquidity generated, retained, and made productive within the chain’s native DeFi and staking architecture (Abgaryan et al., 2024). This suggests that “intrinsic” is less a single metric than a research program: liquidity is treated as endogenous, structural, and often latent.

2. Event-time and order-book microstructure

One influential microstructural formulation defines intrinsic liquidity in event time rather than clock time. In the Intrinsic Network framework, high-frequency price series are decomposed into directional changes and overshoots at thresholds $\delta_1<\delta_2<\dots<\delta_n$. For a driftless Brownian benchmark,

$$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$

so the expected overshoot equals the threshold itself (Golub et al., 2014). Price paths are then encoded as binary states across thresholds, and transitions between those states define a pathwise surprisal

$$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$

After centering and asymptotic normalization, liquidity is defined as

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$

Low $\mathcal{L}$ corresponds to highly surprising trajectories, long overshoots, and illiquidity; high $L(\delta),\,L_{imb}(\delta)$0 corresponds to more typical trajectories and greater liquidity. Empirical examples in FX are reported for the 2007 yen carry-trade unwind and the 2011 EUR/CHF episode around the SNB floor, where the measure deteriorates before major stress events (Golub et al., 2014).

A different but related microstructure line distinguishes intrinsic liquidity from effective liquidity by timescale. On 30-second windows, intrinsic liquidity is identified with the static state of the book, especially one-sided depletion near the best quote. The paper introduces exponential liquidity

$L(\delta),\,L_{imb}(\delta)$1

with $L(\delta),\,L_{imb}(\delta)$2 ticks, and the liquidity imbalance

$L(\delta),\,L_{imb}(\delta)$3

For positive events, the return–liquidity relation is fitted by

$L(\delta),\,L_{imb}(\delta)$4

with reported estimates approximately $L(\delta),\,L_{imb}(\delta)$5 and $L(\delta),\,L_{imb}(\delta)$6, and the fit quality peaks around $L(\delta),\,L_{imb}(\delta)$7 ticks (Corradi et al., 2015). The same paper reports that when $L(\delta),\,L_{imb}(\delta)$8, the frequency of positive returns is roughly double the frequency of negative returns. On 15-minute windows, however, the same authors argue that large price changes are primarily associated with a failure of compensation between market orders and limit orders, that is, with resilience rather than displayed depth. Intrinsic liquidity in the narrow sense is therefore the book’s static fragility; effective liquidity is the market’s dynamic ability to reveal latent liquidity (Corradi et al., 2015).

Taken together, these papers reject a common simplification according to which liquidity is a single book-depth number. In one event-time formulation it is a property of path likelihood; in another it is a property of static near-touch depth; and at longer horizons it becomes a property of flow compensation.

3. Crypto asset-level intrinsic liquidity

In a crypto-asset setting, intrinsic liquidity has been formalized as a latent asset-level property with two complementary components: liquidity jump and liquidity diffusion (Deng et al., 2024). The construction is built on liquidity-adjusted return and volatility. At the daily level, the paper defines two daily liquidity Beta measures,

$L(\delta),\,L_{imb}(\delta)$9

and

$\rho(p),\,q(x)$0

The first ratio is interpreted as the liquidity jump, measuring the magnitude of aggregated daily price jumps and serving as a proxy for daily liquidity magnitude. The second ratio is interpreted as the liquidity diffusion, measuring the volatility of liquidity, i.e. the intraday volatility of the daily liquidity process. In both cases, values much greater than $\rho(p),\,q(x)$1 signal extreme liquidity impact (Deng et al., 2024).

The empirical setting uses Binance tick data aggregated to minute-level dollar amount traded $\rho(p),\,q(x)$2, from which minute-level regular return and volatility, as well as liquidity-adjusted return and volatility, are constructed and then aggregated to daily series. The framework is explicitly motivated by wash trading. To treat wash trading, the authors divide minute-level amounts into quartiles and downweight the upper quartiles by reducing Q3 by 50% and Q4 by 75%. They then compare the treated and untreated series (Deng et al., 2024).

The main empirical result is asymmetric sensitivity of the two intrinsic-liquidity components. With treatment, the mean and median of liquidity jump decline only modestly; reported treated means range from 1.19 for BTC to 1.57 for ADA, compared with 1.40 to 2.02 without treatment. By contrast, liquidity diffusion falls substantially. With treatment, mean diffusion falls to a range of 0.66 to 0.87, and maximum values fall to 0.85 to 2.07 rather than large capped spikes. The paper states that treatment “significantly reduces the level of liquidity diffusion, but only marginally reduces the level of liquidity jump,” and interprets this as evidence that wash trading creates a primarily diffusive signature through many smaller, high-frequency trades rather than a small number of enormous trades (Deng et al., 2024).

The modeling implication is equally specific. The paper uses

$\rho(p),\,q(x)$3

$\rho(p),\,q(x)$4

and

$\rho(p),\,q(x)$5

with AIC used to choose $\rho(p),\,q(x)$6 and $\rho(p),\,q(x)$7 and to select between GARCH and EGARCH. The conclusion is that liquidity adjustment, rather than wash-trading treatment by itself, restores the effectiveness of autoregressive modeling. Liquidity-adjusted Mean-Variance portfolios outperform traditional Mean-Variance portfolios with or without treatment, and the paper argues that aggressive treatment may even remove legitimate high-volume trades for large-cap assets on mainstream unregulated exchanges such as Binance (Deng et al., 2024).

4. Geometric formulations in order books and CFMMs

A strongly geometric interpretation appears in a pregeometric theory of order books. There the market is modeled as a growing relational graph

$\rho(p),\,q(x)$8

with no primitive price axis, no time axis, no intrinsic metric, and no primitive supply/demand curves (Cruz, 24 Jan 2026). Geometry appears only after projection through the graph Laplacian

$\rho(p),\,q(x)$9

whose low-lying eigenvectors define a spectral embedding

$P_{tT},\,\gamma$0

A one-dimensional projection using the first nontrivial eigenvector,

$P_{tT},\,\gamma$1

produces a price-like coordinate. Liquidity is then the projected density

$P_{tT},\,\gamma$2

with the observational mid price defined by balancing projected mass on either side. Supply and demand are the ask-side and bid-side branches of this projected density. Under the minimal single-scale log-slope hypothesis, the projected profiles satisfy

$P_{tT},\,\gamma$3

which integrates to the gamma-like law

$P_{tT},\,\gamma$4

For discrete Level II data, the empirically fitted object is the cumulative integrated-gamma profile

$P_{tT},\,\gamma$5

and its discrete analogue. Using AAPL, NVDA, MSFT, JPM, GS, and TSLA Level II data, the paper reports systematic AIC preference for the integrated-gamma model over cumulative log-normal and truncated cumulative power law alternatives, with GS treated as a near-degenerate case (Cruz, 24 Jan 2026). In this formulation, intrinsic liquidity is the geometry of projected order-book support, structurally constrained by the observational pipeline.

An analogous geometric move appears in CFMM theory, where traditional reserve coordinates $P_{tT},\,\gamma$6 are replaced by spot price $P_{tT},\,\gamma$7 and intrinsic liquidity $P_{tT},\,\gamma$8 (Risk et al., 2 Mar 2026). For a smooth bonding curve $P_{tT},\,\gamma$9, local intrinsic liquidity is defined by

$\ell,\;L(q)$0

The paper emphasizes two properties: locality and invariance. It also states that $\ell,\;L(q)$1 always has the dimension

$\ell,\;L(q)$2

which makes it comparable across CFMM designs. With spot price

$\ell,\;L(q)$3

the reserve functions become

$\ell,\;L(q)$4

Defining

$\ell,\;L(q)$5

these simplify to

$\ell,\;L(q)$6

Pool value is therefore

$\ell,\;L(q)$7

and impermanent loss can be written as a weighted strip of vanilla options. The realized gamma of impermanent loss is exactly

$\ell,\;L(q)$8

so the liquidity density itself is the local curvature of the LP payoff (Risk et al., 2 Mar 2026). Empirically, Uniswap v3 ETH/USDC pools exhibit liquidity concentration by fee tier and an implied-volatility smile consistent with crypto-asset dynamics.

These geometric papers share a precise claim: intrinsic liquidity is not merely an amount of capital. It is a structural object defined by projection or curvature.

5. Fixed-income, yield-curve, and marketability interpretations

In fixed-income theory, intrinsic liquidity has been cast as hidden information about future cash-demand events. In an information-based model of discount bonds, the initial curve is interpreted as a survival function,

$\ell,\;L(q)$9

where $\delta_1<\delta_2<\dots<\delta_n$0 is the time of a liquidity issue or cash-demand event (Brody et al., 2009). With the information process

$\delta_1<\delta_2<\dots<\delta_n$1

the bond price becomes

$\delta_1<\delta_2<\dots<\delta_n$2

The explicit representation is a ratio of posterior survival integrals. In this setting, low bond values correspond to a high perceived chance that cash will be needed before maturity. The paper further shows that bond volatility is determined by weighted perpetual annuities and derives semi-analytic formulas for bond options and swaptions (Brody et al., 2009).

A second bond-market line defines liquidity as the value of the right to choose when to sell. Extending Longstaff and Koziol–Sauerbier to defaultable coupon bonds, the option-based framework prices liquidity as a look-back-like marketability option (Rossi et al., 20 Jan 2025). The defaultable risky discount factor is written

$\delta_1<\delta_2<\dots<\delta_n$3

and a constant liquidity spread $\delta_1<\delta_2<\dots<\delta_n$4 enters through

$\delta_1<\delta_2<\dots<\delta_n$5

The central intrinsic-liquidity relation is

$\delta_1<\delta_2<\dots<\delta_n$6

so liquidity is the discount needed to equate the value under discrete selling opportunities with the continuous-selling benchmark. The numerical study combines G2++ for the risk-free curve, CIR for credit spreads, Monte Carlo simulation, and Newton’s method, and reports plausible probing frequencies of about 14, 17, and 19 days for an unquoted Republic of Italy bond, corresponding to liquidity spreads of about 23 bps, 24 bps, and 27 bps (Rossi et al., 20 Jan 2025).

A more microstructural yield-curve interpretation links liquidity to the transmission of order-flow shocks across maturities. In the stiff-elastic-string framework for the forward rate curve,

$\delta_1<\delta_2<\dots<\delta_n$7

the key liquidity parameter is the tenor-specific vector $\delta_1<\delta_2<\dots<\delta_n$8, where $\delta_1<\delta_2<\dots<\delta_n$9 is the share of forward-rate variance at tenor $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$0 explained by order-flow imbalance (Coz et al., 2024). The main cross-impact relation is

$$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$1

with cross-impact matrix

$$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$2

The single dimensionless stiffness parameter is

$$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$3

Using SOFR and Eurodollar data, the paper reports $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$4 across three sample windows and finds that the most liquid contracts, typically the shortest maturities, have the largest $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$5 (Coz et al., 2024). In this formulation, intrinsic liquidity is a tenor-specific internal parameter of the curve’s response to order-flow surprises.

6. Banking, collateral, and balance-sheet liquidity

In banking models, intrinsic liquidity often means liquidity produced internally from the asset side rather than obtained from outside rescue finance. In a three-date loan-portfolio model with limited liability, the bank raises debt $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$6 and equity $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$7 at $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$8, invests in three loans, faces withdrawals at $$dP_t=\sigma dW_t,\qquad \mathbb{E}[\omega(\delta;\sigma)] = \delta,$$9, and either pays liabilities or becomes insolvent at $$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$0 (Barik et al., 2023). If $$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$1 is the fraction liquidated of loan $$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$2 with haircut $$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$3, liquidation must satisfy

$$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$4

A haircut cap

$$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$5

restricts the feasible portfolio. The paper argues that intrinsic liquidity is the bank’s self-generated capacity to meet withdrawals by monetizing assets, and reports that the haircut-constrained optimal portfolio,

$$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$6

is less illiquid than the unconstrained allocation

$$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$7

It further shows that adding a lower bound on the risk of the liquidated portfolio can force liquidation of riskier assets and preserve safer assets for later (Barik et al., 2023).

A continuous-asset-liquidity approach generalizes the same idea. Assets are ranked on $$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$8 by liquidity, with fire-sale discount

$$\gamma_{s_i,s_j}=-\log \mathbb{P}(s_i\rightarrow s_j).$$9

and central-bank haircut schedule

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$0

(Bindseil et al., 2020). Selling the most liquid assets first yields cumulative loss

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$1

while pledging all assets to the central bank provides refinancing power

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$2

In the pure central-bank-liquidity case, the strict no-run condition is

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$3

In the pure fire-sale case, the no-run equilibrium requires both

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$4

and

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$5

The mixed case implies that banks should fire-sell the most liquid assets and pledge the least liquid eligible assets to the central bank. The collateral framework is therefore modeled not only as a central-bank protection device but also as a financial-stability and non-conventional monetary-policy instrument (Bindseil et al., 2020).

A third balance-sheet perspective argues that CVA and liquidity are incomplete unless unbooked positions are included. Two omitted intrinsic-liquidity effects are emphasized: firm-level assets such as Goodwill that lose value on default, and contingent future funding needs arising from collateralized positions that may become out of the money (Kenyon, 2010). The Goodwill CVA is written

$$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$$6

For collateralized swaps, funding spread over overnight is decomposed into credit spread plus scarcity spread, and the paper derives funding-cost and funding-CVA formulas for future collateral posting. In the cited large-complex-financial-institution example, a reported \$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$74B loss; for 20-year ATM swaps, funding costs are reported around 20–35 bps under flat-funding assumptions, with funding CVA up to about 2% of notional (Kenyon, 2010). Here intrinsic liquidity is not a market-depth statistic at all, but a balance-sheet consequence of default-sensitive assets and future funding obligations.

7. Strategic internalization, DeFi stability, and endogenous liquidity

A large recent literature treats intrinsic liquidity as an explicitly endogenous object. In concentrated-liquidity DEXs, the SILS framework defines real liquidity importance by counterfactual sensitivity rather than by TVL, wallet size, or turnover (RajabiNekoo et al., 25 Jul 2025). Exponential Time-Weighted Liquidity is defined as

$\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$8

with implementation parameter $\mathcal{L} = 1-\Phi\!\left( \frac{\gamma^{[0,T]}_K-K\cdot H^{(1)}}{\sqrt{K\cdot H^{(2)}}} \right).$9. The Liquidity Stability Impact Score is the relative increase in average price impact after excluding one LP,

$\mathcal{L}$0

The framework reports both false positives and false negatives for size- and activity-based whale definitions, and cites extreme LSIS examples around 4.4 million and above 37 thousand, indicating highly skewed concentration of stability provision (RajabiNekoo et al., 25 Jul 2025). The underlying claim is that intrinsic liquidity is the liquidity that actually supports execution quality at active ticks.

Blockchain protocol design extends the same internalization logic to network architecture. In Proof of Efficient Liquidity, intrinsic liquidity is described as liquidity natively generated, retained, and made productive inside the blockchain ecosystem itself, with CDA liquidity recycled into borrowed native staking tokens and PoS security (Abgaryan et al., 2024). Incentives are allocated by a policy

$\mathcal{L}$1

subject to risk and budget constraints, while reward flow is tied to staking rewards through

$\mathcal{L}$2

The protocol also imposes a native-stake threshold

$\mathcal{L}$3

and borrowing ceiling

$\mathcal{L}$4

Intrinsic liquidity here is explicitly native, self-reinforcing, and coupled to staking, fees, and service usage.

In optimal execution and dealer models, internal liquidity is a direct execution resource. One execution framework adds an internal market-making channel to standard interbank limit and market orders, with internal fill intensity

$\mathcal{L}$5

no market impact for internal fills, and optimal internal quote

$\mathcal{L}$6

(Morimoto, 2024). Another FX market-making model treats passive internal exchange orders as transient liquidity state $\mathcal{L}$7 and solves a joint quoting-and-stopping HJBQVI, producing an inventory-dependent threshold policy: take internal liquidity when sufficiently attractive, otherwise skew OTC quotes to make internal execution more favorable (Barzykin et al., 4 Dec 2025). In a multi-broker setting with an informed trader, liquidity is priced through broker-specific $\mathcal{L}$8, the informed trader’s routing satisfies

$\mathcal{L}$9

and the resulting liquidity-price Nash equilibrium is reported to be not Pareto efficient (Donnelly et al., 11 Mar 2025). A related “Liquidity Game” makes utility directly dependent on the liquidity generated by strategic interaction itself, with mixed Nash and Bayesian reasoning applied to a UK bond-market interaction (Vidler et al., 2024).

Contract theory pushes endogeneity one step further. In the screening model of liquidity, date-0 advance

$L(\delta),\,L_{imb}(\delta)$00

is the liquidity instrument, while the residual outside-finance exposure is

$L(\delta),\,L_{imb}(\delta)$01

With non-pledgeability of contingent transfers and affine transfer

$L(\delta),\,L_{imb}(\delta)$02

the lowest-type participation constraint links more contingency to less advance, and the optimal contract preserves outside-finance exposure: $L(\delta),\,L_{imb}(\delta)$03 (Sun, 7 Apr 2026). The central claim is that liquidity helps finance the relationship but weakens screening, so the optimal contract is an interior mix of upfront liquidity and contingent transfer.

The strategic literature therefore converges on a broad conclusion. Intrinsic liquidity is not identical to size, turnover, or raw reserves. It is a state-dependent capacity to stabilize price, absorb flow, generate execution, secure a network, or sustain screening, and that capacity is often revealed only under counterfactual removal, endogenous optimization, or equilibrium analysis.