Simulating Liquidity: Agent-Based Modeling of Illiquid Markets for Fractional Ownership

A. Ege Yilmaz; Aurelio Perucca; Denis Bieri; Lars Fluri; Thomas Ankenbrand

REVIEW 3 major objections 5 minor 15 references

Simulating Liquidity: Agent-Based Modeling of Illiquid Markets for Fractional Ownership

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read An agent-based model of a one-sided fractional-ownership market replicates the platform's liquidity dynamics closely enough to serve as a testbed for alternative trading rules.

desk verdict Genuinely novel application, but the validation claim rests on one aggregate ratio that matches while the components are off by factors of 2.5 to 10. read the letter →

arxiv 2411.13381 v2 pith:KKI34MCA submitted 2024-11-20 q-fin.TR econ.GNq-fin.EC

Lars Fluri , A. Ege Yilmaz , Denis Bieri , Thomas Ankenbrand , Aurelio Perucca This is my paper · ORCID

classification q-fin.TRecon.GNq-fin.EC

keywords agent-basedmodelingfractionalownershipliquiditysecondarymarkettokenizedassetssell-sideofferbookmicrostructuredataaugmentation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that an agent-based model can reproduce the trading liquidity of a real fractional-ownership market—one where only sell offers are listed and no market maker exists—closely enough that the simulator can be used to test alternative market designs. It calibrates three trader types (pure sellers, pure buyers, and buyer-sellers) from 37 trading windows of platform data and compares the simulated outcome against the empirical one. In the baseline simulation the average liquidity ratio is 14%, against an empirical 10%, and the magnitudes of shares traded are comparable. The paper concludes that the model works as a data-augmentation environment and as a basis for studying liquidity in illiquid markets such as fine wines, artworks, cars, and watches.

What carries the argument

The central object is a market-level simulation of one trading day, split into a pre-trading phase (09:00–18:00) in which Pure Sellers and Buyer Sellers build a one-sided offer book, and a trading phase with twelve settlement steps in which Pure Buyers and Buyer Sellers accept offers. Agents are initialized with the exact cash and share endowments of real platform users, and their behavior is specified by empirical activity rates, offer/purchase ratios, uniform offer-price bands $[v_l, v_h] \times p_{ref}$ from Eqs. (1) and (3), and a logistic purchase probability $P(p_i) = 1/(1 + e^{k(p_i - p_{ref})})$ for Pure Buyers. Buyer Sellers filter offers below the reference price and take the cheapest among a random sample of fixed search length. The output that carries the comparison is the liquidity ratio, trades over offered shares, whose simulated value of 14% is compared with the empirical 10%.

What would settle it

Use the platform's full order logs to measure the real distribution of offer prices relative to the reference price and the real order in which offers are accepted, then re-run the same agent model with those empirical distributions in place of the uniform draws and random sampling. If the resulting average liquidity ratio moves away from the empirical 10% by a margin larger than the current 14%-to-10% gap, the baseline match is an artifact of the assumed stochastic rules rather than of the market dynamics.

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Extended reading notes

Core claim

The central claim is that a stochastic agent-based model with three simple, rule-following agent types can approximate the liquidity dynamics of a sell-offer-driven secondary market for fractional shares. The baseline model produces an average liquidity ratio of 14% relative to the empirical 10%, with comparable numbers of offers, trades, and shares traded. The paper further claims that the model responds correctly to parameter changes: raising buyer participation or purchasing power raises the liquidity ratio, while raising sellers' offer probability or offer size lowers it, with some counterintuitive substitution effects between large and small trades. The author's conclusion is that the simulation environment is stable enough to serve as a testbed for liquidity-enhancing market rules and as a source of synthetic market data.

Load-bearing premise

The simulation replaces the platform's actual price-setting and order-matching with hand-set stochastic rules—uniform offer prices in a band around the reference price, Pure Buyers sampling one random offer, and Buyer Sellers seeing only below-valuation offers—and these rules are not estimated from the offer data.

Editorial extensions

If this is right

If the baseline fit is accepted, the simulator can generate synthetic market states that are not available from the thin empirical record, supporting data augmentation for econometric and machine-learning models.
The sensitivity analysis gives the platform operator a quantified map of which design levers move liquidity, e.g., narrowing the allowed offer price band or lowering its midpoint raises the simulated liquidity ratio.
Because the market is one-sided and has no market maker, the model supplies a baseline against which proposed changes—such as a two-sided order book or a market maker agent—can be evaluated without live experimentation.
The paper's planned regression on simulated liquidity data can assign quantitative importance to each parameter, identifying the dominant drivers of liquidity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A test the paper does not run: replace the Pure Buyer's single random offer with the platform's stated FIFO matching and the empirical order of buyer arrivals; if the simulated liquidity ratio moves substantially away from 14%, the baseline fit is carried by matching assumptions rather than price-taking behavior.
The liquidity ratio as defined rewards a market that clears many small offers; the substitution effects in the sensitivity tables imply that a rule change that eliminates small offers could lift the ratio while making it harder for small holders to exit, so the metric may not align perfectly with investor welfare.
If the model is correct, its sensitivity tables imply that price-banding policy—not just agent activity—determines liquidity, and similar one-sided markets (e.g., tokenized real estate, collectibles) could be modeled with the same three-agent architecture after recalibration.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a genuine first — I don't know of another ABM built for a one-sided sell-offer fractional-ownership market with no market maker. It's also honest about being platform-specific. But the central validation claim doesn't hold up. The baseline matches the liquidity ratio (0.139 vs 0.096) and trade count (130 vs 132), yet misses the number of offers by a factor of ~10 (69 vs ~727) and traded shares by ~2.5x (614 vs 246). Those aren't minor misses; they mean the ratio is close only because the simulated offer book has too few, much larger offers. The paper never reports error bars or distributions, so we can't tell if the 4-percentage-point ratio gap is noise.

The model also swaps the platform's FIFO matching for random sampling and uses hand-set uniform price bands without estimating them from the offer data. And there's a structural issue: the model gives each seller at most one offer per trading window, so with 638 seller-type agents it can't produce 727 offers even if every one of them acted. The empirical offer count likely reflects repeated offers or a larger effective seller population, which the model doesn't capture.

What it does well: the sensitivity analysis over 1,000 runs is diligent, the pseudocode is clear, and the authors are upfront that this is early-stage and market-specific. The idea of using an ABM this way for data augmentation and market-design testing is worth exploring. But as a claim to have replicated the market's dynamics, it's not supported.

If I were an editor, I'd send it out — the application is novel enough that a serious referee could push the authors into either fixing the model or reframing the claim as a prototype rather than a validated simulator. But I wouldn't cite it as evidence until at least the offer-count and traded-volume discrepancies are addressed.

Referee Report

3 major / 5 minor

Summary. The paper constructs an agent-based model of a one-sided, market-maker-free secondary market for fractional ownership of illiquid assets, calibrated to proprietary transaction data from a Swiss FinTech platform. Three agent types—Pure Seller, Pure Buyer, and Buyer Seller—are defined using empirical activity ratios, and the baseline simulation is evaluated against the empirical liquidity ratio and number of trades. A sensitivity analysis over 1,000 repeated runs examines the effect of each parameter on the liquidity ratio, number of offers, number of trades, and total shares offered/traded. The central claim is that the baseline model replicates the empirical dynamics sufficiently well to serve as a testbed for market design and data augmentation.

Significance. The paper addresses a genuinely underexplored area: agent-based modeling of illiquid, one-sided offer-book markets for tokenized real assets. The collaboration with an operating platform provides a rare empirical grounding, and the authors share concrete pseudocode and a broad sensitivity analysis. If the model were convincingly validated, it would offer a useful environment for studying liquidity in fractional-ownership markets and for generating synthetic data. The strength of the paper lies in its access to real user endowments and activity data; its weakness is that the current validation is insufficient to support the central replication claim.

major comments (3)

[Section VII, Table III] The baseline model reports 69 offers per trading window and 614.28 total traded shares, whereas the empirical data imply roughly 727 offers per window (26,884 offers over 37 windows, Section IV) and 246 traded shares (Table I). The number of trades is close (130 vs 132), but this is achieved by filling a much larger fraction of a much smaller offer book. The liquidity ratio (0.139 vs 0.096) is therefore not sufficient evidence that the model replicates the market; the authors should compare the full set of metrics and report confidence intervals from the 1,000 repeated runs, explicitly testing whether the empirical values fall within the simulated distribution.
[Section VI-C and Table II] All activation probabilities, offer ratios, and purchase ratios in Table II are computed from the same empirical dataset used to evaluate the baseline liquidity ratio in Section VII. This makes the comparison in-sample rather than a predictive validation. The authors should either split the 37 trading windows into calibration and validation sets, or use a statistical procedure that accounts for parameter uncertainty. As written, the match between simulated and empirical liquidity could be a consequence of the calibration rather than evidence of model validity.
[Section VI-A, Algorithms 2 and 3] The model abstracts the matching mechanism substantially: Pure Buyers sample one random offer (Algorithm 2) and Buyer Sellers sample a limited set of below-valuation offers (Algorithm 3), whereas Section IV describes price-time priority and real-time display of the offer book. These behavioral rules are not estimated from the empirical offer data. Since the composition of traded offers depends on which offers are sampled and accepted, the model may match the aggregate liquidity ratio for the wrong microstructural reasons. The authors should justify these simplifications with data or perform a robustness check under the platform's actual FIFO matching rule.

minor comments (5)

[Section VII] The statement that "the magnitudes of the shares traded in the synthetic versus the empirical market are comparable" is contradicted by the reported values (614.28 vs 246); a factor of 2.5 is not comparable.
[Algorithm 3, line 19] The comment "PS can purchase full offer" is a typo and should read "BS can purchase full offer," since the algorithm describes Buyer Seller behavior.
[Algorithm 4] Algorithm 4 uses a generic variable T for the number of time steps, while the text (Section VI-B) and Table II define n_iter_trade = 12; the notation should be unified.
[Table I] Table I would benefit from reporting the average number of offers per trading window, since the text states 26,884 offers over 37 windows but this key descriptive statistic is omitted from the table.
[Abstract and Section I] The paper promises a "data augmentation environment" but never demonstrates a use of the synthetic data; consider adding a simple illustration of data augmentation or softening this claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the simulated liquidity ratio is an emergent output of empirically calibrated parameters, not a fitted target or a self-citation-derived conclusion.

full rationale

The paper calibrates agent parameters (offer probabilities, offer ratios, purchase ratios, price ranges) from the same 37 trading windows that provide the empirical liquidity ratio, and Section VII then compares the simulated liquidity ratio (0.139) with that empirical ratio (0.096). This is an in-sample calibration check rather than an out-of-sample prediction, and it weakens the strength of the replication claim. However, under the supplied circularity definitions it is not circular: the liquidity ratio in Eq. (5) is computed as total traded shares divided by total offered shares, and it is not defined as, or set equal to, the empirical value. The baseline ratio differs from the target, and the sensitivity tables show that the output varies nontrivially with the calibrated inputs, so the output is not forced by construction. The paper also explicitly acknowledges in Section VIII-A that parameterization is market-specific and does not generalize. No load-bearing self-citations or imported uniqueness theorems appear; the cited literature is used for background motivation. The volume and offer-count mismatches noted by the skeptic are concerns about model accuracy and validation strength, not about circularity. Therefore no significant circularity is present.

Assumptions & free parameters 15 free parameters · 5 assumptions · 0 invented entities

The model is a calibrated simulation, not a derivation. Most free parameters are empirical averages from the same dataset used as the benchmark, while price ranges, matching rules, and search length are hand-set. The price distribution and matching simplifications are not validated against the empirical offer book.

free parameters (15)

PS Offer Probability (P_PS,O) = 0.114
Average ratio of active Pure Sellers per trading window from empirical data (Table I); used to trigger PS offer decisions in Algorithm 1.
PS Offer Ratio (R_PS,O) = 0.603
Average fraction of portfolio offered by active Pure Sellers; empirical value from Table I.
PB Trading Probability (P_PB,T) = 0.092
Average ratio of active Pure Buyers from empirical data (Table I).
PB Purchase Ratio (R_PB,P) = 0.566
Empirical average fraction of cash spent by buying Pure Buyers (Table II); no derivation is shown.
PB Decision Steepness (k_PB) = 2
Chosen by hand; not estimated from data. It controls the logistic acceptance probability in Eq. 2.
BS Offer Probability (P_BS,O) = 0.278
Average ratio of active Buyer Sellers on the sell side from empirical data (Table I).
BS Offer Ratio (R_BS,O) = 0.333
Average fraction of portfolio offered by active Buyer Sellers from empirical data (Table I).
BS Trading Probability (P_BS,T) = 0.104
Average ratio of active Buyer Sellers on the buy side from empirical data (Table I).
BS Purchase Ratio (R_BS,P) = 0.485
Empirical average fraction of cash spent by buying Buyer Sellers (Table II).
BS Search Length (SL_BS) = 5
Chosen by hand; no empirical basis for how many offers a Buyer Seller inspects.
Reference Price (p_ref) = 50
Initial share price in CHF for fractionalized assets; a constant input rather than a fitted parameter, but central to price generation.
Market Price Range (v_m,l, v_m,h) = [0.75, 1.10]
Chosen by hand as the allowable band around the reference price; not estimated from the empirical offer price distribution.
PS Price Range (v_PS,l, v_PS,h) = [0.75, 1.05]
Derived from the market range as [v_m,l, v_m,h - 0.05]; no empirical basis for the 0.05 offset.
BS Price Range (v_BS,l, v_BS,h) = [0.80, 1.10]
Derived as [v_m,l + 0.05, v_m,h]; no empirical basis.
Number of Market Iterations (n_iter,trade) = 12
Maps to 15-minute settlement intervals in the 18:00-21:00 trading phase; a reasonable discretization choice.

assumptions (5)

ad hoc to paper Sell offer prices are uniformly distributed within the allowable price range.
Eqs. 1 and 3 draw prices from uniform distributions; the true empirical price distribution is never shown or tested.
ad hoc to paper Pure Buyer acceptance decisions follow a logistic function of price relative to reference price with steepness k=2.
Eq. 2; k is hand-set, and no fit to empirical purchase rates by price is provided.
domain assumption The platform's FIFO price-time matching can be replaced by random offer sampling and cheapest-below-valuation selection.
Section IV states FIFO by price and timestamp; Algorithms 2 and 3 use random sampling and cheapest selection, which is a different matching rule.
domain assumption Using endowments from the close of 20 June 2024 is representative of all 37 trading windows.
Section VI-B uses a single snapshot for agent cash and asset positions, then compares to aggregate statistics over the whole sample.
domain assumption Pre-trading can be collapsed into a single iteration.
Section VI-B says this is justified because most offers are entered before trading; the paper does not quantify how many or whether timing within the day affects fills.

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Cite this review

Pith. "Pith review of Simulating Liquidity: Agent-Based Modeling of Illiquid Markets for Fractional Ownership." pith.science (2026). https://pith.science/paper/KKI34MCA

@misc{pith2026241113381,
  author       = {Pith},
  title        = {Pith review of: Simulating Liquidity: Agent-Based Modeling of Illiquid Markets for Fractional Ownership},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KKI34MCA}},
  note         = {Machine review of arXiv:2411.13381}
}

read the original abstract

This research investigates liquidity dynamics in fractional ownership markets, focusing on illiquid alternative investments traded on a FinTech platform. By leveraging empirical data and employing agent-based modeling (ABM), the study simulates trading behaviors in sell offer-driven systems, providing a foundation for generating insights into how different market structures influence liquidity. The ABM-based simulation model provides a data augmentation environment which allows for the exploration of diverse trading architectures and rules, offering an alternative to direct experimentation. This approach bridges academic theory and practical application, supported by collaboration with industry and Swiss federal funding. The paper lays the foundation for planned extensions, including the identification of a liquidity-maximizing trading environment and the design of a market maker, by simulating the current functioning of the investment platform using an ABM specified with empirical data.

Figures

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Works this paper leans on

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Liquidity and asset prices

Yakov Amihud, Haim Mendelson, Lasse Heje Pedersen, et al. “Liquidity and asset prices”. In: Foundations and Trends® in Finance 1.4 (2006), pp. 269–364

work page 2006

[2] [2]

The Behavior of the exchange Rate in the genetic Algorithm and experimental Economies

Jasmina Arifovic. “The Behavior of the exchange Rate in the genetic Algorithm and experimental Economies”. In: Journal of Political Economy 104.3 (1996), pp. 510– 541

work page 1996

[3] [3]

Asset Pricing under endogenous Expectations in an artificial Stock Market

W Brian Arthur et al. “Asset Pricing under endogenous Expectations in an artificial Stock Market”. In: The Economy as an evolving complex System II. CRC Press, 2018, pp. 15–44

work page 2018

[4] [4]

Price Discovery and Trading after Hours

Michael J Barclay and Terrence Hendershott. “Price Discovery and Trading after Hours”. In: The Review of Financial Studies 16.4 (2003), pp. 1041–1073

work page 2003

[5] [5]

Economics needs a scientific Revolution

Jean-Philippe Bouchaud. “Economics needs a scientific Revolution”. In: Nature 455.7217 (2008), pp. 1181– 1181

work page 2008

[6] [6]

Evolving Traders and the Business School with genetic Program- ming: A new Architecture of the Agent-based artificial Stock Market

Shu-Heng Chen and Chia-Hsuan Yeh. “Evolving Traders and the Business School with genetic Program- ming: A new Architecture of the Agent-based artificial Stock Market”. In: Journal of Economic Dynamics and Control 25.3-4 (2001), pp. 363–393

work page 2001

[7] [7]

Allocative Efficiency of Markets with zero-intelligence Traders: Market as a partial Substitute for individual Rational- ity

Dhananjay K Gode and Shyam Sunder. “Allocative Efficiency of Markets with zero-intelligence Traders: Market as a partial Substitute for individual Rational- ity”. In: Journal of Political Economy 101.1 (1993), pp. 119–137

work page 1993

[8] [8]

John M. Keynes. The General Theory of Employment, Interest and Money. Palgrave Macmillan, 1936

work page 1936