NEST: Stale-Robust Tokenized-Stock Measurement for a Crypto-Treasury LETF Stack

arXiv:2610.21491 · q-fin.TR, cs.CR · Submitted 2026-10-15 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Security Radio. Generated commentary on the latest security and cryptography papers.

Nadia: Today's paper: "NEST: Stale-Robust Tokenized-Stock Measurement for a Crypto-Treasury LETF Stack".

Elias: The gist The protocol NEST separates shared timing from conditional measurement value to determine if an off-hours tokenized mark adds explanatory power beyond public information in the BTC–MSTR–LETF chain.

Nadia: First, who's behind it and why it matters.

Title and authors: Nadia: To get into it, the paper "NEST: Stale-Robust Tokenized-Stock Measurement for a Crypto-Treasury LETF Stack" is trying to answer if an off-hours tokenized mark adds explanatory power beyond public information in that specific BTC–MSTR–LETF chain.

Elias: It’s focusing on the fact that tokenized equities can trade when the listed market is closed, and they ask: does this mark carry information when we look at it alongside Bitcoin price, MSTR's premarket proxy, and the leveraged ETF?

Nadia: Essentially, it sets up a framework where you test if an off-hours mark is just noise or if it tells you something new that isn't already visible.

Elias: They do this by setting up four steps for admitting such a mark: first clocking things, then conditioning on public controls like MSTR’s premarket price, then making a decision based on an index, and finally auditing how far that cleared mark can actually be used in the market.

Nadia: That sounds like it moves from just a statistical correlation to something more practical about whether this mark is even useful for trading decisions.

Elias: Yeah, it does. They build this framework around a measurement model that starts with the mechanical fit, where the opening gap and the token return share the move from the previous close to that token mark.

The paper's summary: Nadia: So, what they summarize is that raw fit between an off-hours mark and the next opening gap is mechanically driven because both of them start from the same price move from before.

Elias: That shared history identity means if you look at the move through the token mark,Zd, and epsilon d all having mean zero and being uncorrelated with positive variances, then there’s a specific relationship between the opening gap Gd on one hand and that token return Td on the other.

Nadia: The paper then introduces something called the partial determination index or PDI to measure what remains after conditioning on those public controls, such as MSTR’s own premarket price.

Elias: Lemma one shows that this PDI is mathematically equivalent to the change in residual sum of squares, which is just R21 minus R20, and Lemma two gives us a noisy-control interpretation of the PDI <ref:2610.21491#pg1>.

Nadia: So, if the PDI is positive against a benchmark, it means there’s improvement over that benchmark in terms of information content, not necessarily that the mark has a unique source.

Elias: That’s the key insight they are pushing: a positive PDI against a noisy benchmark actually means improvement over that benchmark, not exclusive information origin.

The paper's improvements: Nadia: The authors then move into testing this conditional informativeness using the finite-sample frontier and its power function, FPDI.

Elias: Theorem one restates the classical nested-model test in PDI units and adds this power function, which lets you compare an estimated share directly with what's required for statistical significance <ref:2610.21491#pg1>.

Nadia: This is useful because it turns the test into a design tool; you can use it to figure out how many windows of data you need to see before a PDI above a certain threshold gets detected reliably.

Elias: For example, at eighty percent power and one percent significance, twenty-one-eight windows detect any PDI above zero point zero five two, but in a smaller sample size, you only see PDIs above zero point two one as detectable.

Nadia: Then there's the admissibility layer where they audit product rights, price provenance, and execution costs to determine how far that cleared mark can actually be used in the risk system.

Elias: They also map these slope estimates into specific exposure diagnostics, like determining the one-reset wipeout threshold for a leveraged ETF, which depends on whether the admitted mark updates book leverage or listed-session beta.

Conclusion: Nadia: So, to wrap up the NEST protocol, it shows that most of the raw fit between an off-hours mark and the next opening gap is actually absorbed by public information like Bitcoin price and MSTR’s premarket proxy.

Elias: The central finding is that what's left over after conditioning on all that, including mark age, is a modest increment, about fourteen point zero to seventeen point zero percent of residual gap variation.

Nadia: So they prove the token isn't just some weekend-only signal; it’s a steady complement to the listed stock’s premarket price. It's reusable for deciding when an asynchronous tokenized mark might enter a risk system.

Elias: And that framework, NEST, provides a way to separate that shared history fit from the conditional measurement value using their identity and variance-clock bound. It travels across products while allowing the answer to change based on those admission criteria.

Priya: From my side, what I see is that this method helps us move beyond just observing raw statistics and actually makes a decision about admissibility by mapping it into concrete exposure diagnostics like book leverage or wipeout thresholds.

Nadia: Exactly. It shifts the focus from just finding a correlation to figuring out actionable risk diagnostics based on those inputs.

Elias: So, the NEST protocol is presented as an informative input for monitoring rather than direct evidence of unrestricted ownership or arbitrage in this context.

Doohwi Cha, Minsuk Sung, Minjae Lee, Hyeonjun Yeo, Hanhee Kim, Seunghan Son, Donghwa Seo, Juyeong Lee

Mirae Asset Securities, Seoul, South Korea. · Korea University, Seoul, South Korea. · Independent Researcher, Seoul, South Korea. · Seoul National University, Seoul, South Korea. · DS Investment & Securities, Seoul, South Korea. · EY Consulting · Seoul · South Korea

q-fin.TR, cs.CR

Submitted: 2026-10-15

Updated: 2026-10-15

Comments: 20 pages, 3 figures, 7 tables. Extended version of a paper accepted for publication in the proceedings of MARBLE 2026 (Lecture Notes in Operations Research, Springer Nature)

Code: https://github.com/DefiLlama/api

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 79/100

The gist: The gist The protocol NEST separates shared timing from conditional measurement value to determine if an off-hours tokenized mark adds explanatory power beyond public information in the

Key concepts

Shared-History Identity: This concept quantifies the mechanical relationship between an off-hours token return and the next opening gap. It shows how much of their apparent correlation is due to them sharing the same underlying price move from the previous close, which is a shared history effect rather than new information.
Partial Determination Index (PDI): The PDI measures what remains after conditioning on known public controls, such as Bitcoin prices or premarket stock proxies. A positive PDI indicates that the token mark provides explanatory power beyond what is already accounted for by these public controls.
Finite-Sample Frontier: This tool compares the estimated share of gap variation explained by a token mark against the minimum level required for statistical significance. It helps determine if a measured fit is meaningful or just random noise in a limited sample size.
Admissibility Audit: This final step checks whether an admitted off-hours mark is useful by auditing product rights, price provenance, and execution costs. It ensures the mark can be reliably mapped into the actual exposures of the asset stack.

Terminology

Provenance — 1× in this paper · explained in 5 episodes

Summary

The gist The protocol NEST separates shared timing from conditional measurement value to determine if an off-hours tokenized mark adds explanatory power beyond public information in the BTC–MSTR–LETF chain.

How it works

NEST develops a stale-robust admission protocol that quantifies fit using a shared-history identity and a variance-clock bound, while testing conditional informativeness through the partial determination index (PDI) and its finite-sample frontier. The protocol involves four steps for admitting an off-hours mark: (i) Clock, where every input must be observable by the cutoff, and shared-history and variance-clock diagnostics are reported next to raw fit. (ii) Conditioning, including prespecified controls S such as MSTR’s own premarket price. (iii) Decision, where the mark clears when the estimated PDI exceeds the frontier c.01(n; p) and the HAC check agrees. (iv) Admissibility, which audits product rights, price provenance, a named-venue replication, and execution costs to determine how far a cleared mark can be used.

Measurement Model

The model begins with the mechanical fit from shared history where the opening gap Gd and the token return Td share the move Yd from the previous close to the token mark, raising raw fit mechanically. Proposition 1 establishes a shared-history identity, showing that if Yd, Zd, and εd are mean zero and pairwise uncorrelated with positive variances, the population regression of Gd on Td has a slope bT = σ2Y / (σ2Y + σ2ε) and a fit R2T = σ4Y / ((σ2Y + σ2Z)(σ2Y + σ2ε)).

Conditional measurement is then addressed by the Partial Determination Index (PDI), which measures what remains after conditioning on public controls S, defined as PDITS ≡ Corr2(MSG, MST) = R21 - R20 / (1 - R20). Lemma 1 shows that the PDI is equivalent to the change in residual sum of squares, ∆R2 ≡ R21 - R20 = (1 − R20) PDITS. Lemma 2 provides a noisy-control interpretation, showing that a positive PDI against a noisy benchmark means improvement over that benchmark, not exclusive information origin.

Finite-Sample Frontier and Power

Theorem 1 restates the classical nested-model test in PDI units and adds its power function, FPDI ∼ F′1,ν nθ / (1 − θ). The frontier lets a reader compare an estimated share directly with the share required for significance, and Corollary 1 turns it into a design tool. For instance, at the 80% power level and 1% significance, 218 windows detect any PDI above 0.052, whereas only PDIs above 0.21 are detected in a smaller subsample.

Stack Exposure and Admissibility

An admitted mark is useful only if it can be mapped into the exposures that the stack creates, which involves mapping to gk, β, and f. Lemma 3 defines the daily-reset identity for log LN L0 based on k=1 paths. Corollary 2 determines the one-reset wipeout threshold (∆C/C)wipe = −1/(βλE). Table 7 maps these slope estimates into the one-reset Bitcoin move that sets a two-times LETF to zero, which depends on whether the admitted mark is used to update the book leverage or the listed-session beta.

Results and Conclusion

The central finding is that most of the raw fit between an off-hours mark and the next opening gap is absorbed by public information, leaving a modest, complementary increment of 14.0% to 17.0% of residual gap variation after conditioning on Bitcoin, mark age, and MSTR’s premarket proxy. The protocol proves that the token is a steady complement to the listed stock’s own premarket price, not a weekend-only signal. NEST is therefore a reusable protocol for deciding when an asynchronous tokenized mark may enter a risk system.

Limitations

The evidence is bounded in five ways, including the coarse nature of the premarket proxy, the lack of disclosure regarding historical constituents of the composite, and the fact that calendar subsamples are small for weekend windows. Furthermore, NEST does not identify where information originates and does not forecast post-mark shocks. The executable band relies on primary-market access that most holders lack, meaning admission describes a monitoring input rather than an arbitrage opportunity.

Conclusion

NEST provides a method to separate the shared history fit from conditional measurement value using a shared-history identity and a variance-clock bound. The protocol travels across products while allowing its answer to differ based on admission criteria, making it an informative input for monitoring rather than evidence of unrestricted ownership or arbitrage.

References

The paper cites literature on price discovery across markets, asynchronous and sequential trading biases betas and return moments, tokenized stocks, leveraged ETFs. The references also include work on partial time regressions, information shares for markets with partially overlapping trading hours, and modeling around-the-clock price discovery,,,, and others as listed in the bibliography on page 7 of the paper itself. The references also include work on historical quotation data, DefiLlama API documentation, and Yahoo Finance MSTR stock quote,,, and others as listed in the bibliography on page 5 of the paper itself. The references also include work on nonsynchronous trading, sequential markets, and state space models for around-the-clock price discovery,,, and others as listed in the bibliography on page 5 of the paper itself. The references also include work on seasonal adjustment, multiple regression analysis, and other econometric tools,, and others as listed in the bibliography on page 5 of the paper itself. The references also include work on path-dependence of leveraged ETF returns, tokenized stock markets, and arbitrage limits,, and others as listed in the bibliography on page 5 of the paper itself. The references also include work on cointegrated systems, estimation of common long-memory components, and other relevant econometric studies,, and others as listed in the bibliography on page 5 of the paper itself.

Improvements for AI systems

AI systems can perform stale-robust tokenized-stock measurement by implementing NEST, a protocol that separates this shared-history fit from conditional measurement value. This allows the AI to distinguish between mechanical fit and true conditional informativeness when analyzing off-hours crypto-treasury stocks.
The AI can calculate a partial determination index (PDI), the squared partial correlation between token and gap given public controls, which measures what remains, providing a rigorous metric to test whether an off-hours mark adds explanatory power beyond observable inputs like Bitcoin price or MSTR's premarket proxy.
AI systems can utilize the finite-sample frontier to express the partial-F decision in PDI units, enabling them to determine if a statistical increment is admissible based on a specific required signal share, as described in Theorem 1 and Corollary 1.
The AI can implement an admissibility layer by auditing product rights, price provenance, timestamp, and execution costs, which allows it to decide whether an informative mark is admissible, moving beyond simple statistical association to actionable risk diagnostics.
The AI can translate the admitted mark into specific exposure diagnostics, such as calculating book leverage and determining a one-reset wipeout threshold for the LETF layer, providing a concrete measure of chain risk based on the tokenized input.