The Triadic Stress Index (TSI) takes a network index whose four factors were first observed in soil microbiome co-occurrence networks and applies it, without alteration, to the correlation network of financial assets. We test it on five markets spanning 2006-2026 (equities including banking crises and the AI sector, cryptocurrencies, commodities, foreign exchange and sovereign debt), against three independent definitions of a crisis episode, at a fixed alarm budget, out of sample, with block-bootstrap intervals and a Holm correction across the family of tests. The benchmarks are the Absorption Ratio, the industry standard used by MSCI and central banks; the effective rank and the Vendi score, the sharpest spectral measures available; Ollivier-Ricci curvature; and the global and local balance indices of signed correlation networks. Three comparisons favour the index. It carries a per-node decomposition, diag(A^3), naming which asset is carrying the concentration with no parameter to select, and scores 0.97-0.99 against 0.33-0.84 for the only published per-node alternative, whereas spectral attribution must first choose how many components to read and collapses under a standard but wrong choice. Its alarms are the cleanest of anything tested, 4.0% of them with no matching episode against 14.7% for the effective rank and roughly 59% for the Absorption Ratio. And it beats the Absorption Ratio on detection by 0.273 in F1 out of sample, p<0.0005. The remaining comparisons are ties. Against the effective rank and the Vendi score the index ties in every scheme and both samples, and the margin over the Absorption Ratio narrows under the strictest labelling. On real matrices the far simpler node degree reproduces the attribution. A lead-lag analysis puts the peak cross-correlation at zero lag: this is a coincident state index, not a forecast.
Decentralized finance exposes supervisors to fast-moving, networked credit risks. General-purpose LLM agents fit this setting poorly: they over-read weak evidence and recommend high-stakes interventions, while existing evaluations offer no regulator-aligned way to measure the resulting false alarms. We introduce DeXposure-Claw, a forecast-grounded agentic supervision system that routes LLM decisions through structured evidence: (1) DeXposure-FM, a graph time-series foundation model, forecasts future exposure networks; (2) deterministic monitors and stress scenarios then turn those forecasts into typed alerts, attribution signals, and scenario evidence; and (3) data-health and confidence gates constrain escalation before DeXposure-Claw emits auditable supervisory tickets with rationales. We further develop DeXposure-Bench, a six-axis evaluation harness, whose decision axis scores tickets against a regulator-aligned absolute-loss ground truth and an explicit false-intervention rate. Experiments on five years of weekly real data fully support our system. Code is at https://github.com/EVIEHub/DeXposure-Claw.
Quantum computing poses a real, broad-based, but bounded and substantially mitigable threat to Bitcoin and Ethereum. We separate the two quantum algorithms that public discussion routinely conflates: Shor's algorithm breaks the elliptic-curve signatures (ECDSA over secp256k1, BLS over BLS12-381) that authorize spending, whereas Grover's algorithm does not meaningfully threaten proof-of-work mining, which is protected by a merely quadratic speedup, fault-tolerant per-operation costs, a square-root parallelization wall, and difficulty adjustment. Folding hardware scaling, the falling resource requirement, a fault-tolerance readiness lag, and expert surveys into a single Monte-Carlo forecast yields a wide, bimodal arrival distribution for a cryptographically relevant quantum computer: about a one-in-six chance by 2035, near 30% by 2040, and about 60% by 2050. Exposure is concentrated and mostly migratable: of Bitcoin's roughly six million quantum-exposed coins only about 2.3 million are irreducibly at risk, while 50 to 65% of Ether sits at key-revealed accounts that can adopt post-quantum signatures. A timely migration beats even an optimistic 2035 machine, so the binding constraint is governance, not technology. A survey of the top twenty cryptocurrencies finds none fully post-quantum. Reproducible models accompany every quantitative claim.
We derive five tractable credit risk metrics for DeFi lending vault depositors, grounded in a formal three level decomposition of vault risk into mechanical loss channels (Level 1), governance quality (Level 2) and smart contract code integrity (Level 3). For Level 1, we show that six structural features of onchain execution (oracle execution divergence, endogenous recovery, full information run dynamics, timelock constrained governance, oracle manipulation and congestion driven liquidation failure) break canonical TradFi analogies and generate depositor loss channels absent from standard credit frameworks. Vault credit risk metrics translate these channels into measurable risk components which are aggregated into a vault credit score. The empirical contribution is an implementable estimation architecture for credit risk metrics, including required onchain data, identification strategies for core parameters, partial identification bounds and a coherent stress scenario methodology. The results have direct implications for vault risk management and for minimum transparency standards necessary for depositor risk assessment.
Daily probability changes in Kalshi macro prediction markets forecast cryptocurrency realized volatility through two distinct channels. The monetary policy channel, measured by Fed rate repricing on KXFED contracts, predicts Bitcoin volatility in sample with t = 3.63 and p < 0.001 but exhibits regime dependence tied to the 2024-2025 rate-cutting cycle. The recession risk signal from KXRECSSNBER proves more stable out of sample, delivering an MSFE ratio of 0.979 with Clark-West p = 0.020. The inflation channel, measured by CPI repricing on KXCPI contracts, predicts altcoin volatility for Ethereum, Solana, Cardano, and Chainlink with t-statistics ranging from -2.1 to -3.4 and out-of-sample gains for Ethereum at MSFE = 0.959 with p = 0.010 and Solana at p = 0.048. Both the Bitcoin--Fed-dovish and Chainlink--CPI specifications survive Benjamini-Hochberg correction at q = 0.05. Orthogonalization and baseline comparisons against Fed Funds futures, Treasury yields, and the Deribit implied volatility index confirm that these signals carry information not embedded in conventional financial instruments. The sample covers ten Kalshi event series and six cryptocurrency assets over January 2023 to March 2026.
On-chain lending has expanded across multiple distributed ledgers as DeFi becomes increasingly multi-chain. This environment introduces novel technical and financial mechanisms, particularly cross-blockchain communication and asset transfer protocols, yet cross-chain elements remain understudied in lending protocol risk management. To address this gap, we applied panel regression fixed effects and OLS models to empirically analyze cross-blockchain interoperability solutions, using TVL and total revenue as performance proxies from October 2022 to January 2025. Our data set covers 15 decentralized lending protocols and 53 cross-chain bridges across 9 EVM-compatible blockchains, categorized as Ethereum, alternative layer-1s, and Ethereum layer-2 networks. Results reveal that cross-chain activity impacts on protocol performance. Bridge volume emerges as a critical driver, exerts a significant effect on TVL and revenue across different categories, though the direction of this effect varies heterogeneously. Increased bridge integrations are associated with decreased TVL and protocol revenue across categories, indicating liquidity escapes from those lending ecosystems. Liquidations produce heterogeneous effects across categories. New network launches do not have as significant relationships with TVL and revenue while bridge hacks show a significant and positive relationship. High R-squared values confirm meaningful explanatory power. We further show Ethereum attracts large depositors, while layer-2s skew toward retail participation. We conclude that effective DeFi risk models should incorporate cross-chain metrics and adopt a layer-aware approach to accurately reflect the evolving multi-chain landscape.
Decentralized finance introduces new business models and use cases as part of digital finance. Restaking has recently emerged as a transformative mechanism in DeFi, promising extra yields but introducing complex and interconnected risks. The paper monitors the current restaking landscape, empirically analyzes the revenue drivers of a liquid restaking protocol, and conducts a technical investigation on the emitted risk arising from the interconnection between liquid restaking and other protocols. The revenue dynamics of Renzo Protocol are analyzed by employing an OLS regression model, Granger-causality and random forest feature importance tests. Our results identify that revenue is primarily predicted by the value locked in the underlying EigenLayer ecosystem, the yield of Renzo protocol's liquid restaking token and the multi-blockchain expansion of that token. The multi-blockchain expansion of the liquid restaking token presents a double-edged sword: bridging to other networks is crucial for user adoption, but it adds the bridge risks to the existing risks of restaking. We investigate the cross-contamination risk between different DeFi services and the liquid restaking protocol. By mapping the asset flow across the decentralized finance ecosystem, it is detected that the bridge risk of the current size of Renzo's liquid-restaking assets does not impose a systemic risk on the current restaking and staking ecosystem. To address the potential consequences of the emphasized interconnection risks, we introduce two hypothetical scenarios and a stress test, assuming a large number of compromised liquid restaking tokens and a smart contract logic failure in a DeFi protocol. Considering the overall liquid-restaking protocols and the growing interconnection, this analysis requires further work to explore the growing complexities.
Steven Campbell, Natascha Hey, Ciamac C. Moallemi, Marcel Nutz
Auto-deleveraging (ADL) mechanisms are a critical yet understudied component of risk management on cryptocurrency futures exchanges. When available margin and other loss-absorbing resources are insufficient to cover losses following large price moves, exchanges reduce positions and socialize losses among solvent participants via rule-based ADL protocols. We formulate ADL as an optimization problem that minimizes the exchange's risk of loss arising from future equity shortfalls. In a single-asset, isolated-margin setting, the \emph{minimax leverage} policy -- minimizing the maximum leverage among participants -- is optimal for all monotone risk measures. This policy has a transparent structure: positions are reduced first for the most highly levered accounts, and leverage is progressively equalized via a water-filling (or ``leverage-draining'') rule. The policy is distribution-free, wash-trade resistant, Sybil resistant, and path-independent. It provides a canonical and implementable benchmark for ADL design and clarifies the economic logic underlying queue-based mechanisms used in practice. We further study the multi-asset, cross-margin setting, where the ADL problem becomes genuinely multi-dimensional: the exchange must allocate reductions across accounts with portfolios exposed to correlated price moves. Under the expected loss objective, asset-level shadow prices separate the problem across accounts, yielding a scalable numerical method. Naive gross leverage misleads here, ignoring within-portfolio hedging. When prices are driven by a single risk factor, the optimal policy is again water-filling, but in a factor-adjusted leverage, so better-hedged portfolios are deleveraged less. We apply the framework to the October~10, 2025 Hyperliquid ADL event. Relative to the exchange's realized allocation, our risk-minimizing allocations achieve lower expected shortfall.
Cryptocurrency markets exceed USD 3 trillion in capitalisation, yet practitioners lack an interpretable, channel-decomposed composite for characterising crypto-native systemic stress. We introduce the Aggregated Systemic Risk Index (ASRI), built from four weighted sub-indices -- Stablecoin Concentration Risk (30%), DeFi Liquidity Risk (25%), Contagion Risk (25%, implemented as a TradFi-stress proxy), and Regulatory Opacity Risk (20%) -- with a Diebold--Yilmaz connectedness series computed on the sub-indices as network benchmark. We evaluate ASRI retrospectively against four crises (Terra/Luna, Celsius/3AC, FTX, SVB) and give a methodological account of how autocorrelation- and block-structure-robust inference reshapes apparent crisis-detection strength. The event-study signal is inconclusive: heavily serially correlated (AR(1) $\approx 0.8$--$0.9$), with placebo dates clearing the nominal threshold as often as crises. Fixed-threshold detection flags three of four events with $\approx$19-day average lead ($\approx$5 days under a responsive specification); walk-forward thresholds flag 4/4 but at high false-positive cost -- evidence against look-ahead bias, not a clean prediction record. ASRI's day-level discrimination (AUROC 0.866) beats only the circular D--Y comparator (0.670); it is statistically indistinguishable from its strongest sub-index (0.851), PC1 (0.858), and a standalone VIX series (0.875, $p=0.58$). We read aggregation's value as interpretive -- channel attribution, lead time, and regime structure in one auditable composite -- not as discriminative gain. With four crisis events the binding power limit, ASRI is a transparent, reproducible, retrospective monitoring framework targeting crypto-native vulnerabilities that SRISK and CoVaR are not built to capture, not a validated early-warning system. Out of sample it classifies the 2025 Bybit hack as non-systemic.
Time Series Foundation Models (TSFMs) have emerged as a promising approach for zero-shot financial forecasting, demonstrating strong transferability and data efficiency gains. However, their adoption in financial applications is hindered by fundamental limitations in uncertainty quantification: current approaches either rely on restrictive distributional assumptions, conflate different sources of uncertainty, or lack principled calibration mechanisms. While recent TSFMs employ sophisticated techniques such as mixture models, Student's t-distributions, or conformal prediction, they fail to address the core challenge of providing theoretically-grounded uncertainty decomposition. For the very first time, we present a novel transformer-based probabilistic framework, ProbFM (probabilistic foundation model), that leverages Deep Evidential Regression (DER) to provide principled uncertainty quantification with explicit epistemic-aleatoric decomposition. Unlike existing approaches that pre-specify distributional forms or require sampling-based inference, ProbFM learns optimal uncertainty representations through higher-order evidence learning while maintaining single-pass computational efficiency. To rigorously evaluate the core DER uncertainty quantification approach independent of architectural complexity, we conduct an extensive controlled comparison study using a consistent LSTM architecture across five probabilistic methods: DER, Gaussian NLL, Student's-t NLL, Quantile Loss, and Conformal Prediction. Evaluation on cryptocurrency return forecasting demonstrates that DER maintains competitive forecasting accuracy while providing explicit epistemic-aleatoric uncertainty decomposition. This work establishes both an extensible framework for principled uncertainty quantification in foundation models and empirical evidence for DER's effectiveness in financial applications.
Shiyu Zhang, Zining Wang, Jin Zheng, John Cartlidge
Systemic risk refers to the overall vulnerability arising from the high degree of interconnectedness and interdependence within the financial system. In the rapidly developing decentralized finance (DeFi) ecosystem, numerous studies have analyzed systemic risk through specific channels such as liquidity pressures, leverage mechanisms, smart contract risks, and historical risk events. However, these studies are mostly event-driven or focused on isolated risk channels, paying limited attention to the structural dimension of systemic risk. Overall, this study provides a unified quantitative framework for ecosystem-level analysis and continuous monitoring of systemic risk in DeFi. From a network-based perspective, this paper proposes the DeFi Correlation Fragility Indicator (CFI), constructed from time-varying correlation networks at the protocol category level. The CFI captures ecosystem-wide structural fragility associated with correlation concentration and increasing synchronicity. Furthermore, we define a Risk Contribution Score (RCS) to quantify the marginal contribution of different protocol types to overall systemic risk. By combining the CFI and RCS, the framework enables both the tracking of time-varying systemic risk and identification of structurally important functional modules in risk accumulation and amplification.
The integration of cryptocurrencies into institutional portfolios necessitates the adoption of robust risk modeling frameworks. This study is a part of a series of subsequent works to fine-tune model risk analysis for cryptocurrencies. Through this first research work, we establish a foundational benchmark by applying the traditional industry-standard Geometric Brownian Motion (GBM) model. Popularly used for non-crypto financial assets, GBM assumes Lognormal return distributions for a multi-asset cryptocurrency portfolio (XRP, SOL, ADA). This work utilizes Maximum Likelihood Estimation and a correlated Monte Carlo Simulation incorporating the Cholesky decomposition of historical covariance. We present our stock portfolio model as a Minimum Variance Portfolio (MVP). We observe the model's structural shift within the heavy-tailed, non-Gaussian cryptocurrency environment. The results reveal limitations of the Lognormal assumption: the calculated Value-at-Risk at the 5% confidence level over the one-year horizon. For baselining our results, we also present a holistic comparative analysis with an equity portfolio (AAPL, TSLA, NVDA), demonstrating a significantly lower failure rate. This performance provides conclusive evidence that the GBM model is fundamentally the perfect benchmark for our subsequent works. Results from this novel work will be an indicator for the success criteria in our future model for crypto risk management, rigorously motivating the development and application of advanced models.
This paper measures price differences between Hegic option quotes on Arbitrum and a model-based benchmark built on Black--Scholes model with regime-sensitive volatility estimated via a two-regime MS-AR-(GJR)-GARCH model. Using option-level feasible GLS, we find benchmark prices exceed Hegic quotes on average, especially for call options. The price spread rises with order size, strike, maturity, and estimated volatility, and falls with trading volume. By underlying, wrapped Bitcoin options show larger and more persistent spreads, while Ethereum options are closer to the benchmark. The framework offers a data-driven analysis for monitoring and calibrating on-chain option pricing logic.
This paper examines factors that influence prices of most common five cryptocurrencies such as Bitcoin, Ethereum, Dash, Litecoin, and Monero over 2010-2018 using weekly data. The study employs ARDL technique and documents several findings. First, cryptomarket-related factors such as market beta, trading volume, and volatility appear to be significant determinant for all five cryptocurrencies both in short- and long-run. Second, attractiveness of cryptocurrencies also matters in terms of their price determination, but only in long-run. This indicates that formation (recognition) of the attractiveness of cryptocurrencies are subjected to time factor. In other words, it travels slowly within the market. Third, SP500 index seems to have weak positive long-run impact on Bitcoin, Ethereum, and Litcoin, while its sign turns to negative losing significance in short-run, except Bitcoin that generates an estimate of -0.20 at 10% significance level. Lastly, error-correction models for Bitcoin, Etherem, Dash, Litcoin, and Monero show that cointegrated series cannot drift too far apart, and converge to a long-run equilibrium at a speed of 23.68%, 12.76%, 10.20%, 22.91%, and 14.27% respectively.
Betas from spot regressions are central to asset pricing and risk management, as measures of systematic risk. This paper develops a new estimation and inference framework for spot regressions by leveraging high-frequency candlesticks, extending conventional (open-to-close) returns with intra-period high/low prices. Specifically, I construct candlestick-based estimators of regression parameters, including spot beta, by minimizing a quadratic risk under a fixed-k asymptotic framework. I then develop a feasible hypothesis testing procedure for spot betas with correct asymptotic size. Simulation results show that the proposed estimator reduces estimation risk relative to return-based estimators, especially in small samples, and the test achieves notably higher power. I apply the framework to assess the market neutrality of Bitcoin using 1-minute data on IBIT and SPY, finding deviations from neutrality, particularly in high-volatility periods.
This study aims to detect pump and dump (P&D) manipulation in cryptocurrency markets, where the scarcity of such events causes severe class imbalance and hinders accurate detection. To address this issue, the Synthetic Minority Oversampling Technique (SMOTE) was applied, and advanced ensemble learning models were evaluated to distinguish manipulative trading behavior from normal market activity. The experimental results show that applying SMOTE greatly enhanced the ability of all models to detect P&D events by increasing recall and improving the overall balance between precision and recall. In particular, XGBoost and LightGBM achieved high recall rates (94.87% and 93.59%, respectively) with strong F1-scores and demonstrated fast computational performance, making them suitable for near real time surveillance. These findings indicate that integrating data balancing techniques with ensemble methods significantly improves the early detection of manipulative activities, contributing to a fairer, more transparent, and more stable cryptocurrency market.
Minjung Park, Gyuyeon Na, Soyoun Kim, Sunyoung Moon ยท 6 authors
Abnormal cryptocurrency transactions - such as mixing services, fraudulent transfers, and pump-and-dump operations -- pose escalating risks to financial integrity but remain notoriously difficult to detect due to class imbalance, temporal volatility, and complex network dependencies. Existing approaches are predominantly model-centric and post hoc, flagging anomalies only after they occur and thus offering limited preventive value. This paper introduces HyPV-LEAD (Hyperbolic Peak-Valley Lead-time Enabled Anomaly Detection), a data-driven early-warning framework that explicitly incorporates lead time into anomaly detection. Unlike prior methods, HyPV-LEAD integrates three innovations: (1) window-horizon modeling to guarantee actionable lead-time alerts, (2) Peak-Valley (PV) sampling to mitigate class imbalance while preserving temporal continuity, and (3) hyperbolic embedding to capture the hierarchical and scale-free properties of blockchain transaction networks. Empirical evaluation on large-scale Bitcoin transaction data demonstrates that HyPV-LEAD consistently outperforms state-of-the-art baselines, achieving a PR-AUC of 0.9624 with significant gains in precision and recall. Ablation studies further confirm that each component - PV sampling, hyperbolic embedding, and structural-temporal modeling - provides complementary benefits, with the full framework delivering the highest performance. By shifting anomaly detection from reactive classification to proactive early-warning, HyPV-LEAD establishes a robust foundation for real-time risk management, anti-money laundering (AML) compliance, and financial security in dynamic blockchain environments.
Sabrina Aufiero, Silvia Bartolucci, Fabio Caccioli, Pierpaolo Vivo
This work explores the formation and propagation of systemic risks across traditional finance (TradFi) and decentralized finance (DeFi), offering a comparative framework that bridges these two increasingly interconnected ecosystems. We propose a conceptual model for systemic risk formation in TradFi, grounded in well-established mechanisms such as leverage cycles, liquidity crises, and interconnected institutional exposures. Extending this analysis to DeFi, we identify unique structural and technological characteristics - such as composability, smart contract vulnerabilities, and algorithm-driven mechanisms - that shape the emergence and transmission of risks within decentralized systems. Through a conceptual mapping, we highlight risks with similar foundations (e.g., trading vulnerabilities, liquidity shocks), while emphasizing how these risks manifest and propagate differently due to the contrasting architectures of TradFi and DeFi. Furthermore, we introduce the concept of crosstagion, a bidirectional process where instability in DeFi can spill over into TradFi, and vice versa. We illustrate how disruptions such as liquidity crises, regulatory actions, or political developments can cascade across these systems, leveraging their growing interdependence. By analyzing this mutual dynamics, we highlight the importance of understanding systemic risks not only within TradFi and DeFi individually, but also at their intersection. Our findings contribute to the evolving discourse on risk management in a hybrid financial ecosystem, offering insights for policymakers, regulators, and financial stakeholders navigating this complex landscape.
Extreme volatility, nonlinear dependencies, and systemic fragility are characteristics of cryptocurrency markets. The assumptions of normality and centralized control in traditional financial risk models frequently cause them to miss these changes. Four components-volatility stress testing, stablecoin hedging, contagion modeling, and Monte Carlo simulation-are integrated into this paper's modular simulation framework for crypto portfolio risk analysis. Every module is based on mathematical finance theory, which includes stochastic price path generation, correlation-based contagion propagation, and mean-variance optimization. The robustness and practical relevance of the framework are demonstrated through empirical validation utilizing 2020-2024 USDT, ETH, and BTC data.
Blockchain-based decentralised lending is a rapidly growing and evolving alternative to traditional lending, but it poses new risks. To mitigate these risks, lending protocols have integrated automated risk management tools into their smart contracts. However, the effectiveness of the latest risk management features introduced in the most recent versions of these lending protocols is understudied. To close this gap, we use a panel regression fixed effects model to empirically analyse the cross-version (v2 and v3) and cross-chain (L1 and L2) effectiveness of liquidation mechanisms, measured through TVL and total revenue as proxies for performance of the two most popular lending protocols, Aave and Compound, during the period Jan 2021 to Dec 2024. Our analysis reveals that liquidation events in v3 of both protocols lead to an increase in total value locked and total revenue, with stronger impact on the L2 blockchain compared to L1. In contrast, liquidations in v2 have an insignificant impact, which indicates that the most recent v3 protocols have better risk management than the earlier v2 protocols. We also show that L1 blockchains are the preferred choice among large investors for their robust liquidity and ecosystem depth, while L2 blockchains are more popular among retail investors for their lower fees and faster execution.
In this paper, we propose an analytical method to compute the collateral liquidation probability in decentralized finance (DeFi) stablecoin single-collateral lending. Our approach models the collateral exchange rate as a zero-drift geometric Brownian motion, and derives the probability of it crossing the liquidation threshold. Unlike most existing methods that rely on computationally intensive simulations such as Monte Carlo, our formula provides a lightweight, exact solution. This advancement offers a more efficient alternative for risk assessment in DeFi platforms.
As restaking protocols gain adoption across blockchain ecosystems, there is a need for Actively Validated Services (AVSs) to span multiple Shared Security Providers (SSPs). This leads to stake fragmentation which introduces new complications where an adversary may compromise an AVS by targeting its weakest SSP. In this paper, we formalize the Multiple SSP Problem and analyze two architectures : an isolated fragmented model called Model $\mathbb{M}$ and a shared unified model called Model $\mathbb{S}$, through a convex optimization and game-theoretic lens. We derive utility bounds, attack cost conditions, and market equilibrium that describes protocol security for both models. Our results show that while Model $\mathbb{M}$ offers deployment flexibility, it inherits lowest-cost attack vulnerabilities, whereas Model $\mathbb{S}$ achieves tighter security guarantees through single validator sets and aggregated slashing logic. We conclude with future directions of work including an incentive-compatible stake rebalancing allocation in restaking ecosystems.
Agustin Muรฑoz Gonzalez, Juan Ignacio Sequeira, Ariel Dembling
This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool's value using a combination of European calls and puts. Furthermore, we establish a result guaranteeing hedging coverage for all final prices within a predefined interval. These theoretical results motivate a numerical example where we illustrate the strangle strategy using real cryptocurrency options data from Deribit, one of the most liquid markets available.
Lending within decentralized finance (DeFi) has facilitated over \$100 billion of loans since 2020. A long-standing inefficiency in DeFi lending protocols such as Aave is the use of static pricing mechanisms for loans. These mechanisms have been shown to maximize neither welfare nor revenue for participants in DeFi lending protocols. Recently, adaptive supply models pioneered by Morpho and Euler have become a popular means of dynamic pricing for loans. This pricing is facilitated by agents known as curators, who bid to match supply and demand. We construct and analyze an online learning model for static and dynamic pricing models within DeFi lending. We show that when loans are small and have a short duration relative to an observation time $T$, adaptive supply models achieve $O(\log T)$ regret, while static models cannot achieve better than $ฮฉ(\sqrt{T})$ regret. We then study competitive behavior between curators, demonstrating that adaptive supply mechanisms maximize revenue and welfare for both borrowers and lenders.