The stability of markets hosting leveraged exchange-traded products is governed not by any single product's loop gain but by the spectral radius of a loop-gain matrix, and scalar per-product monitoring underestimates system feedback by construction. Recent work measures the self-reinforcement of a leveraged fund's daily close rebalancing through a scalar loop gain and treats cross-asset spillovers as bias. We model complexes on correlated underlyings as a coupled feedback system with matrix gain L and show that scalar monitoring has two blind spots: (i) cycle amplification, since rho(L) >= max_i l_ii for nonnegative coupling, strict under two-way coupling; and (ii) transmitted displacement, which arises already under one-way coupling and is invisible to the receiver's own gain. We give a reduced-form estimator of L requiring only prices and public fund assets -- no signed order flow -- via cross-asset overnight reversals, reporting its measurement-convention sensitivity explicitly. In simulation the spectral radius is recovered with RMSE 0.005 at T=250, a lead-lag confounder yields a 2% false-alarm rate, and in a calibrated blind-spot configuration the scalar monitor reports "safe" and the matrix monitor "unsafe" on 100% of paths. In the 2026 Korean single-stock LETF episode we detect transmission from the SK Hynix complex into Samsung Electronics' closing price (DiD z=-2.82; exact randomization p=0.0055 against 182 control pairs), scaling with the sender's rebalancing capital; conservatively, about 41% of Samsung's closing displacement variance is imported -- invisible to its own "moderate" gain of 0.24. The same estimator returns nulls for the U.S. MSTR-Bitcoin-Coinbase complex, whose capital is comparable but whose closing venue is far deeper. Monitoring should be organized around the (complex x venue) matrix, not around products.
Proof-of-stake protocols lock tokens into staking positions, shrinking the tradable float. We develop a continuous-time model in which price-impact volatility is a convex decreasing function of the float. Two results emerge. Conditional return variance amplifies as the float contracts, with amplification accelerating in high-staking regimes. Protocol changes that shift the long-run staking target produce persistent volatility regime transitions, with convergence speed governed by protocol adjustment capacity. Liquid-staking tokens attenuate both effects, with attenuation increasing in their liquidity parameter.
We study the Banach dual of the one-parameter stochastic integral δ_L(u) = ∫₀^T u_t dL_t for a symmetric γ-stable Lévy process with γ ∈ (1,2). The natural integrand exponent is p ∈ (1,γ): the small-jump integrability ∫|z|^p ν_γ(dz) < ∞ holds iff p < γ, so this is not an arbitrary L^p but the unique scale dictated by the singularity of the Lévy measure at the origin. On this scale, the operator-covariant derivative D_L := δ_L^* : L^q(Ω) → H_L^* is the Banach dual of the one-parameter integral. Since p < 2, the Riesz identification H_L^* ≅ H_L is unavailable, and the Banach setting is forced. The principal result is structural: D_L is strictly more restricted than the standard Malliavin add-a-point operator D_{t,z}F = F(ω + δ_(t,z)) − F(ω) on Poisson space, which is the dual of the full two-parameter compensated Poisson integral ∫∫ h(s,z) Ñ(ds,dz). By Lévy-Itô, the one-parameter integrand of δ_L has the special form h(s,z) = u(s) · z — linear in z — whereas full martingale representation on Lévy space uses general h(s,z). The representability obstruction quantifies the resulting gap precisely: centered functionals depending nonlinearly on jump sizes — canonically, the centered large-jump count #{|ΔL_s| > 1} − E[#{|ΔL_s| > 1}] — lie in ker(D_L) yet are detected by the standard add-a-point operator. The obstruction is a property of the one-parameter integral, not a feature of jump processes themselves. The factorization (Theorem A) holds on the closed proper subspace im(δ_L) ⊊ L^p_0(Ω) and characterizes precisely which functionals admit one-parameter representation. Theorem B (product rule with Leibniz defect) is a standalone duality identity: its proof uses only the definition of D_L, the Lévy-Itô formula, and Hölder's inequality, and it does not invoke (H3) or the factorization machinery. Theorem C — the strongest technical result — identifies ker(D_L) and the annihilator of im(δ_L) via L^q-L^p truncation in the jump variable, showing the annihilator is infinite-dimensional even within the first chaos. The framework has been formally verified in the Lean 4 proof assistant (2,439 lines, zero sorry, zero axioms) using Mathlib. To our knowledge, this is the first formalization of the operator-covariant derivative framework with its representability obstruction in any proof assistant. The formalization includes proved Poisson mean and variance identities, a constructed compound Poisson path, a compensated-integral interface with derived Banach-side consequences, a concrete first-chaos orthogonality model, and the full abstract theorem pipeline — all machine-checked from clearly isolated stochastic-analysis assumptions.
We study permissionless spot--perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot inventory and derivative margin under on-chain liquidity and execution frictions. The paper delivers three results. First, it solves a static control problem for the collateral share and shows that the risk-constrained formulation provides a more robust operating benchmark relative to the economic optimum. In comparative calibration, the required collateral rises monotonically under volatility stress. The collateral is the lowest for BTC and increases significantly for long tail assets such as LINK and DOGE. Second, the paper derives an asymmetric dynamic extension in which the lower boundary of intervention is solvency driven, and the upper boundary is determined by a trade-off between carry-loss and the cost of rebalancing. Monte Carlo simulation shows that the lower boundary remains structurally relevant, whereas meaningful interior upper triggers survive mainly in the regimes with high carry and low costs. Third, the paper validates an execution-aware implementation with live routed execution and historical backtests. The execution layer shows that the realized wedges are significant, but become worse in the case of selling the basis. This justifies a minimum effective rebalancing size and a positive execution buffer. The historical validation shows that in the case of a fixed control rule the realized performance is predominantly explained by the funding environment.
This paper develops a deep reinforcement learning framework for cryptocurrency portfolio management in which transaction costs are derived from the Riemannian geometry of the underlying volatility model rather than assumed constant. A Proximal Policy Optimisation agent is trained on a reward function grounded in non-equilibrium thermodynamics: we use the free-energy Bellman equation, in which transaction costs are the geodesic slippage on the Fisher information manifold of a maximum-entropy Markov-switching GARCH model, and regime-transition costs are the Wasserstein-2 distance between the calm and turbulent return distributions. A thermodynamic Carnot bound on portfolio efficiency is established and empirically validated. Five hypotheses are tested across Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash over January 2017 to March 2026. The geometric-cost agent achieves statistically superior Sharpe ratios relative to flat-fee baselines on four of five assets; portfolio turnover is reduced by 56 to 83 percent relative to signal-following; the thermodynamic friction point at which the agent prefers no-trade is asset-specific and ordered by turbulent half-life; a joint topological and geometric circuit breaker reduces Maximum Drawdown by 28 to 38 percent; and ablation confirms that every component of the observation vector contributes a statistically significant performance gain. The framework requires liquid cryptocurrency markets with validated parametric volatility models; transferability to other asset classes requires upstream recalibration.
Using a comprehensive dataset from Deribit, we show that Bitcoin options trading activity is concentrated around two distinct intraday periods: 8:00–9:00 GMT and 14:00–15:00 GMT, relative to other hours of the day. The latter peak coincides with the opening of the New York Stock Exchange and is largely absent on weekends, suggesting spillovers from traditional equity markets to the Bitcoin options market. In contrast, the concentration of trading activity around the 8:00–9:00 GMT period appears to be driven by investors rolling over and re-establishing expiring options around the 8:00 GMT settlement, as this effect persists on both weekdays and weekends, and is stronger on days with more expiring contracts and for contracts with shorter maturities. These findings highlight how institutional trading conventions shape intraday activity in cryptocurrency derivatives and provide the first systematic evidence of intraday patterns in Bitcoin options trading.
Rizqi Akbar Makarim, Desinta Maheswari, Aqila Dina Pramustiwi, Kartika Ayu Rahmawati · 5 authors
The volatility of cryptocurrency markets has increased substantially in recent years, particularly for Ethereum (ETH), which exhibits fat-tailed distributions and persistent volatility clustering that traditional linear models are unable to capture. This study aims to analyze and model the volatility of ETH/USD using high-frequency hourly data to determine the most appropriate volatility model for describing Ethereum’s intraday market dynamics. The dataset consists of 8,760 hourly closing prices from October 31, 2024 to October 31, 2025, obtained through the CryptoCompare API. The methodological framework includes data preprocessing, log-return transformation, stationarity analysis using the Augmented Dickey–Fuller test, detection of heteroskedasticity via the ARCH–LM test, and estimation of several ARCH and GARCH model specifications. The results show that ETH/USD returns are stationary, non-normally distributed, and exhibit clear volatility clustering. Among the ARCH models, only ARCH(1) adequately captures short-term fluctuations, while ARCH(2) provides no additional benefit. In contrast, GARCH models demonstrate superior performance in capturing both short-term shocks and long-term persistence. Based on AIC, BIC, and log-likelihood values, GARCH(1,2) emerges as the best-performing model, offering the highest flexibility in representing Ethereum’s persistent and reactive volatility patterns. These findings confirm that ETH/USD volatility is predictable and can be modeled statistically. Future research may incorporate asymmetric GARCH extensions or external explanatory variables to improve predictive performance.
P Praveen Kumar, Dudimetla Pravalika, B. S. Dileep Kumar, Gattu Akshitha · 5 authors
The rapid advancement of blockchain technology has introduced new possibilities for secure digital ownership and transparent fundraising through Non-Fungible Tokens (NFTs).However, most existing charity platforms remain centralized, limiting transparency, accountability, and verifiable proof of donations.Donors often lack visibility into how funds are utilized, while reliance on intermediaries increases risks such as data manipulation, reduced auditability, and decreased trust.To address these issues, this work proposes a decentralized charity auction framework that leverages blockchain technology and NFT-based asset representation.The system is developed using the Django web framework integrated with Web3 infrastructure and smart contracts.In this model, each auction item is tokenized as a unique NFT, ensuring authenticity, traceability, and immutable ownership.The platform allows users to act as donors or auctioneers, enabling participation in NFT-based charity auctions.Users can place bids or contribute funds, with all transactions securely recorded on a blockchain ledger.At the end of each auction, NFT ownership is automatically transferred to the highest bidder or contributor, providing verifiable proof of participation.By removing intermediaries and incorporating a transparent, incentive-driven mechanism, the proposed system enhances donor trust and engagement.It ensures tamper-proof record-keeping and clear fund flow, strengthening accountability within charitable ecosystems.This framework demonstrates a scalable and efficient approach to modern fundraising, showcasing the potential of blockchain and NFTs in improving trust and transparency in charity applications.
This deposit contains the Lean 4 formal verification companion (BanachLevyComplete.lean, 2,439 lines) for the paper "Operator Factorization Beyond Hilbert Spaces: Representability Obstructions, Leibniz Defects, and Chaos Characterizations for Stable Lévy Processes" by Ramiro Fontes. The file has zero sorry declarations and zero axiom declarations. It integrates three layers: Part 1 — Poisson infrastructure: The symmetric γ-stable Lévy measure density with proved symmetry and nonnegativity. The Poisson mean identity E[Poisson(λ)] = λ and variance identity Var(Poisson(λ)) = λ, proved as theorems via a recurrence lemma and HasSum assembly. A canonical Poisson random variable constructed on (ℕ, poissonMeasure(λT)) with its distribution proved by Measure.map_id. Stable measure moment computations and the Blumenthal–Getoor dichotomy. Quadratic defect sharpness for the variance swap payoff. Part 2 — Lévy–Itô framework: The Itô formula for compound Poisson processes proved as a finite telescoping sum via Finset.sum_range_sub. A compound Poisson path defined as a concrete function, proved to start at zero and to have the correct terminal value. The compensated Poisson integral constructed as an L² limit of compound Poisson finite sums, with linearity inherited from finite-sum linearity and centering derived via tendsto_nhds_unique. Truncation convergence, centering, the predictable module structure, and chaos orthogonality derived from the compensated-integral interface. The first Poisson chaos realized concretely on (ℕ, poissonMeasure) with orthogonality proved via tsum_mul_left. The L² Cauchy estimate for the ε → 0 approximation proved, with the M → ∞ direction documented as requiring Lp (not L²) convergence. Part 3 — Banach energy space framework: The operator-covariant derivative D constructed via mk_dual (not axiomatized). The fluctuation factorization (Theorem A), representability obstruction, product rule with jump defect (Theorem B), and chaos characterization (Theorem C) verified. The centered obstruction witness derived from primitive stable-noise data: evenness from absolute-jump structure, positive variance from λ > 0 and T > 0 via mul_pos, nonzero from positive variance, and the obstruction from representability_obstruction. The Hilbert bridge showing the Banach framework specializes when the jump defect vanishes. The remaining primitive inputs are concentrated in two places: the Banach-side Lp-convergence layer for the compensated integral as M → ∞, and a full bottom-up Poisson-random-measure realization. These are isolated as explicit structure fields rather than hidden proof gaps. Together with the companion OperatorDerivative.lean (5,184 lines, zero sorry, one axiom) for the Hilbert paper, this constitutes 7,623 lines of formally verified stochastic calculus. To our knowledge, the Poisson mean and variance identities, the first Poisson chaos orthogonality, and the compound Poisson Itô formula via finite telescoping are among the first such formalized results in Lean 4.
This paper develops a deep reinforcement learning (DRL) framework for cryptocurrency portfolio management in which transaction costs are derived from the Riemannian geometry of the underlying volatility model rather than assumed constant. A Proximal Policy Optimisation (PPO) agent is trained on a reward function derived from non-equilibrium thermodynamics: the free-energy Bellman equation, in which (i) transaction costs are the geodesic slippage S∗ on the Fisher information manifold of a maximum-entropy Markov-switching GARCH model, and (ii) regime-transition costs are the Wasserstein-2 distance Wt between the calm and turbulent return distributions. The agent is embedded in the WOW-E-W quadrilogy, a four-paper research programme that integrates statistical mechanics, fluid dynamics, Riemannian information geometry, and thermodynamic control into a unified cryptocurrency risk architecture. The PPO agent observes an 11-dimensional state vector ot that combines turbulent-regime probabilities \( \hat{\xi}_t(2) \) and parameter estimates \( \hat{\theta}_t \) from a maximum-entropy Markov-switching GARCH model, a viscosity-filtered velocity signal ht and gate states zt, rt from a GRU viscosity filter, and the Fisher curvature Gt, Ricci scalar κt, Betti numbers β0,t, β1,t,Wasserstein dissipation Wt, and topological alarm dI(t) from the Riemannian execution geometry layer. The framework establishes a thermodynamic Carnot bound on portfolio efficiency: η ≤ 1 − Hturb/Hcalm, where Hturb and Hcalm are the maximum-entropy values of the turbulent and calm regime distributions. Five hypotheses are tested across Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash over January 2017 to March 2026: the geometric-cost PPO agent achieves higher Sharpe ratio than Buy-and-Hold, Greedy signal-following, and flat-fee PPO baselines (bootstrap p &lt; 0.05 for four of five assets); portfolio turnover is reduced by 56 to 83 percent relative to signal-following; the thermodynamic friction point at which the agent prefers no-trade is asset-specific and ranges from 0.6 percent (Bitcoin) to 1.8 percent (Ethereum), ordered by turbulent half-life (Spearman ρ = 0.94, p = 0.017); a joint topological and geometric circuit breaker reduces Maximum Drawdown by 28 to 38 percent; and ablation confirms that every component of ot contributes a statistically significant performance gain (Diebold-Mariano p &lt; 0.05 for at least four of five assets per component). The framework requires liquid cryptocurrency markets with validated parametric volatility models; transferability to other asset classes requires upstream recalibration and is an explicitly bounded limitation.
We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with finitely many critical points, recently proven in [1]. Our approach is based on the stochastic representation formula of the associated advection-diffusion equation and yields two short proofs. The first uses a stochastic integration-by-parts argument and gives optimal mixing under the weakest regularity assumption required in the zero-diffusion case, answering Question II in [1, Section 4]. The second adopts a dynamical systems perspective and provides a proof of shear-induced mixing that, to our knowledge, is new even in the zero-diffusivity setting.
Najaf Iqbal, Muhammad Abubakr Naeem, Hang Luo, Walid Bakry
Using 5-minute data of 16 cryptocurrency tokens belonging to 5 different categories (AI, Gaming, Meme, Layer 1/2, and FAN tokens), we investigate the risk transmission in higher moments, i.e. realized volatility (RV), realized skewness (RS), and realized kurtosis (RK), employing the TVP-VAR framework and robustness tests. We also perform six sub-sample investigations on various geopolitical and other systemic events. Ethereum, Binance Coin, and Ripple are strongly related to other tokens. Sandbox, Decentraland, and Enjin Coin lead spillover transmission, while Numeraire, Measurable Data Token, and Cryptex Finance absorb most of the shocks. The connections are stronger regarding RV than RS and RK, showing potential for tail-risk reduction, which is heterogeneous regarding extreme events. AI tokens are the least connected during normal conditions as well as most of the extreme events, except the US presidential Election, which puts these tokens in the centre of the system. The Israel-Palestine war, the FTX collapse, and the SEC approval of the first Bitcoin ETF are among the most important events regarding enhancement in the higher-moment risk transmission. Token market investors/traders and regulators can draw essential insights from our findings.
The cryptocurrency market offers significant investment opportunities, but with high levels of financial risk compared to traditional asset classes. This study analyzes the daily returns of Bitcoin and Ethereum, focusing on tail behavior and peakedness to assess risk. Using the flexible Generalized Tempered Stable (GTS) distribution, we capture significant deviations from normality. Results show Bitcoin returns are more concentrated around the mean, with 80 % of returns between$-1.27 \%$and 2.84 %, while Ethereum is more dispersed-only 40 % of its returns fall in that range. Bitcoin's distribution is more sharply peaked; Ethereum has heavier tails and greater exposure to extreme fluctuations. These findings underscore the importance of using advanced models like the GTS for accurate risk management and portfolio optimization in cryptocurrencies.
Abstract With the introduction of spot Ethereum ETFs, Ethereum plays an increasingly important role in the cryptocurrency market. In this paper, we propose a Bayesian modelling framework incorporating a mixture copula for co-modelling Ethereum returns with Bitcoin or FTSE 100 returns. The mixture copula is designed as a combination of the Clayton copula and its three rotations, Frank, and Gaussian copulas. It provides substantial flexibility for handling a variety of dependency structures. The Bayesian approach offers the advantage of jointly estimating both the margins and copulas and simulating future returns in a coherent procedure. Using 10 different risk or risk-return measures, we provide updated empirical evidence on Ethereum’s role in both cryptocurrency and mixed portfolios. The analysis not only evaluates its diversification potential numerically but also sheds light on how the optimal allocations vary across distinct risk preferences and portfolio objectives. Moreover, based on the data of 2017–2024, we estimate that Ethereum futures has a hedging effectiveness on Bitcoin of about 30–40% across different risk preferences. Beyond these findings, the Bayesian mixture copula framework represents a methodological contribution to the modelling of complex dependence structures between financial returns. Taken together, our study delivers new insights that are particularly relevant in light of the evolving cryptocurrency landscape and the increasing integration of digital assets into mainstream investment practice.
In recent years, investors have shown growing interest in diversified multi-asset indices that incorporate crypto assets, with Bitcoin at the forefront. The launch of exchange-traded products, the growing acceptance of Bitcoin among institutional investors, and its increasing weight in financial markets all highlight the strategic importance of this asset. Bitcoin has exhibited extraordinary returns in the past, yet as a standalone investment it appears less attractive to risk-averse investors due to extreme volatility and severe drawdowns. The relevant question is therefore whether including Bitcoin in a diversified multi-asset portfolio can enhance performance without deteriorating its overall risk profile, and what allocation methods provide a credible way to achieve this balance. Classical allocation methods offer contrasting perspectives. Mean–variance optimisation explicitly incorporates expected returns, but it is highly sensitive to estimation error, which often results in unstable allocations. Empirical evidence even shows that simple rules such as the naïve 1/N portfolio often outperform mean–variance optimisation out of sample [DeMiguel et al., 2007]. Risk-based approaches, such as minimum variance or risk parity, are more stable but ignore expected returns altogether, which is problematic when dealing with an asset that exhibits an unusually high mean return. Robust optimisation provides a natural way to reconcile these two approaches. By incorporating parameter uncertainty directly into the optimisation problem, robust methods allow expected returns to influence the allocation while penalising excessive reliance on noisy estimates. This framework is particularly well-suited for Bitcoin, whose characteristics amplify estimation risk. The aim of this thesis is to study the construction of a multi-asset index including Bitcoin, with a particular focus on the use of robust optimisation techniques. More specifically, the objective is both to assess whether the inclusion of Bitcoin can enhance the performance of a diversified portfolio without materially worsening its risk profile, and to evaluate whether robust optimisation provides more stable and credible allocations than classical approaches such as mean–variance, risk parity, or equal-weighting. Performance and stability are examined through backtests and Monte Carlo simulations.
We present the most complete unified taxonomy of Black-Scholes option price sensitivities (Greeks) available in the literature, encompassing 21 distinct measures through third order: first-order (Delta, Vega, Theta, Rho), second-order (Gamma, Vanna, Charm, Vomma, Veta, Vera, Dual Delta, Dual Gamma), third-order (Speed, Zomma, Color, Ultima, DvannaDvol, DvommaDspot), and portfolio-level (Dollar Delta, Dollar Gamma, Lambda). For each Greek we provide: (i) a fully explicit derivation from the dividend-adjusted Black-Scholes formula showing every application of the chain rule and product rule, (ii) alternative derivation paths including risk-neutral expectation differentiation and heat equation Green’s function representations, (iii) closed-form expressions for both European calls and puts, (iv) identification of put-call parity equivalences, (v) complete asymptotic analysis (deep ITM/OTM, short/long-dated, zero/high vol limits), (vi) monotonicity and convexity properties with extrema locations, (vii) dimensional analysis for practitioner interpretation, and (viii) practical trading context. We derive the Black-Scholes PDE from first principles via Itô’s lemma and the replicating-portfolio argument, establish the risk-neutral pricing connection, and prove the key symmetry lemma that simplifies every Greek derivation. The Gamma-Theta tradeoff is proved directly from the PDE with trading implications. The Vanna-Volga pricing method is derived from smile replication principles. We provide a complete treatment of sticky-strike versus stickydelta hedging conventions, delta hedging theory with continuous and discrete P&L analysis, Greeks under stochastic volatility (Heston model), numerical methods for Greeks computation (finite differences, pathwise, likelihood ratio, and adjoint algorithmic differentiation), and the behavior of Greeks near expiry including pin risk. A differential-geometric interpretation frames the Greeks as gradient, Hessian, and third-order tensor components on the six-dimensional Black-Scholes parameter manifold, with the PDE as a constraint surface. Fourth-order Greeks are derived and a convergence analysis of the Taylor price expansion justifies the third-order truncation for perturbations up to 10% of spot. Publication-quality three-dimensional surface visualizations for all 21 Greeks reveal the topology of each sensitivity across its natural parameter space. Formal proofs of all 12 put-call parity equivalences, a complete 21 Greek formula reference card, and a comprehensive monotonicity and extrema table are provided as appendices. A Python implementation with numerical verification against finite differences accompanies the paper, with over 50 figures. To our knowledge, this constitutes the most comprehensive rigorously derived reference for Black-Scholes Greeks in a single document.
Cascading liquidations across decentralized finance (DeFi) lending protocols represent a systemic risk that standard empirical models often fail to capture. To quantify this phenomenon, we apply a 3-variate Hawkes process to model crossprotocol liquidation clustering among Aave V3, Compound V3, and Morpho on Ethereum. Using 7,500 on-chain liquidation events spanning 2023-01-01 through 2025-12-31, we estimate exponential triggering kernels via maximum likelihood estimation and validate the approach against nonparametric spectral estimates. The results indicate a stable, subcritical regime (ρ = 0.725) characterized by statistically significant off-diagonal excitation. The strongest cross-protocol channel runs from Morpho to Compound V3 (branching ratio Γ = 0.418), while selfexcitation ratios range from 0.28 to 0.32. Directional predictive dependence tests confirm asymmetric spillover effects. Furthermore, likelihood-based comparisons demonstrate that crossprotocol excitation significantly outperforms self-excitation-only and common-factor baselines, including models with ETH return controls. Placebo permutations verify that this off-diagonal structure is not an artifact of shared timing. Ultimately, while the findings document robust cross-protocol clustering consistent with spillover channels, we emphasize that Hawkes crossexcitation captures directional predictive dependence rather than strict structural causation.
We develop optimal transport stress testing, liquidation cost modeling, and fund-level capital allocation for lending against prediction market collateral. Building on a companion paper that derives first-passage default probabilities under Hawkes-driven jump-discussion dynamics, this paper addresses three challenges that arise when operating the lending protocol at scale. First, we introduce a Wasserstein stress testing methodology that generates synthetic tail scenarios for markets with insufficient historical depth, proving that it achieves strictly higher effective sample sizes than classical Entropy Pooling when the stress region lies outside the empirical support. We further establish an adversarial robustness guarantee: the stressed risk estimate remains bounded even under worst-case perturbations of the empirical distribution within a Wasserstein ball- a formal resilience property that no existing decentralized finance stress testing methodology provides.
Decentralized Finance (DeFi) lending and borrowing protocols enable investors to take leveraged long and short positions on digital assets without centralized intermediaries, but expose them to a distinctive form of risk: on-chain liquidation triggered by debt and collateral value fluctuations. In this work, we provide a detailed formalization of Aave's lending, borrowing, and liquidation mechanisms, grounded in the protocol's open-source implementation. In doing so, we propose a mathematical modeling of the risk of liquidation, including some stochastic approximations with the purpose of efficient analysis, with different applications. Among them, portfolio optimization problem.
We introduce a model-free structural framework to value liabilities of firms whose primary assets are digital assets typically Bitcoin. Our no-arbitrage approach prices convertible debts and extracts the risk-neutral probabilities of their terminal states using the market information of Bitcoin options, thereby bypassing the restrictive assumptions of traditional structural models. We perform comparative statics analysis to demonstrate how the resulting bond spreads and option values are structurally determined. We then test the framework in a real-world case study of MicroStrategy's convertible bonds, finding that it generates accurate, market-consistent valuations in an out-of-sample setting. Together, our theoretical and empirical results establish a robust, market-based blueprint for pricing the emerging class of crypto-backed credit in general.
We formulate and solve stochastic control problems that model the core yield-generating strategy of the Ethena protocol, a decentralized finance (DeFi) stablecoin that earns yield by combining a long position in staked Ethereum (stETH) with an equal-sized short position in ETH perpetual futures. The combined position is delta-neutral with respect to the ETH spot price, yet earns carry from two sources: staking rewards on the stETH leg, and funding-rate payments received from long perpetual holders when the perpetual trades at a premium to spot. A key feature of our model is that the control -- the rate of simultaneously buying stETH and shorting the perpetual -- exerts two distinct types of price impact. \textit{Permanent} impact shifts the mid-market prices of both legs, compressing the basis and permanently eroding future funding income. \textit{Temporary} impact reflects execution slippage on each leg. We study both an infinite-horizon discounted problem and a finite-horizon problem in which the protocol maximizes total wealth up to a fixed date $T$, subject to a terminal cost for liquidating any remaining position. In both cases the optimal control is obtained explicitly.