arXiv subjects

Zachary Feinstein

Publications and source records attributed to Zachary Feinstein.

At least 19 recordsLinked to original sources

arXiv2026

Mandate without Managers: Automated Market Makers as Verifiable Portfolio Products

Automated market makers (AMMs) are typically interpreted and evaluated as decentralized exchanges. Herein, we take the perspective envisioned by Balancer that an AMM can also be viewed as a portfolio technology that programmatically enforces an economic mandate. In particular, we follow the geometric mean market maker (G3M) invariant employed by that protocol in order to enforce a target-weighted portfolio. We introduce a multi-asset fee structure to the G3M under which competitive arbitrage implements a band-rebalancing strategy with mis-weighting bounded ex ante, allowing compliance with the mandate to be verified directly from the pool's observable holdings. We then compare simulated G3M portfolios against the realized performance of VBIAX, EQL, and EDOW on annualized returns and tracking error against the portfolio mandate. Across these historical case studies, and using arbitrage-only order flow, the G3M is found to outperform the incumbent funds in both metrics for certain fee ranges.

q-fin.TR↗

arXiv2026

Designing On-Chain Options: Amortizing Perpetual Options

Financial options are fundamental to traditional markets, enabling strategies ranging from hedging to speculating. Yet, while the Automated Market Maker paradigm has revolutionized decentralized spot markets, no equivalent standard has emerged for on-chain options. Typical designs attempt to replicate centralized exchange mechanics, requiring high-frequency oracles and robust liquidation engines which may fail during stress events. This paper presents a design for amortizing perpetual options tailored to the operational and adversarial constraints of blockchain environments. Leveraging this primitive, we introduce a decentralized market framework with minimal consistency requirements. We demonstrate that this contract functions as a foundational risk primitive for DeFi, enabling applications such as endogenous collateralization and explicitly priced de-peg insurance, thereby showing that this design provides a layer for mutualizing tail risk across protocols without reliance on centralized clearing institutions.

q-fin.MF↗

arXiv2026

Liquidation Dynamics in DeFi and the Role of Transaction Fees

Liquidation of collateral are the primary safeguard for solvency of lending protocols in decentralized finance. However, the mechanics of liquidations expose these protocols to predatory price manipulations and other forms of Maximal Extractable Value (MEV). In this paper, we characterize the optimal liquidation strategy, via a dynamic program, from the perspective of a profit-maximizing liquidator when the spot oracle is given by a Constant Product Market Maker (CPMM). We explicitly model Oracle Extractable Value (OEV) where liquidators manipulate the CPMM with sandwich attacks to trigger profitable liquidation events. We derive closed-form liquidation bounds and prove that CPMM transaction fees act as a critical security parameter. Crucially, we demonstrate that fees do not merely reduce attacker profits, but can make such manipulations unprofitable for an attacker. Our findings suggest that CPMM transaction fees serve a dual purpose: compensating liquidity providers and endogenously hardening CPMM oracles against manipulation without the latency of time-weighted averages or medianization.

q-fin.MF↗

arXiv2025

Amortizing Perpetual Options

In this work, we introduce amortizing perpetual options (AmPOs), a fungible variant of continuous-installment options suitable for exchange-based trading. Traditional installment options lapse when holders cease their payments, destroying fungibility across units of notional. AmPOs replace explicit installment payments and the need for lapsing logic with an implicit payment scheme via the decay of the claimable notional. This amortization ensures all units evolve identically, preserving fungibility. We demonstrate that AmPO valuation can be reduced to an equivalent vanilla perpetual American option on a dividend-paying asset. This enables analytical expressions for the exercise boundaries and risk-neutral valuations for calls and puts. These formulas and relations allow us to derive the Greeks and study comparative statics with respect to the amortization rate. Illustrative numerical case studies demonstrate how the amortization rate shapes option behavior and reveal the resulting tradeoffs in the effective volatility sensitivity.

q-fin.PR↗

arXiv2025

The Price of Liquidity: Implied Volatility of Automated Market Maker Fees

An automated market maker (AMM) provides a method for creating a decentralized exchange on the blockchain. For this purpose, individual investors lend liquidity to the AMM pool in exchange for a stream of fees earned from its operations as a market maker. Within this work, we reinterpret the loss-versus-rebalancing as the implied fee stream generated by an AMM so that a risk-neutral investor is indifferent in the decision of providing liquidity. With this implied fee structure, we propose a novel fixed-for-floating swap on the fees generated by an AMM in order to quote the implied volatilities and implied correlations of digital assets. We apply this theory to realized fees in different markets to empirically validate the relevance of the deduced fee-based volatility.

q-fin.MF↗

arXiv2025

Computing all Nash equilibria of low-rank bi-matrix games

We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained games, along with a necessary and sufficient condition for when such reductions exist. Building on this framework, we present three approaches for computing the set of extremal Nash equilibria, based on vertex enumeration, polyhedral calculus, and vector linear programming. Numerical case studies demonstrate the effectiveness of the proposed reduction and solution methods.

math.OC↗

arXiv2025

Identifying Risk Variables From Raw ESG Data Using Its Hierarchical Structure

Environmental, Social, and Governance (ESG) data provides non-financial insights into corporations. In this study, we aim to identify relevant ESG raw variables to assess financial risk, measured by logarithmic volatility of return. We propose a framework specifically designed for ESG datasets characterized by a hierarchical data structure and a significantly larger number of variables than observations. We show that raw variables selected by the proposed framework are significantly more relevant to financial risk than aggregated ESG scores. Furthermore, these selected risk variables provide additional insights beyond the traditional financial factors. We validate the robustness of this framework using out-of-sample data. We illustrate our framework using company data from various sectors of the US economy. We further identify the specific ESG risk variables relevant to large and small companies within each sector.

q-fin.RM↗

arXiv2025

Can Nash inform capital requirements? Allocating systemic risk measures

Systemic risk measures aggregate the risks from multiple financial institutions to find system-wide capital requirements. Though much attention has been given to assessing the level of systemic risk, less has been given to allocating that risk to the constituent institutions. Within this work, we propose a Nash allocation rule that is inspired by game theory. Intuitively, to construct these capital allocations, the banks compete in a game to reduce their own capital requirements while, simultaneously, maintaining system-level acceptability. We provide sufficient conditions for the existence and uniqueness of Nash allocation rules, and apply our results to the prominent structures used for systemic risk measures in the literature. We demonstrate the efficacy of Nash allocations with numerical case studies using the Eisenberg-Noe aggregation mechanism.

q-fin.RM↗

arXiv2024

A Derivative Pricing Perspective on Liquidity Tokens in Constant Product Market Makers

In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees earned from the market making operations. This position is represented by a liquidity token, whose prevailing on-chain price is effectively the initial deposited assets. Though this price is well-defined, we treat the liquidity token as a derivative position in the prices of the underlying assets for the CPMM in order to deduce risk-neutral pricing and hedging formulas, not dissimilar to the Black-Scholes result. Adopting this perspective, in a frictionless environment, hedging the CPMM liquidity token under fair valuation should produce a riskless process, which therefore grows at the risk-free rate, something that is not seen in empirical case studies under the prevailing price. With our novel pricing formula, we construct a method to calibrate a volatility to data which provides an updated (non-market) valuation which is consistent with the (near-continuous) replication strategy out-of-sample. We conclude with a discussion of novel AMM design considerations motivated by this derivative-pricing perspective.

q-fin.MF↗

arXiv2024

On the Separability of Vector-Valued Risk Measures

Risk measures for random vectors have been considered in multi-asset markets with transaction costs and financial networks in the literature. While the theory of set-valued risk measures provide an axiomatic framework for assigning to a random vector its set of all capital requirements or allocation vectors, the actual decision-making process requires an additional rule to select from this set. In this paper, we define vector-valued risk measures by an analogous list of axioms and show that, in the convex and lower semicontinuous case, such functionals always ignore the dependence structures of the input random vectors. We also show that set-valued risk measures do not have this issue as long as they do not reduce to a vector-valued functional. Finally, we demonstrate that our results also generalize to the conditional setting. These results imply that convex vector-valued risk measures are not suitable for defining capital allocation rules for a wide range of financial applications including systemic risk measures.

q-fin.RM↗

arXiv2024

The not-so-hidden risks of 'hidden-to-maturity' accounting: on depositor runs and bank resilience

We introduce a simple model of depositor runs to capture run risks at financial institutions based on their balance sheet composition. Specifically, we consider a reduced potential to raise capital from liquidity buffers under stress, during a stylized run driven by depositor scrutiny and further fueled by fire sales in response to withdrawals. The setup is inspired by the Silicon Valley Bank meltdown in March 2023 and concerns about the role of held-to-maturity portfolios. In particular, we apply our model to show the build-up of balance sheet vulnerabilities at Silicon Valley Bank before its default. More generally, the model may serve as a tool for analyzing which characteristics of the balance sheet are critical for banking system regulators to adequately assess run risk and resilience. Furthermore, we extend the model to include a tractable optimization problem which addresses the designation of held-to-maturity assets and provides a simple approach to quantifying banks' ability to hold those assets without resorting to remarking. To illustrate this framework, we calibrate the parameters to Silicon Valley Bank's balance sheet data and examine the bank's funding risk and implied risk tolerance in the years 2020--22 leading up to its collapse.

q-fin.RM↗

arXiv2024

Large Language Model in Financial Regulatory Interpretation

This study explores the innovative use of Large Language Models (LLMs) as analytical tools for interpreting complex financial regulations. The primary objective is to design effective prompts that guide LLMs in distilling verbose and intricate regulatory texts, such as the Basel III capital requirement regulations, into a concise mathematical framework that can be subsequently translated into actionable code. This novel approach aims to streamline the implementation of regulatory mandates within the financial reporting and risk management systems of global banking institutions. A case study was conducted to assess the performance of various LLMs, demonstrating that GPT-4 outperforms other models in processing and collecting necessary information, as well as executing mathematical calculations. The case study utilized numerical simulations with asset holdings -- including fixed income, equities, currency pairs, and commodities -- to demonstrate how LLMs can effectively implement the Basel III capital adequacy requirements. Keywords: Large Language Models, Prompt Engineering, LLMs in Finance, Basel III, Minimum Capital Requirements, LLM Ethics

q-fin.RM↗

arXiv2024

Statistical Validation of Contagion Centrality in Financial Networks

In this paper, we introduce an impact centrality measure to evaluate shock propagation on financial networks capturing a notion of contagion and systemic risk contributions, permitting comparisons of these risks over time. In addition, we provide a statistical validation method when the network is estimated from data, as is done in practice. This statistical test allows us to reliably assess the computed centrality values. We validate our methodology on simulated data and conduct empirical case studies using financial data. We find that our proposed centrality measure increases significantly during times of financial distress and is able to provide insights into the (market implied) risk-levels of different firms and sectors.

q-fin.MF↗

arXiv2023

Price-mediated contagion with endogenous market liquidity

Price-mediated contagion occurs when a positive feedback loop develops following a drop in asset prices which forces banks and other financial institutions to sell their holdings. Prior studies of such events fix the level of market liquidity without regards to the level of stress applied to the system. This paper introduces a framework to understand price-mediated contagion in a system where the capacity of the market to absorb liquidated assets is determined endogenously. In doing so, we construct a joint clearing system in interbank payments, asset prices, and market liquidity. We establish mild assumptions which guarantee the existence of greatest and least clearing solutions. We conclude with detailed numerical case studies which demonstrate the, potentially severe, repercussions of endogenizing the market liquidity on system risk.

q-fin.RM↗

arXiv2023

Approximating the set of Nash equilibria for convex games

In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To avoid dealing with a non-convex ordering cone, an equivalent characterization of the set of Nash equilibria as the intersection of the Pareto optimal points of $N$ multi-objective problems (i.e.\ with the natural ordering cone) is proven. So far, algorithms to compute the exact set of Pareto optimal points of a multi-objective problem exist only for the class of linear problems, which reduces the possibility of finding the true set of Nash equilibria by those algorithms to linear games only. In this paper, we will consider the larger class of convex games. As, typically, only approximate solutions can be computed for convex vector optimization problems, we first show, in total analogy to the result above, that the set of $\epsilon$-approximate Nash equilibria can be characterized by the intersection of $\epsilon$-approximate Pareto optimal points for $N$ convex multi-objective problems. Then, we propose an algorithm based on results from vector optimization and convex projections that allows for the computation of a set that, on one hand, contains the set of all true Nash equilibria, and is, on the other hand, contained in the set of $\epsilon$-approximate Nash equilibria. In addition to the joint convexity of the cost function for each player, this algorithm works provided the players are restricted by either shared polyhedral constraints or independent convex constraints.

math.OC↗

arXiv2023

Modeling Inverse Demand Function with Explainable Dual Neural Networks

Financial contagion has been widely recognized as a fundamental risk to the financial system. Particularly potent is price-mediated contagion, wherein forced liquidations by firms depress asset prices and propagate financial stress, enabling crises to proliferate across a broad spectrum of seemingly unrelated entities. Price impacts are currently modeled via exogenous inverse demand functions. However, in real-world scenarios, only the initial shocks and the final equilibrium asset prices are typically observable, leaving actual asset liquidations largely obscured. This missing data presents significant limitations to calibrating the existing models. To address these challenges, we introduce a novel dual neural network structure that operates in two sequential stages: the first neural network maps initial shocks to predicted asset liquidations, and the second network utilizes these liquidations to derive resultant equilibrium prices. This data-driven approach can capture both linear and non-linear forms without pre-specifying an analytical structure; furthermore, it functions effectively even in the absence of observable liquidation data. Experiments with simulated datasets demonstrate that our model can accurately predict equilibrium asset prices based solely on initial shocks, while revealing a strong alignment between predicted and true liquidations. Our explainable framework contributes to the understanding and modeling of price-mediated contagion and provides valuable insights for financial authorities to construct effective stress tests and regulatory policies.

q-fin.CP↗

arXiv2023

Decentralized Prediction Markets and Sports Books

Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function.

q-fin.MF↗

arXiv2023

Stochastic Cell Transmission Models of Traffic Networks

We introduce a rigorous framework for stochastic cell transmission models for general traffic networks. The performance of traffic systems is evaluated based on preference functionals and acceptable designs. The numerical implementation combines simulation, Gaussian process regression, and a stochastic exploration procedure. The approach is illustrated in two case studies.

cs.LG↗