arXiv subjects

Ariah Klages-Mundt

Publications and source records attributed to Ariah Klages-Mundt.

13 recordsLinked to original sources

arXiv2023

Oracle Counterpoint: Relationships between On-chain and Off-chain Market Data

We investigate the theoretical and empirical relationships between activity in on-chain markets and pricing in off-chain cryptocurrency markets (e.g., ETH/USD prices). The motivation is to develop methods for proxying off-chain market data using data and computation that is in principle verifiable on-chain and could provide an alternative approach to blockchain price oracles. We explore relationships in PoW mining, PoS validation, block space markets, network decentralization, usage and monetary velocity, and on-chain Automated Market Makers (AMMs). We select key features from these markets, which we analyze through graphical models, mutual information, and ensemble machine learning models to explore the degree to which off-chain pricing information can be recovered entirely on-chain. We find that a large amount of pricing information is contained in on-chain data, but that it is generally hard to recover precise prices except on short time scales of retraining the model. We discuss how even noisy information recovered from on-chain data could help to detect anomalies in oracle-reported prices on-chain.

cs.CR↗

arXiv2023

What Drives the (In)stability of a Stablecoin?

In May 2022, an apparent speculative attack, followed by market panic, led to the precipitous downfall of UST, one of the most popular stablecoins at that time. However, UST is not the only stablecoin to have been depegged in the past. Designing resilient and long-term stable coins, therefore, appears to present a hard challenge. To further scrutinize existing stablecoin designs and ultimately lead to more robust systems, we need to understand where volatility emerges. Our work provides a game-theoretical model aiming to help identify why stablecoins suffer from a depeg. This game-theoretical model reveals that stablecoins have different price equilibria depending on the coin's architecture and mechanism to minimize volatility. Moreover, our theory is supported by extensive empirical data, spanning $1$ year. To that end, we collect daily prices for 22 stablecoins and on-chain data from five blockchains including the Ethereum and the Terra blockchain.

cs.GT↗

arXiv2023

Optimal Intervention in Economic Networks using Influence Maximization Methods

We consider optimal intervention in the Elliott-Golub-Jackson network model \cite{jackson14} and we show that it can be transformed into an influence maximization-like form, interpreted as the reverse of a default cascade. Our analysis of the optimal intervention problem extends well-established targeting results to the economic network setting, which requires additional theoretical steps. We prove several results about optimal intervention: it is NP-hard and cannot be approximated to a constant factor in polynomial time. In turn, we show that randomizing failure thresholds leads to a version of the problem which is monotone submodular, for which existing powerful approximations in polynomial time can be applied. In addition to optimal intervention, we also show practical consequences of our analysis to other economic network problems: (1) it is computationally hard to calculate expected values in the economic network, and (2) influence maximization algorithms can enable efficient importance sampling and stress testing of large failure scenarios. We illustrate our results on a network of firms connected through input-output linkages inferred from the World Input Output Database.

cs.GT↗

arXiv2022

Designing Autonomous Markets for Stablecoin Monetary Policy

We develop a new type of automated market maker (AMM) that helps to maintain stability and long-term viability in a stablecoin. This primary market AMM (P-AMM) is an autonomous mechanism for pricing minting and redemption of stablecoins in all possible states and is designed to achieve several desirable properties. We first cover several case studies of current ad hoc stablecoin issuance and redemption mechanisms, several of which have contributed to recent stablecoin de-peggings, and formulate desirable properties of a P-AMM that support stability and usability. We then design a P-AMM redemption curve and show that it satisfies these properties, including bounded loss for both the protocol and stablecoin holders. We further show that this redemption curve is path independent and has properties of path deficiency in extended settings involving trading fees and a separate minting curve. This means that system health weakly improves relative to the path independent setting along any trading curve and that there is no incentive to strategically subdivide redemptions. Finally, we show how to implement the P-AMM efficiently on-chain.

cs.CR↗

arXiv2022

SoK: Decentralized Finance (DeFi)

Decentralized Finance (DeFi), a blockchain powered peer-to-peer financial system, is mushrooming. Two years ago the total value locked in DeFi systems was approximately 700m USD, now, as of April 2022, it stands at around 150bn USD. The frenetic evolution of the ecosystem has created challenges in understanding the basic principles of these systems and their security risks. In this Systematization of Knowledge (SoK) we delineate the DeFi ecosystem along the following axes: its primitives, its operational protocol types and its security. We provide a distinction between technical security, which has a healthy literature, and economic security, which is largely unexplored, connecting the latter with new models and thereby synthesizing insights from computer science, economics and finance. Finally, we outline the open research challenges in the ecosystem across these security types.

cs.CR↗

arXiv2022

While Stability Lasts: A Stochastic Model of Non-Custodial Stablecoins

The `Black Thursday' crisis in cryptocurrency markets demonstrated deleveraging risks in over-collateralized non-custodial stablecoins. We develop a stochastic model that helps explain deleveraging crises in these over-collateralized systems. In our model, the stablecoin supply is decided by speculators who optimize the profitability of a leveraged position while incorporating the forward-looking cost of collateral liquidations, which involves the endogenous price of the stablecoin. We formally characterize regimes that are interpreted as stable and unstable for the stablecoin. We prove bounds on quadratic variation and the probability of large deviations in the stable domain and we demonstrate distinctly greater price variance in the unstable domain. We identify a deflationary deleveraging spiral by means of a submartingale. These deleveraging spirals, which resemble short squeezes, lead to faster collateral drawdown (and potential shortfalls) and are accompanied by higher price variance, as experienced on Black Thursday. We conclude by discussing non-custodial ways in which the issues raised in this paper can be mitigated.

q-fin.TR↗

arXiv2022

Decentralized Governance of Stablecoins with Closed Form Valuation

We model incentive security in non-custodial stablecoins and derive conditions for participation in a stablecoin system across risk absorbers (vaults/CDPs) and holders of governance tokens. We apply option pricing theory to derive closed form solutions to the stakeholders' problems, and to value their positions within the capital structure of the stablecoin. We derive the optimal interest rate that is incentive compatible, as well as conditions for the existence of equilibria without governance attacks, and discuss implications for designing secure protocols.

econ.GN↗

arXiv2021

(In)Stability for the Blockchain: Deleveraging Spirals and Stablecoin Attacks

We develop a model of stable assets, including non-custodial stablecoins backed by cryptocurrencies. Such stablecoins are popular methods for bootstrapping price stability within public blockchain settings. We derive fundamental results about dynamics and liquidity in stablecoin markets, demonstrate that these markets face deleveraging feedback effects that cause illiquidity during crises and exacerbate collateral drawdown, and characterize stable dynamics of the system under particular conditions. The possibility of such `deleveraging spirals' was first predicted in the initial release of our paper in 2019 and later directly observed during the `Black Thursday' crisis in Dai in 2020. From these insights, we suggest design improvements that aim to improve long-term stability. We also introduce new attacks that exploit arbitrage-like opportunities around stablecoin liquidations. Using our model, we demonstrate that these can be profitable. These attacks may induce volatility in the `stable' asset and cause perverse incentives for miners, posing risks to blockchain consensus. A variant of such attacks also later occurred during Black Thursday, taking the form of mempool manipulation to clear Dai liquidation auctions at near zero prices, costing $8m.

q-fin.TR↗

arXiv2020

BDoS: Blockchain Denial of Service

Proof-of-work (PoW) cryptocurrency blockchains like Bitcoin secure vast amounts of money. Their operators, called miners, expend resources to generate blocks and receive monetary rewards for their effort. Blockchains are, in principle, attractive targets for Denial-of-Service (DoS) attacks: There is fierce competition among coins, as well as potential gains from short selling. Classical DoS attacks, however, typically target a few servers and cannot scale to systems with many nodes. There have been no successful DoS attacks to date against prominent cryptocurrencies. We present Blockchain DoS (BDoS), the first incentive-based DoS attack that targets PoW cryptocurrencies. Unlike classical DoS, BDoS targets the system's mechanism design: It exploits the reward mechanism to discourage miner participation. Previous DoS attacks against PoW blockchains require an adversary's mining power to match that of all other miners. In contrast, BDoS can cause a blockchain to grind to a halt with significantly fewer resources, e.g., 21% as of March 2020 in Bitcoin, according to our empirical study. We find that Bitcoin's vulnerability to BDoS increases rapidly as the mining industry matures and profitability drops. BDoS differs from known attacks like Selfish Mining in its aim not to increase an adversary's revenue, but to disrupt the system. Although it bears some algorithmic similarity to those attacks, it introduces a new adversarial model, goals, algorithm, and game-theoretic analysis. Beyond its direct implications for operational blockchains, BDoS introduces the novel idea that an adversary can manipulate miners' incentives by proving the existence of blocks without actually publishing them.

cs.CR↗

arXiv2020

Stablecoins 2.0: Economic Foundations and Risk-based Models

Stablecoins are one of the most widely capitalized type of cryptocurrency. However, their risks vary significantly according to their design and are often poorly understood. We seek to provide a sound foundation for stablecoin theory, with a risk-based functional characterization of the economic structure of stablecoins. First, we match existing economic models to the disparate set of custodial systems. Next, we characterize the unique risks that emerge in non-custodial stablecoins and develop a model framework that unifies existing models from economics and computer science. We further discuss how this modeling framework is applicable to a wide array of cryptoeconomic systems, including cross-chain protocols, collateralized lending, and decentralized exchanges. These unique risks yield unanswered research questions that will form the crux of research in decentralized finance going forward.

econ.GN↗

arXiv2020

Cascading Losses in Reinsurance Networks

We develop a model for contagion in reinsurance networks by which primary insurers' losses are spread through the network. Our model handles general reinsurance contracts, such as typical excess of loss contracts. We show that simpler models existing in the literature--namely proportional reinsurance--greatly underestimate contagion risk. We characterize the fixed points of our model and develop efficient algorithms to compute contagion with guarantees on convergence and speed under conditions on network structure. We characterize exotic cases of problematic graph structure and nonlinearities, which cause network effects to dominate the overall payments in the system. We lastly apply our model to data on real world reinsurance networks. Our simulations demonstrate the following: (1) Reinsurance networks face extreme sensitivity to parameters. A firm can be wildly uncertain about its losses even under small network uncertainty. (2) Our sensitivity results reveal a new incentive for firms to cooperate to prevent fraud, as even small cases of fraud can have outsized effect on the losses across the network. (3) Nonlinearities from excess of loss contracts obfuscate risks and can cause excess costs in a real world system.

q-fin.RM↗

arXiv2014

A table of elliptic curves over the cubic field of discriminant -23

Let F be the cubic field of discriminant -23 and O its ring of integers. Let Gamma be the arithmetic group GL_2 (O), and for any ideal n subset O let Gamma_0 (n) be the congruence subgroup of level n. In a previous paper, two of us (PG and DY) computed the cohomology of various Gamma_0 (n), along with the action of the Hecke operators. The goal of that paper was to test the modularity of elliptic curves over F. In the present paper, we complement and extend this prior work in two ways. First, we tabulate more elliptic curves than were found in our prior work by using various heuristics ("old and new" cohomology classes, dimensions of Eisenstein subspaces) to predict the existence of elliptic curves of various conductors, and then by using more sophisticated search techniques (for instance, torsion subgroups, twisting, and the Cremona-Lingham algorithm) to find them. We then compute further invariants of these curves, such as their rank and representatives of all isogeny classes. Our enumeration includes conjecturally the first elliptic curves of ranks 1 and 2 over this field, which occur at levels of norm 719 and 9173 respectively.

math.NT↗

arXiv2012

A Database of Elliptic Curves over Q(sqrt(5)) - First Report

We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms of weight (2,2) over Q(sqrt(5)), and via a variety of methods we constructed corresponding elliptic curves, including (again, conjecturally) all elliptic curves over Q(sqrt(5)) that have conductor with norm less than or equal to 1831.

math.NT↗