(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.Comment: To be published in Cryptoeconomic Systems 202

Optimal Intervention in Economic Networks using Influence Maximization Methods

We consider optimal intervention in the Elliott-Golub-Jackson network model and show that it can be transformed into an influence maximization problem, 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 additionally hard to approximate 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

While Stability Lasts: A Stochastic Model of Stablecoins

The `Black Thursday' crisis in cryptocurrency markets demonstrated deleveraging risks in over-collateralized lending and stablecoins. We develop a stochastic model of over-collateralized stablecoins that helps explain such crises. 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 stable and unstable domains for the stablecoin. We prove bounds on the probabilities of large deviations and quadratic variation in the stable domain and distinctly greater price variance in the unstable domain. The unstable domain can be triggered by large deviations, collapsed expectations, and liquidity problems from deleveraging. We formally characterize a deflationary deleveraging spiral as a submartingale that can cause such liquidity problems in a crisis. We also demonstrate `perfect' stability results in idealized settings and discuss mechanisms which could bring realistic settings closer to the idealized stable settings

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 liquidity pools and 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 a noisy trustless data source such as this can be helpful toward minimizing trust requirements of oracle designs

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

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

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