Authors:
(1) Zhenbang Feng, Department of Electrical and Computer Engineering, Viterbi School of Engineering, University of Southern, California Los Angeles, CA, USA (jasonfen@usc.edu);
(2) Hardhik Mohanty, Department of Electrical and Computer Engineering, Viterbi School of Engineering, University of Southern, California Los Angeles, CA, USA (hmohanty@usc.edu);
(3) Bhaskar Krishnamachari, Department of Electrical and Computer Engineering, Viterbi School of Engineering, University of Southern, California Los Angeles, CA, USA (bkrishna@usc.edu). Authors: Authors: (1) Zhenbang Feng, Department of Electrical and Computer Engineering, Viterbi School of Engineering, University of Southern, California Los Angeles, CA, USA (jasonfen@usc.edu); (2) Hardhik Mohanty, Department of Electrical and Computer Engineering, Viterbi School of Engineering, University of Southern, California Los Angeles, CA, USA (hmohanty@usc.edu); (3) Bhaskar Krishnamachari, Department of Electrical and Computer Engineering, Viterbi School of Engineering, University of Southern, California Los Angeles, CA, USA (bkrishna@usc.edu). Editor’s note: This article is part of a broader study. You’re reading part 1 of 5. Read the rest below. Editor’s note: This article is part of a broader study. You’re reading part 1 of 5. Read the rest below. Editor’s note: This article is part of a broader study. You’re reading part 1 of 5. Read the rest below. Table of Links Abstract and I. Introduction
II. The Mechanism
III. Price-Stabilizing Mechanisms, IV. Simulating DAI & V. Simplified Mathematical Model for DAI
VI. How Collateral Price Impacts Derivative Price
VII. Risk Factors for Stable Derivatives & VIII. Conclusions and References Abstract and I. Introduction Abstract and I. Introduction II. The Mechanism II. The Mechanism III. Price-Stabilizing Mechanisms, IV. Simulating DAI & V. Simplified Mathematical Model for DAI III. Price-Stabilizing Mechanisms, IV. Simulating DAI & V. Simplified Mathematical Model for DAI VI. How Collateral Price Impacts Derivative Price VI. How Collateral Price Impacts Derivative Price VII. Risk Factors for Stable Derivatives & VIII. Conclusions and References VII. Risk Factors for Stable Derivatives & VIII. Conclusions and References Abstract In decentralized finance (DeFi), stablecoins like DAI are designed to offer a stable value amidst the fluctuating nature of cryptocurrencies. We examine the class of crypto-backed stable derivatives, with a focus on mechanisms for price stabilization, which is exemplified by the well-known stablecoin DAI from MakerDAO. For simplicity, we focus on a single-collateral setting. We introduce a belief parameter to the simulation model of DAI in a previous work (DAISIM), reflecting market sentiments about the value and stability of DAI, and show that it better matches the expected behavior when this parameter is set to a sufficiently high value. We also propose a simple mathematical model of DAI price to explain its stability and dependency on ETH price. Finally, we analyze possible risk factors associated with these stable derivatives to provide valuable insights for stakeholders in the DeFi ecosystem. I. INTRODUCTION In the modern decentralized finance (DeFi) ecosystem, stablecoins have emerged to counter the volatility inherent to cryptocurrencies like Bitcoin or Ethereum [1]. Pegged to stable reserves such as fiat currencies, precious metals, or a diversified portfolio of assets, stablecoins try to maintain a consistent value. These stable derivatives are mechanisms for hedging risks, speculating on future price movements, and improving capital efficiency [2]. The stability of these tokens is maintained using a range of strategies, such as backing by fiat currencies, crypto-assets, or the use of algorithmic techniques that drop the need for conventional asset collateral. Such innovations in stabilization techniques highlight the versatility and adaptability of stablecoins in the digital age, reflecting a significant step forward in the quest for stability in the dynamic landscape of DeFi. Among the plethora of stablecoins, DAI from MakerDAO stands out as a flagship stable derivative designed to maintain a steady value relative to $1 (USD). Initially released as a single-collateral derivative known as SAI, it has evolved into a more sophisticated multi-collateral format to enhance stability and resilience. Expanding upon this secure foundation, the transition from SAI to DAI brought about the capacity to accept multiple types of cryptocurrency as collateral, not just Ethereum (ETH). This diversification of backing assets significantly enhances the stability of DAI. The MakerDAO protocol allows users to mint SAI by creating collateralized debt positions (CDPs), which are essential components of the system [3]. In these smart contract driven constructs, users must deposit ETH as collateral, over-collateralizing to accommodate for volatility in order to produce SAI and maintain its peg to $1. Once minted, DAI serves as a versatile tool, functioning as a medium of exchange, a store of value, and a unit of account. The protocol also provides users an opportunity to earn interest on their DAI holdings through the DAI Savings Rate. DAI’s transparent and decentralized governance exercised by MKR token holders ensures that it remains stable. MKR token holders cast votes on vital protocol decisions, such as which assets qualify as collateral and the risk parameters for these assets. Furthermore, the transparent recording of every transaction, voting on the blockchain, and DAI’s adoption in over 400 different apps and services spanning wallets, DeFi platforms, and games reinforce its position as a reliable and integral component of the modern cryptocurrency landscape. Research on stablecoins is still emerging, with a few key studies paving the way for our investigation. Lyons et al. [4] provided a foundational understanding of the functional efficiency of stablecoins by scrutinizing the mechanisms through which they maintain their peg in the digital economy. Building on this, Mita et al. [5] categorized the stablecoins based on the nature of their collateral and analyzed them through the lens of traditional economic models such as Hayek money and Tobin tax. Furthermore, Mundt et al. [6] delved into noncustodial stablecoins, revealing how liquidation protocols and investor behavior shape their stability, particularly in tumultuous market conditions. Complementing these theoretical perspectives, Gudgeon et al. [7] critically assessed the security of governance in platforms like MakerDAO, a key aspect of stablecoin infrastructure. On a more practical note, Kothari et al. [8] utilized simulations to offer insight into the demand dynamics for asset-backed stablecoins amidst external price shocks, a crucial factor for understanding market resilience. Finally, Clark et al. [9] provided a broad survey that contextualizes the stablecoin landscape, setting the context for more detailed analysis. Drawing from these insights, our work aims to add to the understanding of DAI within DeFi, especially how it maintains its value in various economic conditions. Synthetix and Mirror Protocol represent pivotal advancements in blockchain-based synthetic derivatives, both drawing on mechanisms similar to the DAI stablecoin from MakerDAO for maintaining price stability. Synthetix [10] allows users to create synthetic assets known as Synths, which track the value of real-world assets like fiat currencies, cryptocurrencies, and cryptocurrency indexes, and commodities such as gold and silver. The primary mechanism for minting Synths in Synthetix involves over-collateralization with the native cryptocurrency of the platform, SNX. The minted Synths are backed by a 600% collateralization ratio determined by community governance. Synthetix uses a combination of staking rewards and exchange fees to incentivize users to maintain the peg of Synths. The platform relies on decentralized oracles to provide accurate and real-time price feeds of the underlying assets. Mirror Protocol [11] operates on the Terra blockchain and enables the creation of synthetic assets called Mirrored Assets (mAssets). These crypto tokens are utilized to track the price of real-world assets such as stocks. Mirror Protocol primarily uses Terra stablecoins like UST to mint mAssests with 150% over-collateralization. The value of mAssets is maintained through a combination of minting liquidations, arbitrage, and governance. Mirror also relies on decentralized price oracles to provide real-time data on the prices of the underlying real-world assets. Both platforms exemplify the synergy between cryptocurrency innovation and traditional financial stability, mirroring DAI’s approach of using over-collateralization and real-time data to maintain a stable asset value. This paper sets out to enhance the simulation models for DAI stablecoin, particularly focusing on the associated risk factors and the efficacy of its price stabilization mechanisms. Utilizing empirical data and employing a variety of modeling methods, we plan to delve into the complex factors that influence the value of the DAI peg. Building on previous work, DAISIM [12], we consider the impact of beliefs and narratives, which appear to play a significant role in DAI’s valuation alongside the more technical aspects of its protocol. Our analysis aims to shed light on the nuanced interaction between market behavior and the design of the protocol that together maintains DAI’s stability. In particular, our contributions can be listed as follows: • We introduce a belief parameter that captures market sentiment about DAI’s valuation and stability in the modeling of the DAI stablecoin used in DAISIM. We show that setting this parameter to a sufficiently high value results in the DAI converging to a value close to $1 (USD). • We present a mathematical model that captures the stability mechanism of DAI in relation to ETH price fluctuations. This model offers a quantitative understanding of the influence of ETH price on the behavior of DAI stablecoin under different market conditions. • We provide a risk analysis for stable derivatives. This includes examining the impacts of various factors, such as oracle reliability, debt ceiling, and smart contract vulnerabilities, on the stability and operation of these stablecoins. The remainder of this paper is organized as follows: Section II offers a detailed analysis of the DAI mechanism, its structure, user interaction, and the role of price oracles. Section III discusses the mechanisms for price stabilization of DAI. Section IV introduces DAISIM and our revised objective function. Section V presents the simplified theoretical foundation of this model. Section VI explores the relationship between collateral price and derivative price using empirical data and simulations. Section VII examines various risk factors in stable derivatives. The paper concludes with Section VIII summarizing our findings and insights. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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