[Paper Review] Understand Volatility of Algorithmic Stablecoin: Modeling, Verification and Empirical Analysis

Wenqi Zhao, Hui Li+1 more|arXiv (Cornell University)|Jan 21, 2021

Blockchain Technology Applications and Security17 references4 citations

TL;DR

This paper develops a formal modeling and verification framework to analyze the volatility of algorithmic stablecoins, applying it to Basis Cash using real Ethereum transaction data. It identifies that design flaws—particularly broken expansion and contraction mechanisms—lead to volatility in practice, with empirical evidence showing price surges during failed expansions and prolonged de-pegging during ineffective contractions.

ABSTRACT

An algorithmic stablecoin is a type of cryptocurrency managed by algorithms (i.e., smart contracts) to dynamically minimize the volatility of its price relative to a specific form of asset, e.g., US dollar. As algorithmic stablecoins have been growing rapidly in recent years, they become much more volatile than expected. In this paper, we took a deep dive into the core of algorithmic stablecoins and shared our answer to two fundamental research questions, i.e., Are algorithmic stablecoins volatile by design? Are they volatile in practice? Specifically, we introduced an in-depth study on three popular types of algorithmic stablecoins and developed a modeling framework to formalize their key design protocols. Through formal verification, the framework can identify critical conditions under which stablecoins might become volatile. Furthermore, we performed a systematic empirical analysis on real transaction activities of the Basis Cash stablecoin to relate theoretical possibilities to market observations. Lastly, we highlighted key design decisions for future development of algorithmic stablecoins.

Motivation & Objective

• To investigate whether algorithmic stablecoins are inherently volatile by design, focusing on structural mechanisms that may undermine price stability.
• To assess whether such volatility manifests in real-world market behavior, particularly in high-impact events like rapid price swings.
• To bridge theoretical modeling with empirical data by analyzing actual transaction patterns on Ethereum for Basis Cash during late 2020 to early 2021.
• To identify critical failure points in algorithmic supply adjustment mechanisms—expansion and contraction—that lead to instability.
• To inform future stablecoin design by highlighting key parameters such as intervention frequency, participation incentives, and ecosystem integration.

Proposed method

• Developed a formal modeling framework based on state transition systems to represent the core protocols of three algorithmic stablecoin types: rebase-style, seigniorage share, and partial-collateral.
• Applied formal verification techniques to detect conditions under which stablecoin mechanisms fail to maintain price pegs, particularly focusing on expansion and contraction validity.
• Used Dune Analytics to extract real transaction data from Ethereum, including BAC minting, burning, and yield-farming activity for Basis Cash.
• Mapped theoretical model states (e.g., DEX in Buy/Sell mode) to real market behavior to validate whether predicted volatility conditions occurred.
• Correlated spikes in demand and low participation in contraction with observed price deviations from the $1 peg.
• Conducted a systematic empirical analysis comparing theoretical failure modes with actual market events between December 2020 and January 2021.

Experimental results

Research questions

• RQ1 Are algorithmic stablecoins volatile by design due to inherent structural flaws in their supply adjustment mechanisms?
• RQ2 Do theoretical instability conditions—such as failed expansion or contraction—actually manifest in real market data?
• RQ3 What are the key market behaviors that trigger or prevent successful stabilization during expansion and contraction phases?
• RQ4 How do external incentives like yield-farming affect the stability of algorithmic stablecoins during expansion?
• RQ5 What design parameters most significantly influence the success or failure of algorithmic price stabilization?

Key findings

• The formal verification framework identified that broken expansion and contraction mechanisms—where DEX remains in Buy or Sell state despite intended actions—can lead to volatility.
• Empirical data confirmed that during expansion on December 14–15, 2020, BAC’s price rose by 15.72% and 8.40% respectively, despite active minting, due to high demand from yield-farming incentives.
• On December 14, 2020, 92% of newly minted BAC entered yield-farming pools within two hours, indicating that speculative demand overwhelmed the expansion mechanism.
• During contraction from January 11, 2021 onward, BAC remained below peg despite repeated contraction entries, due to low participation in burning BAC for BAB.
• The number of burned BAC during this period was significantly lower than in earlier phases, indicating a lack of confidence in redemption mechanisms.
• The study concluded that contraction mechanisms are more critical than expansion for stability, as price declines are harder to reverse than price increases.