Detecting Depegs: Safer Passive Liquidity Provision on Curve Finance

Table of Contents

1 Introduction

This research provides evidence for how quantitative metrics and detection algorithms can be constructed to keep liquidity providers (LPs) informed in real-time about potential stablecoin and liquid staking derivative depegs. The study focuses on Curve Finance's StableSwap pools and develops a sophisticated detection system.

1.1 Background

Stablecoins and liquid staking derivatives are tokens pegged to underlying floating currencies. Stablecoins are generally pegged to the U.S. Dollar, while liquid staking derivatives are pegged to ETH or other network tokens. Organizations maintain redemption mechanisms, but if traders lose faith, prices can decline in secondary markets - a process called depegging.

2 Methodology

We construct a suite of metrics designed to detect potential asset depegs based on price and trading data from Curve Finance pools.

2.1 Depeg Detection Metrics

The detection system incorporates multiple metrics including price deviation, trading volume anomalies, liquidity pool imbalances, and historical volatility patterns. These metrics are combined to create a comprehensive risk assessment framework.

2.2 Bayesian Online Changepoint Detection

We fine-tune a Bayesian Online Changepoint Detection (BOCD) algorithm to alert LPs of potential depegs. The BOCD model processes streaming data and identifies structural breaks in time series data in real-time.

3 Experimental Results

The changepoint detection algorithm was trained and tested against Curve LP token prices for 13 StableSwap pools throughout 2022 and 2023.

3.1 USDC Depeg Detection

Our model, trained on 2022 UST data, successfully detected the USDC depeg in March 2023 at 9pm UTC on March 10th, approximately 5 hours before USDC dipped below 99 cents. This early detection provided significant warning to liquidity providers.

3.2 Performance Evaluation

The system demonstrated few false alarms during the 17-month testing period, showing robust performance across multiple depeg events including UST, USDC, and stETH depegs.

4 Technical Implementation

4.1 Mathematical Framework

The Bayesian Online Changepoint Detection algorithm is based on the following mathematical formulation:

The run length $r_t$ at time $t$ represents the time since the last changepoint. The probability of the run length is updated recursively:

$P(r_t | x_{1:t}) = \sum_{r_{t-1}} P(r_t | r_{t-1}) P(x_t | r_{t-1}, x_t^{(r)}) P(r_{t-1} | x_{1:t-1})$

Where $x_t^{(r)}$ represents the data since the last changepoint, and the hazard function $H(r_t)$ determines the probability of a changepoint:

$P(r_t | r_{t-1}) = \begin{cases} H(r_{t-1} + 1) & \text{if } r_t = 0 \\ 1 - H(r_{t-1} + 1) & \text{if } r_t = r_{t-1} + 1 \\ 0 & \text{otherwise} \end{cases}$

4.2 Code Implementation

class BayesianChangepointDetector:
    def __init__(self, hazard_function, observation_likelihood):
        self.hazard = hazard_function
        self.observation_likelihood = observation_likelihood
        self.run_length_posterior = [1.0]
        
    def update(self, new_observation):
        # Predict step
        predictive_probs = []
        for r in range(len(self.run_length_posterior)):
            prob = self.run_length_posterior[r] * (1 - self.hazard(r))
            predictive_probs.append(prob)
        
        # Changepoint probability
        changepoint_prob = sum([self.run_length_posterior[r] * 
                              self.hazard(r) for r in range(len(self.run_length_posterior))])
        predictive_probs.insert(0, changepoint_prob)
        
        # Update step
        updated_probs = []
        for r, prob in enumerate(predictive_probs):
            if r == 0:
                likelihood = self.observation_likelihood(new_observation)
            else:
                # Update sufficient statistics for run length r
                likelihood = self.observation_likelihood(new_observation, r)
            updated_probs.append(prob * likelihood)
        
        # Normalize
        total = sum(updated_probs)
        self.run_length_posterior = [p/total for p in updated_probs]
        
        return self.run_length_posterior[0]  # Return changepoint probability

5 Future Applications

This research can be extended to dynamically de-risk Curve pools by modifying parameters in anticipation of potential depegs. Future applications include:

• Real-time risk management APIs for DeFi protocols
• Dynamic pool parameter adjustment based on risk signals
• Cross-protocol depeg detection systems
• Insurance products for liquidity providers
• Regulatory monitoring tools for stablecoin issuers

6 Original Analysis

The research by Cintra and Holloway represents a significant advancement in real-time risk management for decentralized finance. Their application of Bayesian Online Changepoint Detection to stablecoin depeg scenarios demonstrates how sophisticated statistical methods can be adapted for blockchain financial markets. The methodology bears similarity to change point detection techniques used in traditional finance, such as those described in the seminal work by Adams and MacKay (2007) on Bayesian online changepoint detection, but adapted for the unique characteristics of automated market makers.

What makes this approach particularly innovative is its real-time capability and minimal false positive rate. Unlike traditional financial surveillance systems that might rely on simpler threshold-based alerts, the Bayesian framework incorporates uncertainty quantification and sequential updating. This aligns with modern machine learning approaches in anomaly detection, similar to techniques used in cybersecurity and network monitoring. The system's ability to detect the USDC depeg 5 hours in advance is remarkable, considering that most market participants were caught by surprise during the Silicon Valley Bank collapse.

The research builds upon established principles from both classical statistics and modern machine learning. The mathematical foundation draws from Bayesian inference methods similar to those used in Gaussian process regression and sequential Monte Carlo, as referenced in works like "Pattern Recognition and Machine Learning" by Bishop (2006). However, the application to DeFi liquidity provision represents a novel contribution. The system's performance across 13 different pools over 17 months with minimal false alarms suggests robust generalization capabilities.

Compared to other DeFi risk management approaches, such as the oracle-based price feeds used in lending protocols or the circuit breaker mechanisms in some centralized exchanges, this methodology offers a more proactive and nuanced approach. It doesn't just react to price movements but identifies structural changes in market behavior patterns. This could potentially be integrated with dynamic AMM parameter adjustment systems, similar to the work on programmable liquidity by Angeris et al. (2021) on improved price oracles, creating a comprehensive risk management framework for decentralized exchanges.

The practical implementation as an API for liquidity providers demonstrates the immediate applicability of the research. This bridges the gap between academic methodology and real-world utility, addressing a critical need in the rapidly evolving DeFi ecosystem. As stablecoin markets continue to grow and face regulatory scrutiny, such detection systems will become increasingly valuable for both participants and regulators.

7 References

1. Adams, R.P., & MacKay, D.J.C. (2007). Bayesian Online Changepoint Detection. University of Cambridge.
2. Bishop, C.M. (2006). Pattern Recognition and Machine Learning. Springer.
3. Angeris, G., et al. (2021). Improved Price Oracles: Constant Function Market Makers. Proceedings of the ACM on Measurement and Analysis of Computing Systems.
4. Bolger, M., & Hon, H. (2022). When the Currency Breaks. Llama Risk Research.
5. Egorov, M. (2019). StableSwap - efficient mechanism for Stablecoin liquidity. Curve Finance Whitepaper.
6. Goodfellow, I., et al. (2016). Deep Learning. MIT Press.