Default Probability

Default Probability is expressed as a percentage or basis points (bps), providing a standardized, numerical measure of credit risk. It moves beyond binary 'safe/unsafe' assessments to a probabilistic framework, enabling precise risk-adjusted decision-making for lenders and protocol designers.

Unlike traditional finance where ratings are updated periodically, on-chain default probability is often calculated in real-time using live blockchain data. It reacts dynamically to changes in:

• Collateralization Ratio: The primary driver of risk in overcollateralized lending.
• Asset Volatility: Increased price swings raise the probability of a position becoming undercollateralized.
• Liquidity Depth: The ease of liquidating a position affects potential loss given default.

Default Probability is not a raw observation but the output of a risk model. Common model inputs include:

• On-Chain Data: Loan-to-Value (LTV), health factor, wallet transaction history.
• Market Data: Asset price volatility, trading volume, and liquidity.
• Protocol Parameters: Liquidation thresholds, auction mechanisms, and stability fee rates. Models range from simple heuristic rules to complex statistical or machine learning approaches.

In DeFi, default probability is a key variable for smart contract automation. It directly triggers protocol actions without human intervention:

• Automatic Liquidations: When probability nears 100%, liquidation bots are incentivized to close the position.
• Dynamic Interest Rates: Protocols like Aave adjust borrowing rates based on pool utilization and perceived risk.
• Credit Limit Adjustments: Protocols may lower the maximum LTV for an asset class if its aggregate default risk increases.

Accurate default probability assessment allows for optimized capital allocation. Lenders can demand a risk premium (higher interest) for riskier loans, aligning returns with risk taken. Protocols use it to set risk-adjusted capital requirements, determining how much collateral is needed to back a unit of debt, which is fundamental to capital efficiency in lending markets.

Default Probability (PD) is one component of Expected Loss (EL). The full calculation is: EL = PD × LGD × EAD.

• Loss Given Default (LGD): The percentage of exposure lost if default occurs, influenced by collateral value and liquidation efficiency.
• Exposure at Default (EAD): The total value owed at the time of default. Understanding PD in isolation is insufficient; it must be analyzed alongside LGD to gauge total risk.

Based on the Black-Scholes-Merton option pricing framework, this model treats a company's equity as a call option on its assets. Default occurs when asset value falls below a debt threshold. In DeFi, this is adapted to assess protocol solvency by modeling protocol Total Value Locked (TVL) as assets and outstanding debt positions as liabilities.

• Key Inputs: Asset volatility, debt level, risk-free rate.
• Output: Distance-to-default, converted to a probability.
• DeFi Adaptation: Uses on-chain metrics like collateralization ratios and asset price volatility from oracles.

These models directly model the default intensity or hazard rate—the instantaneous likelihood of default—using observable market data, without explaining the firm's internal capital structure. They are commonly used for pricing credit derivatives.

• Key Inputs: Market prices of bonds, credit default swaps (CDS), or, in DeFi, insurance premium rates.
• Process: Default is treated as an unpredictable event with a time-varying probability.
• Advantage: More flexible for fitting market-implied credit spreads observed in protocols like Maple Finance or Clearpool.

Leverages historical on-chain data to predict default risk. Models are trained on features like:

• Wallet Behavior: Transaction frequency, diversification, and liquidation history.
• Protocol Health: Collateral volatility, liquidity depth, and governance activity.
• Position Metrics: Loan-to-Value (LTV) ratios, health factors, and time since last top-up.

Algorithms (e.g., gradient boosting, neural networks) identify complex, non-linear patterns not captured by traditional models, providing dynamic, real-time risk scores for addresses or pools.

A discrete classification approach that assigns points to various risk factors, which are summed to create a score correlated with default probability. Common in traditional consumer credit (FICO scores) and adapted for DeFi.

• DeFi Factors: May include collateral type score, wallet age, repayment history, and exposure concentration.
• Process: Each factor is weighted based on historical default analysis.
• Output: A simple, interpretable score (e.g., 1-1000) or a risk band (e.g., AA, B, C). Used by underwriting platforms for permissioned pools.

Derives default probability directly from the trading prices of credit instruments. The core formula translates a Credit Default Swap (CDS) spread into a risk-neutral probability:

Default Probability ≈ Spread / (1 - Recovery Rate)

• In TradFi: The CDS spread is a premium paid for default protection.
• In DeFi Analog: Platforms like Arbitrum's Sentry or insurance protocols (Nexus Mutual, UnoRe) create synthetic credit markets. Their premium rates for covering smart contract or slashing risk serve as a proxy for market-implied default probability.

Uses historical default and loss data from analogous entities or past market cycles to estimate future probabilities. This frequentist approach calculates probability as:

Default Probability = (Number of Defaults) / (Total Number of Obligors)

• Application: Used to calibrate other models or for new asset classes with limited data.
• DeFi Use Case: Analyzing historical liquidation rates for specific collateral types (e.g., stETH or GMX) on lending protocols like Aave or Compound to infer future stress probabilities.
• Limitation: Assumes the future will resemble the past, a challenge in rapidly evolving crypto markets.

Loss Given Default (LGD) is the amount of capital a lender loses when a borrower defaults, expressed as a percentage of the total exposure. It is calculated as 1 - Recovery Rate. LGD depends on the collateral value, liquidation process efficiency, and market conditions. Default Probability (PD) and LGD are combined to calculate Expected Loss (EL = PD x LGD x Exposure). In overcollateralized DeFi loans, LGD can be low if liquidations are timely, but can spike during market volatility or liquidity crunches.

Credit Scoring is the process of assessing a borrower's creditworthiness, typically resulting in a numerical score (e.g., FICO). It uses historical data to predict future repayment behavior. In DeFi, on-chain credit scoring is an emerging field that analyzes wallet transaction history, reputation, collateral diversity, and protocol interactions to estimate default probability. Unlike traditional scores, these aim to be permissionless and transparent, using public blockchain data.

Counterparty Risk is the probability that one party in a financial contract will fail to fulfill its obligations. It is a broader concept than default probability, encompassing settlement failures and operational issues. In decentralized finance, smart contract risk and oracle failure are significant counterparty risks alongside borrower default. Assessing default probability is a direct method to quantify the borrower-specific component of overall counterparty risk in lending agreements.

Expected Loss (EL) is the anticipated average loss on a loan or portfolio over a specific period. It is the fundamental equation of credit risk: EL = Probability of Default (PD) x Loss Given Default (LGD) x Exposure at Default (EAD). EL is used for provisioning capital and pricing loans. A protocol's risk parameters (like collateral factors and liquidation bonuses) are directly tuned to manage the EL by influencing both the PD (via health thresholds) and the LGD (via liquidation incentives).