Risk Assessment and Price Prediction in DeFi Lending Protocol

Context

In a DeFi lending protocol, users can deposit their cryptocurrencies to earn interest or borrow against their deposits.
To maintain the system’s stability and minimize risks, it’s crucial to predict the future prices of the deposited assets and assess
the risk of potential defaults.

Application of Statistical Knowledge

Time Series Analysis:

• Objective: Forecast the future prices of cryptocurrencies deposited in the protocol.
• Method: Use ARIMA (AutoRegressive Integrated Moving Average) models to analyze historical price data of the assets. This involves:
  • Autoregression (AR): Modeling the asset’s price based on its own previous prices.
  • Integration (I): Differencing the data to make it stationary.
  • Moving Average (MA): Modeling the price based on past forecast errors.

Example: (in python)

        from statsmodels.tsa.arima.model import ARIMA

        # Historical price data of an asset
        prices = [100, 101, 102, 99, 98, 100, 105, 110]

        # Fit an ARIMA model
        model = ARIMA(prices, order=(5, 1, 0))  # ARIMA(5,1,0) for example
        fitted_model = model.fit()

        # Forecast future prices
        forecast = fitted_model.forecast(steps=5)
        print(forecast)

Result:

[111.34947962 109.87730409 107.19799682 107.3496682  110.34564499]

Probability Theory:

• – Objective: Estimate the probability of default (PD) for borrowers.
• – Method: Use logistic regression to model the likelihood of default based on borrower characteristics and market conditions.

Example: (in python)

        from sklearn.linear_model import LogisticRegression
        import numpy as np

        # Example data: [Credit Score, Collateral Ratio]
        X = np.array([[700, 0.8], [650, 0.6], [800, 0.9], [600, 0.5]])
        # Labels: 1 indicates default, 0 indicates no default
        y = np.array([0, 1, 0, 1])

        # Fit a logistic regression model
        model = LogisticRegression()
        model.fit(X, y)

        # Predict the probability of default for a new borrower
        new_borrower = np.array([[720, 0.75]])
        pd = model.predict_proba(new_borrower)
        print(pd)

Result:

[[9.99943485e-01 5.65154001e-05]]

Modern Machine Learning Algorithms:

• Objective: Enhance the accuracy of both price predictions and risk assessments.
• Method: Implement a Gradient Boosting Machine (GBM) for price prediction and risk assessment.

import numpy as np
from sklearn.ensemble import GradientBoostingRegressor, GradientBoostingClassifier

# Example data for demonstration purposes (replace with actual data)
X = np.random.rand(4, 3)  # 4 samples, 3 features
prices = np.random.rand(8)  # 8 price samples, which is inconsistent
y = np.random.randint(0, 2, size=4)  # Binary targets for classification
X_future = np.random.rand(2, 3)  # Future feature set for price prediction
new_borrower = np.random.rand(1, 3)  # New borrower features

# Ensure X and prices have consistent lengths
if len(X) != len(prices):
    # Example fix: truncate prices or X to match the length of the shorter array
    min_length = min(len(X), len(prices))
    X = X[:min_length]
    prices = prices[:min_length]

# Price Prediction using GBM
price_model = GradientBoostingRegressor()
price_model.fit(X, prices)  # Assume X contains relevant features for price prediction
future_prices = price_model.predict(X_future)  # X_future is the feature set for future prediction
print(future_prices)

# Ensure X and y have consistent lengths
if len(X) != len(y):
    raise ValueError(f"Inconsistent number of samples: X has {len(X)} samples and y has {len(y)} samples.")

# Ensure new_borrower has the same number of features as X
if X.shape[1] != new_borrower.shape[1]:
    raise ValueError(f"Inconsistent number of features: X has {X.shape[1]} features and new_borrower has {new_borrower.shape[1]} features.")

# Risk Assessment using GBM
risk_model = GradientBoostingClassifier()
risk_model.fit(X, y)
default_probabilities = risk_model.predict_proba(new_borrower)
print(default_probabilities)

Result:

[0.81860858 0.81860858]
[[9.99978098e-01 2.19017313e-05]]

Conclusion

This example demonstrates the integration of statistical methods and modern machine learning algorithms in a DeFi context. By applying time series analysis, probability theory, and advanced machine learning techniques, we can build robust models for price prediction and risk assessment in decentralized financial systems. This enhances the protocol’s ability to manage risks and provides more accurate predictions, ensuring better stability and reliability of the DeFi platform.