Quantitative Risk Models: Credit and Market Risk

Module: Fintech AI | Difficulty: Advanced

Credit VaR

Copula Models

Gaussian Copula

Default Correlation

import numpy as np
from scipy.stats import norm

class CreditVaR:
    def __init__(self, pd, lgd, correlation_matrix):
        self.pd = pd; self.lgd = lgd; self.corr = correlation_matrix
    def gaussian_copula_var(self, n_simulations=10000, confidence=0.99):
        n_assets = len(self.pd)
        # Generate correlated defaults
        mvn_samples = np.random.multivariate_normal(
            np.zeros(n_assets), self.corr, n_simulations)
        uniform_samples = norm.cdf(mvn_samples)
        # Determine defaults
        defaults = uniform_samples < self.pd
        # Calculate portfolio loss
        losses = np.sum(defaults * self.lgd, axis=1)
        return np.percentile(losses, confidence * 100)

Research Insight: The Gaussian copula was infamously used to price CDOs before the 2008 crisis. It underestimates tail dependence — the tendency for many defaults to occur simultaneously. Student-t copulas and vine copulas better capture tail risk.