Compare two stochastic models for synthetic credit indexes. In the first model, a random variable represents a default of an asset (section 7.2.2). Assume annual periods, constant recovery rate, and constant equal correlation among assets. In the second model, a random variable represents the time to default of an asset (section 7.2.3). In both models use the initial asset rating to derive an effective annual default rate. Implement both models with Monte Carlo simulation. Assume a portfolio of 100 credits: 5 AAA, 10 AA, 30 A, 45 BBB, 5 BB, and 5 B. Assume the liability structure has attachment points at 0%, 3%, 7%, 10%, 20%, and 30%. Estimate the probability distributions of losses after one and five years. Compare the means and standard deviations of these two distributions. Compare the percentage of mass in the tail beyond 3% loss. Explain why the distributions differ.
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