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Answer: The Gaussian copula model is initially applied to calculate joint default probabilities among the reference entities, then these probabilities are used to determine the expected cash flows from the CDO tranches which, in turn, are discounted back to present value based on the spread payments approach.
## Explanation Option A correctly describes the valuation process for synthetic CDOs using the Gaussian copula model and spread payments approach: 1. **Gaussian Copula Model**: This model is used first to calculate **joint default probabilities** among the reference entities in the portfolio. The Gaussian copula allows modeling the correlation structure between defaults, which is crucial for CDO valuation. 2. **Expected Cash Flows**: The joint default probabilities are then used to determine the **expected cash flows** from the CDO tranches. Different tranches (equity, mezzanine, senior) have different exposure to default losses based on their attachment and detachment points. 3. **Spread Payments Approach**: Finally, these expected cash flows are **discounted back to present value** using the spread payments approach, which considers the premium payments and potential loss payments. **Why other options are incorrect:** - **Option B**: Incorrectly reverses the order - the Gaussian copula doesn't synthesize default intensities; it models joint default probabilities directly. - **Option C**: Incorrectly suggests using historical data for spreads first and then using copula for time-to-default predictions. - **Option D**: Incorrectly describes establishing an overall risk premium first and then reallocating it, which doesn't match the actual valuation methodology. The correct sequence is: Copula → Joint Default Probabilities → Expected Cash Flows → Discounting via Spread Payments Approach.
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Which of the following accurately describes the process of valuing a synthetic CDO using the spread payments approach and the Gaussian copula model?
A
The Gaussian copula model is initially applied to calculate joint default probabilities among the reference entities, then these probabilities are used to determine the expected cash flows from the CDO tranches which, in turn, are discounted back to present value based on the spread payments approach.
B
First, the spread payments approach calculates individual entity's default intensities, and then the Gaussian copula model synthesizes these into a multidimensional distribution to estimate the likelihood of simultaneous defaults; this information is used to price the CDO tranches.
C
In this method, the spread payments approach initially estimates the fair spreads for each tranche based on historical data. Subsequently, the Gaussian copula model predicts the time to default for each referenced entity, and these predictions are used to adjust the estimated cash flows.
D
The valuation process starts by utilizing the spread payments approach to establish an overall risk premium for the CDO. Then, the Gaussian copula model simulates correlated defaults across the portfolio to reallocate this premium among the different tranches according to their specific credit risks.