From pricing to rating structured credit products and vice-versa

Conclusion

In this document, we have presented a theoretical modelling framework for designing and rating a Dynamic Proportion Portfolio Insurance (DPPI)) product, an innovation in the world of synthetic structured credits providing a capital guarantee to the investor.

We first outline the main steps of Collateral Synthetic Obligation risk-neutral pricing in the well-known one factor gaussian copula model, which we further develop and supplement for rating DPPIs. However, the latter requires to evaluate an expected loss function L^(M) under the historical risk measure: various discrete and continuous random processes are introduced for describing risk factors such as defaults, rating transitions, Credit Default Swap (CDS) spread levels and recovery rates. Process parametres calibrated on historical data are assumed to be provided by Moody's, a rating agency. We then rely upon a C++ implementation to run Monte-Carlo simulations and estimate L^(M).

The combination of several innovative investment rules such as a dynamic leverage function, contingent coupon payments, the removal of downgraded assets, lock-in and lock-out features, allows us to minimize L^(M), achieve the target rating of Aa3 in the base case scenario and pass all required stress scenarios.

Finally, we describe the «gap-risk» hedging issue faced by the investment bank when granting a capital guarantee to the investor. We show that in a simplified framework, it can be measured through a default-count equivalent function closely related to the DPPI's structural features.

Appendix

Figure 8: Parametres of Moody's CDS spread processes

Figure 9: Correlation matrix of Moody's CDS spread processes

Figure 10: Moody's 10Y corporate rating transition matrix

Moody's risk factors

Optimized DPPI parametres

Figure 11: DPPI optimized structural features

Figure 12: DPPI reference portfolio
41

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