The Art of Credit Derivatives: Demystifying the Black Swan

15

Structured Credit Products: CPPI and CPDO

The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man.

Bernard Shaw

15.1 INTRODUCTION

Two recent innovative structured credit products are credit Constant Proportion Portfolio Insurance (CPPI) and credit Constant Proportion Debt Obligation (CPDO). The invested capital is put in a risk-free bond and a position is taken on credit derivatives. In a CPPI the principal is guaranteed at maturity and the goal is to maximize the portfolio value. In a CPDO the target is a significant excess return over the risk-free rate, subject to the constraint of being highly rated.

Essential to the pricing of CPPI and CPDO is the determination by the structurer of the so-called gap risk - that is, the risk of the portfolio value falling below some low barrier, the bond floor for a CPPI and the cash-out barrier for a CPDO. Due to the leveraged nature of the investment and to possible jumps in the spreads, one may lose more than the amount allocated to the risky part. In this chapter we present two simple Monte Carlo-based approaches to determine the risks on CPPI and CPDO structures. In the first algorithm, the spread dynamic is generated using the usual Gaussian framework, and in the second we use a Lévy-based process. We show that when using the Gaussian framework and not accounting for the possibilities of jumps, an enormous model ...