Valuation and Hedging
In this chapter we concentrate on risk management and hedging of portfolio structures, and model errors.
22.1 VALUATION EXAMPLES
The aim of this section is to present some graphical and numerical results to show the impact of different correlation on the pricing of portfolio CD products, and to show the impact of various other factors on CDO pricing. Numerical results quoted in this section are based on 10 000 simulations for a 100 name portfolio: otherwise it is generally immaterial whether a Monte Carlo model or an SCF pricing approach is followed.
22.1.1 F2D Baskets
We have already seen the 0% correlation and the 100% correlation results for the fair value premium on a F2D. Figure 22.1
shows the pattern of fair value spread for a two name basket as correlation varies from 0 to 1. We assume the CDS premiums for the names are 82 bp and 123 bp, and we assume both names have the same recovery. Some further pricing results specific to standard traded CDO structures appear in section 22.4.
1. What happens at negative correlation on the two name basket? If correlation is minus 100% what does that mean for the simulated random numbers? If the simulated random number means that one name defaults early, show that the other name defaults late. Hence show that the curve in Figure 22.1
continues rising as correlation becomes increasingly negative.
2. At minus 100% correlation the above shows that you would pay more than 82 bp + 123 bp for the F2D ...