The Mathematics of Financial Modelingand Investment Management

22-Credit Risk Model Derivs Page 726 Wednesday, February 4, 2004 1:12 PM

726 The Mathematics of Financial Modeling and Investment Management

EXHIBIT 22.8 Independent Assets

Outcome In Venn Diagram Probability

Both asset A and asset B Anywhere in overlap of pAB

default both circles

Asset B defaults and asset A Anywhere in B but not in pB – pAB

does not default overlap

Asset A defaults and asset B Anywhere in A but not in pA – pAB

does not default overlap

Neither asset defaults Outside both circles 1 – (pA + pB – pAB)

Either asset A or asset B or Anywhere within outer pA + pB – pAB

both assets default perimeter of circles

EXHIBIT 22.9 Case of High Default Correlation

In the case default of the stronger asset is always associated with default of the weak-

er asset.