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.