If you are a rating company or investment bank and interested in these algorithms please contact us at armin @ approximity dot com. Existing models do not attempt multi-firm, multi-liability and multi-priority cross-ownership in a structural way.

The general case:

• Models the XOS of assets and liabilities for groups of firms.
• Multiple different classes of liabilities, e.g. debt and derivatives.
• Multiple different priorities of claims are allowed.
• Directly incorporates counterparty risk at the multi-firm level into derivatives pricing and general asset pricing.
• Underlying exogenous assets can be stochastically dependent.
• Situations where valuation is impossible (no equilibria/multiple equilibria) exist.
• It should be possible to extend any model based on the original Mer- ton Model (for instance the Moody’s KMV model) to incorporate cross-ownership along the lines of this paper.

Tom Fischer’s latest slides: statistik.mathematik.uni-wuerzburg.de/~fischer/papers/DGVFM_Fischer_XOS.pdf

The full article: arxiv.org/abs/1005.0768

The image below from the NY Times shows a good application of Tom’s XOS work.