On Correlations between a Contract and Portfolio and Internal Capital Alliocation
Quant Isle Ltd.
January 19, 2012
RETHINKING VALUATION AND PRICING MODELS: LESSONS LEARNED FROM THE CRISIS AND FUTURE CHALLENGES, C. Wehn, C. Hoppe, G. Gregoriou, eds., Elseiver, 2012
A rated company, which conforms with regulations such as Basel II, III or Solvency II, is expected to maintain capital adequacy with a certain high probability. This probability undergoes a change when deals are added or removed from the book of business. To compensate for the change resulting from new deals or deals with deteriorating performance one has to allocate or borrow additional capital, while deals which have matured or which economics has improved trigger capital release and repayment. Analytical formula for quantile (or VaR) change is derived for the case when individual correlated deals are much smaller than the company portfolio. While capital allocation is found to depend on fine details of the company portfolio p\&l distribution function, we establish necessary conditions under which capital allocation by deal could be done at the mean-variance level. If these conditions are not met then high-order correlations between the deal and company portfolio cannot be ignored.
Keywords: Capital allocation, return on capital, value-at-risk, Basel recommendations, Solvency II regulations, default probability, profit and loss distribution, portfolio aggregation
Date posted: March 4, 2012 ; Last revised: October 22, 2013
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