Economic Neutral Position: How to best replicate not fully replicable liabilities?

Abstract

Financial undertakings often have to deal with liabilities of product type in the form “non-hedgeable claim size times value of a tradeable asset”, e.g. foreign property insurance claims in foreign currency multiplied by foreign exchange rate to convert to local currency. Which strategy of investing in the tradeable asset is risk minimal? We generalize the Gram–Charlier series for the sum of two dependent random variables, which allows us to expand the capital requirements for liabilities of product structure based on value-at-risk and expected shortfall. We derive a stable and fairly model independent approximation of the risk minimal asset allocation in terms of the claim size distribution and the moments of the asset return distribution. With the results, a correct and easy-to-implement modularization of capital requirements into a market risk and a non-hedgeable risk component becomes possible.