The "Excess Volatility" Reinsurance Treaty

In this paper we propose a new reinsurance treaty called “Excess Volatility” (XV). This treaty aims at reducing the volatility of the underwriting result of a non-life insurance company. The volatility reduction is one of the key issues in today’s highly competitive insurance environment where premium margins are eroding.

The XV treaty is based upon reciprocity between the direct insurer and the reinsurer: losses and profits are exchanged in order to stabilize the underwriting result over time. For this purpose a peculiar payment function is defined, providing a modular and flexible hedging instrument for the direct insurer and the reinsurer. Premiums are computed using the Proportional Hazard transform premium principle proposed by Wang (1995). The first results confirm the model is able to provide the needed protection against deviations in the loss experience, at a relatively low price.

KEYWORDS: Reinsurance, Volatility reduction, Proportional Hazard transform, Reciprocity.