Computing bounds on the expected payoff of Alternative Risk Transfer products

The demand for integrated risk management solutions and the need for new sources of capital have led to the development of innovative risk management products that mix the characteristics of traditional insurance and financial products. Such products, usually referred as Alternative Risk Transfer (ART) products include: (re)insurance contracts that bundle several risks under a single policy; multi-trigger products where the payment of benefits depends upon the occurrence of several events; and insurance linked securities that place insurance risks in the capital market. Pricing of these complex products usually requires tailor-made complex valuation methods that combine derivative pricing and actuarial science techniques for each product, as well as strong distributional assumptions on the ART’s underlying risk factors. We present here an alternative methodology to compute bounds on the price of ART products when there is limited information on the distribution of the underlying risk factors. In particular, we develop a general optimization-based method that computes upper and lower price bounds for different ART products using market data and possibly expert information about the underlying risk factors. These bounds are useful when the structure of the product is too complex to develop analytical or simulation valuation methods, or when the scarcity of data makes it difficult to make strong distributional assumptions on the risk factors. We illustrate our results by computing bounds on the price of a floating retention insurance contract, and a catastrophe equity put (CatEPut) option.