Application of the Option Market Paradigm to the Solution of Insurance Problems [Author's Reply]

In his 2000 discussion of my 1997 paper, Stephen Mildenhall chided me for overstating the similarity between options and insurance. He accepted the main point of the paper; namely, that the close resemblance between call option and excess of loss concepts can lead to insights about insurance and reinsurance risk management and product development. However, at a detailed level he dismissed my assertion that “the pricing mathematics is basically the same” for options and insurance, politely describing it as “inappropriate.” He was correct in doing so. Unfortunately, in emphasizing the difference in the details of the pricing of call options and excess insurance, he missed the opportunity to show how these differences can be explained within a single pricing framework, though different from the one I originally presented. The purpose of this response is first to acknowledge my error at the formula level, but then to move beyond it to illustrate how Black-Scholes and excess insurance pricing are consistent, even if the pricing formula details are different.