Authors’ Reply: Two Paradigms for the Market Value of Liabilities - Discussion by David F. Babbel; Michael Cohen; J. Peter Duran; Luke N. Girard; Thomas S.Y. Ho; Craig Merrill

Abstract

In this article, we express a concern that certain commonly accepted methods of predicting mortality will likely prove to be inadequate in the future. Specifically, the Lee-Carter method, which overall has been empirically successful, uses auto-regressive moving average (ARMA) technology and contains no structural mortality equation. This structure means that no information other than previous history can be introduced. We argue that rapid advances in medical science are taking place and that failure to reflect this information in our projection methodology will make resulting projections unsuitable.     

Authors’ Reply: Forecasting Social Security Actuarial Assumptions - Discussion by John A. Beekman; Cecil J. Nesbitt; Krzysztof M. Ostaszewski; Gregory Savord; Richard S. Foster,October 1997

Abstract

This study provides an economic analysis of life insurance company expenses and develops a methodology for the construction of benchmark expense factors. These benchmarks can facilitate the pricing of new business, cost control within companies, and expense comparisons among companies. We derive the expense factors by estimating a cost function wherein total general expenses are modeled as a function of input prices and physical outputs, and the physical outputs are proxies for the cost drivers of the different lines of business. This methodology has two important advantages: first, the derived expense factors are independent of the methods that insurers use in allocating total expenses across lines of business. Second, the estimated cost function explicitly accounts for different degrees of economies of scale and consequently in the present value of marginal expenses across insurers. Hence, this study demonstrates that economies of scale and, in turn, size must be considered when constructing an expense table.     

Authors’ Reply: Building Better Retirement Income Models - Discussion by Robert J. Myers; Anna Rappaport,January 1997

Abstract

In recent decades, as the use of derivatives by financial institutions has expanded, the shortcomings of historical cost accounting approaches have become increasingly apparent. Since derivatives can create large exposures to risk that go unnoticed under historical standards, the accounting industry has focused on how to change the standards so that these risks are reflected appropriately in a company’s accounting statements. New standards such as SFAS 115 and SFAS 133 have been adopted in part to achieve this goal. However, both of these standards use a piecemeal approach to risk measurement that may be adding to the problem rather than creating a solution. This paper will use a simple equity-indexed annuity to illustrate the problem with historical cost accounting and with the standards that have been adopted to correct it. The paper then argues that the only legitimate means of reflecting risk properly on a company’s accounting statements is to adopt full fair value accounting for all assets and liabilities on the company’s books.     

Authors’ Reply: Corporate Hedging in the Insurance Industry: The Use of Financial Derivatives by U.S. Insurers - Discussion by L. Lee Colquitt; Arlette C. Wilson; Gray G. Venter; Morton Lane; Joan Lamm-Tennant,January 1997

Abstract

This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The time of ruin is analyzed in terms of its Laplace transforms, which can naturally be interpreted as discounting. Hence the classical risk theory model is generalized by discounting with respect to the time of ruin. We show how to calculate an expected discounted penalty, which is due at ruin and may depend on the deficit at ruin and on the surplus immediately before ruin. The expected discounted penalty, considered as a function of the initial surplus, satisfies a certain renewal equation, which has a probabilistic interpretation. Explicit answers are obtained for zero initial surplus, very large initial surplus, and arbitrary initial surplus if the claim amount distribution is exponential or a mixture of exponentials. We generalize Dickson’s formula, which expresses the joint distribution of the surplus immediately prior to and at ruin in terms of the probability of ultimate ruin. Explicit results are obtained when dividends are paid out to the stockholders according to a constant barrier strategy.     

Author’s Reply: Skewness and Stock Option Prices - Discussion by Terence Chan,Michel Jacques,Heinz H. Mu¨ller,Geérard Pafumi,Elias S.W. Shiu,and Serena Tiong,July 1997

Abstract

In recent years, the combined effects of deregulation in financial services, along with advances in telecommunications and information technology, are forcing far-reaching changes upon the insurance industry. The result is the industry is becoming more competitive. The emerging role of electronic commerce (e-commerce) is particularly important and interesting to study.

I offer a brief survey of the role of e-commerce in the insurance industry. The paper is organized in the following manner: Section 1 summarizes Internet trends and discusses various related public policy issues; Section 2 addresses online insurance supply and demand; Section 3 discusses the economics of disintermediation and reintermediation and explains how this applies to e-commerce in the insurance industry. Finally, Section 4 offers a set of concluding remarks.     

Author’s Reply: Principal Applications of Bayesian Methods in Actuarial Science: A Perspective - Discussion by Marjorie A. Rosenberg; M. Mendoza; Francisco José VáZquez-Polo; James C. Hickman; Donald A. Jones; Enrique de Alba; David P. M. Scollnik

Abstract

This paper considers the pricing of equity-indexed annuities (EIAs). Traditionally, the values of the guarantees embedded in these contracts are priced by modeling the underlying index fund while keeping the interest rates constant. The assumption of constant interest rates becomes unrealistic in pricing and hedging the EIAs since the embedded guarantees are often of much longer maturity. To solve this problem, the authors propose an economic model that has the flexibility of modeling the underlying index fund as well as the interest rates. Some popular EIAs are illustrated to assess the implication of the proposed model.