Craig B. Merrill

Economic Valuation Models for Insurers

Recently much attention has been given to the approaches insurers undertake in valuing their liabilities and assets. For example, in 1994 the American Academy of Actuaries created a Fair Valuation of Liabilities Task Force to address the issue. In 1997, the Academy established a Valuation Law Task Force and a Valuation Tools Working Group to investigate the various valuation approaches extant and to make recommendations on which models are best suited to the task. Much of the published work has focused on attributes of the various models, their strengths and shortcomings. Some of the work has addressed the larger questions, but in our view, it is useful and necessary to provide a taxonomy of approaches and evaluate them in a systematic way in accordance with how well they achieve their aims. In this paper we focus primarily on the economic valuation of insurance liabilities, although we do address some valuation issues for assets. We begin in Section I by defining insurance liabilities. Next, in Section II, we discuss the criteria for a good economic valuation model. This is followed by a taxonomy of valuation models in Section III. In Section IV, we examine insurance liabilities in the context of this taxonomy and identify the minimum requirements of an economic valuation approach that purports to value them adequately. An illustration of the application of a modern valuation model is given in Section V. We conclude in Section VI by discussing some limitations of our analysis, and offer some recommendations for implementation.

Fair Value of Liabilities: The Financial Economics Perspective

Abstract In this paper we present the fundamental approaches of financial economics to valuation. Three methods are demonstrated by which financial economists account for risk. We illustrate how these methods relate to one another and how they can be applied in the valuation of risky corporate bonds, guaranteed investment contracts (GICs) with and without interest rate contingencies, and whole life insurance. Next, we discuss how these models treat orthogonal risks, such as the kind often covered by insurance contracts. Demand side and supply side diversification are treated, and liquidity risk is then considered. We conclude with a summary of the benefits of decomposition and transparency.

The Effect of Transaction Size on Off-the-Run Treasury Prices

This paper examines intra-day trading data from the inter-dealer broker market for U.S. Treasury securities and measures the degree of price pressure in the off-the-run Treasury market. As is well known, securities that would appear to be very close substitutes, i.e., on-the-run and off-the-run Treasury bonds, behave as if there is some degree of market segmentation. This is the first systematic study of the off-the-run Treasury note and bond market focused entirely on a price pressure effect using intra-day data. The paper analyzes price pressure through matched pairs of securities that differ only in liquidity.

Toward a Unified Valuation Model for Life Insurers

Recently much attention has been given to the approaches insurers undertake in valuing their liabilities and assets. For example, in 1994 the American Academy of Actuaries created a Fair Valuation of Liabilities Task Force to address the issue.1 In 1997, the Academy established a Valuation Law Task Force and a Valuation Tools Working Group to investigate the various valuation approaches extant and to recommend the models best suited to the task. FASB and IASB have also been exploring the issue.

INSURANCE THEORY AND CHALLENGES FACING THE DEVELOPMENT OF MICROINSURANCE MARKETS

Microinsurance institutions and instruments have developed rapidly over the last decade, with policies covering tens of millions at the base of the economic pyramid. Ranging from simple policies providing life or health insurance to complex policies covering catastrophic risks for small landholders, it is a market with proven potential that demands closer attention. This paper provides a review of the nascent academic literature and then suggests some critical elements of insurance theory that may help us understand the challenges facing microinsurance markets and how these markets can better serve the needs of their customers. Although the basic theory is well known, application to microinsurance markets reveals interesting variations on known results.

Were There Fire Sales in the RMBS Market

Many observers have argued that the fall in RMBS prices during the crisis was partly caused by fire sales. We provide an explanation for why financial institutions may have engaged in fire sales using a unique dataset of RMBS transactions for insurance companies. We show that risk-sensitive capital requirements and mark-to-market accounting can jointly create incentives for capital-constrained financial institutions to engage in fire sales of stressed securities because the increased risk can make it too expensive to hold such securities. Further, we find that, in general, RMBS prices behaved as would be expected in the presence of fire sales.

Why Were There Fire Sales of Mortgage-Backed Securities by Financial Institutions during the Financial Crisis?

Much attention has been paid to the large decreases in value of non-agency residential mortgage-backed securities (RMBS) during the financial crisis. Many observers have argued that the fall in prices was partly caused by fire sales. We use capital requirements and accounting rules to identify circumstances where financial institutions had incentives to engage in fire sales and then examine whether such sales occurred. For financial institutions subject to credit-sensitive capital requirements, capital requirements increase as an assets credit becomes impaired. When accounting rules require such an assets value to be marked-to-market and the fair value loss to be recognized in earnings, a capital-constrained firm can improve its capital position by selling the credit-impaired asset even if it has to accept a liquidity discount to do so. In contrast, a financial firm whose fair value losses are not recognized in earnings for the purpose of calculating capital requirements is more likely to satisfy capital requirements by selling liquid assets whose value has not fallen and hence would be unlikely to engage in fire sales. Using a sample of 5,000 repeat transactions of non-agency RMBS by insurance companies from 2006 to 2009, we show that insurance companies that became more capital-constrained because of operating losses (uncorrelated with RMBS credit quality) and also recognized fair value losses sold comparable RMBS at much lower prices than other insurance companies during the crisis.

INTEREST-RATE OPTION PRICING REVISITED

When valuing derivative securities, if no arbitrage opportunities exist, then the value of the derivative must equal the value of a portfolio of fundamental securities that replicates the payoffs of the contract being valued. The purpose of this note is to point out the care that must be exercised when choosing fundamental securities with which to replicate the cash flows of more complex securities. Often, the choice of fundamental, or replicating, securities is driven by the existence of a known solution for their value. An example of this approach is Turnbull and Milne (1 99 l ) , who use the contingent claims framework to derive closed-form solutions for options written on a variety of interest-rate contingent securities. They value each interest-rate contingent security relative to the exogenously given term structure of interest rates. Using this approach, they are able to derive closed-form solutions not only for simple contracts, such as options on discount Treasury bonds, but also for more complex contracts, such as options on interest rate futures contracts. As shown by Boyle and Turnbull (1989) or Turnbull and Milne ( 1 99 1) a European put option on a T-bill can be used to replicate the payoff on an interest rate cap. They use this relationship because there are known solutions for the value of a European option on a T-bill. In replicating the interest rate cap, the appropriate number of put options