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1、From：NORTH AMERICAN ACTUARIAL JOURNAL,VOLUME 6, NUMBER 1, Jan 2002Fair Value of Liabilities:The Financial Economics PerspectiveDavid F. BabbelJeremy Gold, FSACraig B. Merrill*September, 2001ABSTRACTThe fundamental approaches of financial economics to valuation are presented. Three methods are demons

2、trated 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, GICS with and without interest rate contingencies, and whole life insurance. Next, we discuss how these models treat ort

3、hogonal risks, such as the kind often covered by insurance contracts. Demand-side and supply-side diversification are treated. Liquidity risk is then considered. We conclude with a summary of the benefits of decomposition and transparency.1. INTRODUCTIONThere has been considerable discussion of a va

4、riety of issues related to fair value in the actuarial literature, in conferences, and among individuals interested in this topic. Unfortunately, we seem to be failing to communicate due, in part, to a lack of a consistent paradigm and objectives. In this discussion paper we present a few concepts t

5、hat we hope will be of use in the broader discussion of fair value of liabilities. The financial economics paradigm is not the only perspective that is relevant to the fair value debate. Obviously, there is an entire body of literature and practice in accounting, actuarial science, taxation, and reg

6、ulation that will bear sway in the fair value debate. It is important, however, that the final form of fair value accounting does not deviate from well-established valuation principles that are tested by the entire world capital markets on a daily basis. Those valuation principles which emerge from

7、the finance and economics literature and practice that do not hold up to empirical testing are rejected. That rejection often takes the form of market failure by those who implement unsound strategies.The American Academy of Actuaries, the International Actuarial Association, the * The authors are,

8、respectively, Professor of Insurance and Finance, Wharton School, University of Pennsylvania; Proprietor of Jeremy Gold Pensions, New York, and Associate Professor of Finance, Marriott School of Management, Brigham Young University. They are indebted to many members of the American Academy of Actuar

9、ies valuation task force, especially Marsha Wallace, who helped them refine their ideas on this topic, and to three anonymous referees of this Journal, but take all responsibility for the views herein expressed, and any errors contained in this paper. Portions of this paper were published as “The Bu

10、llet GIC as an Example,” in Risk and Rewards, February 2001.FASB, the IASB, the SEC and others have organized committees and task forces and sponsored symposia discussing issues relating to the valuation of insurance liabilities.The goal of this paper is to review fundamental approaches to valuation

11、 from a financial economics perspective. Then we will discuss the treatment of default risk, the pricing of risks that are orthogonal to the market, and to the impact of illiquidity on insurance liability valuation.2. FUNDAMENTAL APPROACHES TO VALUATIONIn the absence of observable market prices, the

12、re are at least three theoretically correct methods for estimating the value of a series of (potentially risky) future cash flows. One, discount the true probability-weighted future cash flows using discount rates that is the sum of a risk-free rate and a risk premium. Two, modify the probabilities

13、of the risky future cash flows to account for risk and discount at risk-free interest rates. Three, modify the risky cash flows to account for risk and discount at risk-free rates. There are examples where the option pricing model has been successfully applied to thinly traded securities. Probably t

14、he most prominent are certain kinds of mortgagebacked securities (MBS). The underlying prepayment risk was not actively traded until the creation of MBS. Uncertainty surrounding prepayment risk, and perhaps other risks not being modeled in the contingent cash flows, were, and still are, accounted fo

15、r using an option-adjusted spread (OAS). In essence, the prepayment and other risks are modeled and priced using the OAS as an increment to the risk premium and the interest rate contingencies are priced using a risk neutral measure over future possible interest rates. The OAS can be thought of as a

16、 fudge factor added to the discount process that reconciles the models with the market. This is an important example of how transparency and market mechanisms can improve market efficiency.3. DEFAULT RISKAnother example of an application of the option pricing model to thinly traded assets is the pri

17、cing of corporate bonds. Merton (1974), as well as Black and Scholes (1973),suggested that corporate securities could be viewed as options on the underlying assets of the company.1 Other names applied to this model include the martingale measure, risk-neutral probability, or hedging model.2 OAS is i

18、ncluded in MBS models because of sub-optimal exercise of the prepayment option. Financial economists typically model prepayment behavior with a flexible functional form, but the function never fits the behavior exactly; rather, there is always noise surrounding the estimates. Even though the deviati

19、ons may be independent and symmetric the impact of the deviations is asymmetric to the investor. For example, surprise prepayment when interest rates are low leads to greater cost due toworsened reinvestment opportunities than when interest rates are high. Moreover, OAS arises because of the asymmet

20、ric costs of modeling error.3 These models are too simplistic for pricing corporate bonds in practice. This model is, however, sufficient to illustrate the key concepts that are relevant to this discussion. Extensions that accommodate the complexities of these bonds include Duffee (1999), Duffie and

21、 Lando (2000), Duffie and Singleton (1999), Jarrow and Turnbull (1995), Kim, Ramaswamy, and Sundaresan (1993).The underlying assets include plant and equipment, franchise value, customer relationships, etc. These parts of the asset value are difficult to observe and price. Nonetheless, the model has

22、 still been used successfully in pricing credit derivatives. The inability to observe the value of assets is less of a concern for insurance liabilities where the vast majority of assets are financial and easily observed.Consider a simple non-financial company with equity holders and a single bond i

23、ssuance. Note that the bondholders are entitled to the value of the assets up to the face amount of the debt and that the equity holders are entitled to the value of the assets in excess of that amount. This means that we can view equity as a call option on the assets with a strike price equal to th

24、e face value of the debt. For a zero coupon bond, in a world of constant interest rates, the value of equity is given by the Black-Scholes call option formula. Extensions for coupon bonds have also been derived. The value of the bond is given by subtracting the equity call option from the underlying

25、 assets. Thus, the bondholders are described as owning the assets and selling a call option to equity holders.3.1 A Bullet GICTo illustrate these valuation principles in an insurance context, we will focus on the simplest insurance liability with a fixed, promised payment at the end of the period th

26、e bullet GIC. In its simplest form the bullet GIC is little more than a zero-coupon bond. The fair value of the bullet GIC could be determined using any of the valuation approaches discussed above. There are several reasons, however, that we suggest it should be valued as a risk-free zero-coupon bon

27、d minus a put option. As before, no correctly implemented valuation approach is more theoretically correct than any other correctly implemented valuation approach. The choice of valuation methodology is often driven by practical considerations.If the bullet GIC were the only type of liability issued

28、 by an insurance company we could just calculate the market value in the most convenient way possible. We could simply look to the secondary market, thin though it might be, and price accordingly. Alternatively, we might look to the creditworthiness of the issuer and add a spread to Treasury STRIP r

29、ates to discount the promised cash flow from the bullet GIC. The liabilities of an insurer, however, are much more complex than a simple bullet GIC. It is when we turn to the more complex liabilities that the decomposition into a risk-free liability and a risk-based put option becomes particularly d

30、esirable.3.2 A Bullet GIC with Interest Rate ContingenciesConsider a stylized window bullet GIC as a very simple extension. The window gives an investor the option either to buy a GIC now at a set interest rate, or to wait some amount of time and buy a GIC that offers either prevailing market rates

31、or a guaranteed minimum rate, whichever is greater. The decision to take advantage of the window feature of the GIC will be made based on current market interest rates at the inception of the window GIC and at the time of the closing of the window. Thus, the window GIC has interest rate contingency

32、in its potential cash flows. In other words, the possible cash flows, and their timing, depend upon the evolution of market interest rates during the open window period. In terms of valuation, we can decompose the value of the window GIC into a default risk-free window GIC and a default risk-based p

33、ut option value. 3.3 Whole Life InsuranceEven more complex than the GICs discussed above would be an insurance company liability such as whole life insurance. Whole life includes not only interest rate contingencies, it also includes other risks, specifically, mortality risk. Consider a very simple

34、form of whole life insurance that offers protection against mortality risk with a level annual premium for the duration of a policyholders life. The policy offers only the right to surrender and take away any cash value in the policy but no policy loan, settlement options, or other typical policy op

35、tions.4. ORTHOGONAL RISKSMore general insurance liabilities pose even greater challenges for valuation. There are underwriting risks, mortality or casualty risks, operating and expense risks, non-optimal use by policyholders of options granted in the policy, etc. However, as shown above, and discuss

36、ed in Babbel and Merrill (1999), these risks can be incorporated into a model with interest rate risks. If the other risks are orthogonal (uncorrelated) to interest rate or market risks, they are not directly “priced.” If, however, they are not orthogonal or not diversifiable, then they must be pric

37、ed in the model. It is common, as in the case of mortgage-backed securities, to add an option-adjusted spread (which can be positive or negative) into an interest rate contingent valuation in order to account for non-interest rate risk that is not diversifiable or is not completely orthogonal to int

38、erest rate or market risk.4.1 Naturally Orthogonal Risks and Acquired BetaSeveral equilibrium pricing models have appeared in the financial economics literature.Common among most of these models is that orthogonal risks do not command a “market premium,” whereas systematic risks do. In this section,

39、 we will consider one of the earliest of these equilibrium pricing models, the Capital Asset Pricing Model (CAPM, Sharpe,1964), to illustrate these concepts. Thus, we are assuming a world consistent with the CAPM assumptions. We will then contrast these pricing insights from theory against what we o

40、bserve in practice, and discuss how orthogonal risk pricing should be reported.4.2 Diversification of Naturally Orthogonal RisksPure zero-sum wagers may influence an individuals portfolio but do not impact the market portfolio. However, certain naturally orthogonal risks exist in the market even bef

41、ore a security interest is created by a wager. These risks may often be described as “insurance.”Note that the Arizona rain is an uncertain event but does not, all of itself, impact the market. If, however, the rain does benefit or injure wealth, the benefit or the injury becomes an element of the m

42、arket portfolio. Crop futures may 4 Financial economists use the term “priced” as an actuary might say “charged for” in a premium calculation or accounted for when included in an insurance liability. It specifically means that the premium or liability includes an amount above and beyond the mean val

43、ue of the random variable.reflect one form of “securitization by wager” applicable to weather uncertainty. Insurance represents another such securitization that usually applies only to an injurious outcome.Insurance is usually characterized by two elements that may or may not apply to other risks: a

44、dverse selection and moral hazard. Dealing with these elements is invariably costly at the customer level and may also have an impact in institutional transactions such as reinsurance. The cost of adverse selection becomes an insurance expense generally known as underwriting. Moral hazard gives rise

45、 to the expenses associated with claims settlement.4.3 Demand Side DiversificationConsider n identical and independent risks (e.g., home fire insurance).The individual acquires his individual risk along with homeownership. Absent adverse sel-ection, moral hazard and some administrative difficulties,

46、 each risk averse homeowner would rather bear one-nth of the total risk than all of his own. Suppose we could implement this risk sharing by trading shares of the individual risks in a perfect market. Then, as n grows large, the risk of each individual diminishes. In the limit, each individual may p

47、ay the expected loss discounted for the period at the risk-free rate.In reality, the expenses of insurance require that risk averse insureds must pay premiums in excess of the expected loss. The premium must be sufficient to cover all the expenses and a viable market can exist only when there are n

48、riskbearers who are sufficiently risk averse to pay the premiums (Pratt, 1964). Further, in reality, the insurance and the enabling entity will be viable only when there is sufficient additional capital available to develop an arbitrarily high probability of solvency. Due to the operation of the Law

49、 of Large Numbers, the amount of capital required per unit of insurance decreases although the total capital required is an increasing function of n. For small values of n,the cost of such capital is prohibitive to the insured and, thus, we expect to observe large risk pools.4.4 Supply Side DiversificationWe have seen that insurance diversifies demand side (customer) risks by pooling. But the providers of capital still require recompense for the residual risk of the pool despite the fact t