Market Value Of Insurance Liabilities

Abstract

With Statement of Financial Accounting Standards 115 (FASB 1993), insurers are now in the awkward situation that almost half of the balance sheet is marked to market. This has created a material inconsistency with the way liabilities are reported, thus diminishing the usefulness of financial reporting to shareholders and potential new investors. Discussion has emerged in the industry about the process of market valuing liabilities. The American Academy of Actuaries has formed a “Fair Valuation of Liabilities” task force to compare and review various alternative methodologies. During 1995 the Society of Actuaries and New York University jointly sponsored a conference on “Fair Value of Insurance Liabilities.” Motivated by the conference, this paper attempts to bridge the gap between option pricing and actuarial appraisal methodologies. The author suggests we refocus attention toward the assumption-setting process, which is the key driver of a fair valuation. In this regard, this paper attempts to advance practice and methodology with respect to life insurance company valuation.     

Guarantees in With-Profit and Unitized With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option

The purpose of the article is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The article extends the techniques developed by Haberman, Ballotta, and Wang (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing “machinery,” underpinned by Monte Carlo techniques for the computation of fair values. The article addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade‐offs between these parameters.     

Which approach to accounting for employee stock options best reflects market pricing?

We use a residual income valuation framework to compare equity valuation implications of four approaches to employee stock options (ESOs) accounting: APB 25 “recognize nothing”, SFAS 123 (revised) “recognize ESO expense”, FASB Exposure Draft “recognize and expense ESO asset” and “recognize ESO asset and liability”. Theoretical analysis shows only grant date recognition of an asset and liability, and subsequent marking-to-market of the liability, results in accounting numbers that capture the dilution effects of ESOs on current shareholder value. Out-of-sample equity market value prediction tests and in-sample comparisons of model explanatory power also support the “recognize ESO asset and liability” method.     

Issues in the Drive to Measure Liabilities at Fair Value

This paper compares the discussion on liability measurement in Accounting The0y Monograph 10 with the liability measurement requirements in recent international proposals on accounting for financial instruments. Rather than conducting a detailed review of the Monograph, the paper examines three major issues which wawant amplifjing, extending or criticising: What is “fair value”? Why fair value liabilities? Should fair value include an entity's own credit risk? The focus is on financial liabilities such as “plain vanilla” debt; other financial liabilities, such as insurance obligations, pensions, wawanties and environmental damage restoration involve additional considerations and are therefore not considered.     

On accounting standards and fair valuation of life insurance and pension liabilities

The actuarial profession is increasingly teaming up with financial economists for a fruitful cooperation on the proper valuation of life insurance and pension (L&P) liabilities. This has been a natural consequence of a recent sharply increased focus on market values in financial reports of L&P companies from regulators, standard setters, the financial press, stakeholders, and others with an interest in the L&P business.

This article provides a financial economist's point of view on recent developments in relation to the fair valuation of L&P liabilities. The role of accounting standards and the background for the international harmonization in this field are first discussed. We then review and explain the concept of fair value and provide a general view on appropriate techniques for estimating fair values of L&P liabilities in accordance with the definition of the concept. The paper also contains a section which briefly reviews recent and quite innovative regulatory initiatives in relation to market value reporting in the Danish market for life and pension insurance.     

Market Value Margin für die Fair Value-Bilanzierung versicherungstechnischer Verpflichtungen : Ableitung auf Basis des CAPM

The International Accounting Standards Board (IASB) started a project on Insurance Accounting to apply the principles of fair value to insurance businesses. The so called ?asset and liability approach“ would focus on the balance sheet, with both assets and liabilities being reported at fair values, while income and expenses are defined in terms of changes in the values of those assets and liabilities. Indeed, there are no deep and liquid markets for insurance liabilities. Thus, the fair value has to be calculated as a theoretical value, using assumptions concerning future events, risk provisions and discount rates. Both in theory and in practice a generally accepted modelling of fair value is missing. Particularly with regard to the deviation of a Market Value Margin (MVM), which reflects the premium that a marketplace participant would demand for bearing the uncertainty inherent in the cash flows, there is a need for adequate modelling. Transforming the CAPM for determining risk loads in insurance will mean measuring the correlation between insurance companies’ returns from underwriting and market returns on its shareholders’ equity. The criticism on an underwriting beta focuses on (a) the basic assumptions of the CAPM, (b) the absence of active markets for insurance liabilities and (c) the unreliability of estimating underwriting betas.     

价值管理视角下的商业银行资产负债模型

以价值管理为核心的商业银行资产负债模型将资产负债管理相关要素纳入统一的分析框架内,实现了价值创造和风险控制的有机结合,促使银行资产负债管理行为与银行价值最大化的基本目标协同一致。基于价值管理的资产负债理论模型为中国银行业在内部资金转移定价、贷款定价及利率风险计量等资产负债管理核心领域的实践提供了有益的参考。推进中国银行业资产负债管理向价值管理转型还必须从银行内外部同时着手,在银行内部积极吸收借鉴国外成熟的理论模型,加快开发资产负债决策支持系统,同时,大力推进金融市场和金融基础设施建设。     

Equity Risk Premium

Abstract

The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.

The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about ?1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.

This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.     

Asset Pricing of Insurance Loss Liabilities: Some Examples

I construct examples of valuing insurance loss liabilities with asset pricing models, comparing the Rubinstein‐Leland model with the better‐known CAPM. The two models give different values only if the loss payment is asymmetric and correlated with the market portfolio, conditions which can result from the nature of the underlying loss or from the impact of insolvency on the insurer's payment.
In examples where insolvency is not possible and there is no liquidity cost of raising new equity on short notice, the value of a loss liability is equal to the value of the underlying loss, i.e., of the promised coverage, and depends neither on (1) the size of the loss pool; nor on (2) the unsystematic risk of the insurer's liabilities; nor on (3) the composition of an insurer's investment portfolio; nor on (4) the amount of insurer equity.
These factors do affect the value of a loss liability in examples where insolvency and liquidity costs are considered. Other things equal, if a factor increases the likelihood of insolvency, the fair value of a loss liability is lower because the insured is partially self‐insuring; but the liquidity cost of maintaining solvency by raising new equity on short notice is higher, implying a higher fair value of the loss liability.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

Strategisches Asset-Liability Management in der Versicherungswirtschaft — Ein Ansatz zur integrierten Bilanzstrukturoptimierung

Asset-Liability Management has gained increased significance within the German insurance industry. This was mainly driven by recent capital market developments. In fact, insurers have encountered challenges to earn given interest guarantees. Regulatory changes also require more sophisticated ALM-tools. Solvency II will change the underlying paradigm and shift balance sheets perception towards a market value oriented view. Especially liabilities will have to be accounted for using the fair value approach. Most ALM-tools appear to be unable to cope with these demands. To improve this current practice, in this paper a Markowitz-approach is employed in order to generate an integrated method for the optimization of assets and liabilities in the life insurance industry. This technique aims to link new regulatory requirements to the latest capital market theory and therefore delivers a procedure for an integrated asset allocation policy in the insurance industry.     

Fuzzy Financial Pricing of Property-Liability Insurance

Abstract

This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach.     

Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility

We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze.     

Immediate Annuity Pricing in the Presence of Unobserved Heterogeneity

Abstract

One of the acknowledged difficulties with pricing immediate annuities is that underwriting the annuitantis life is the exception rather than the rule. In the absence of underwriting, the price paid for a life-contingent annuity is the same for all sales at a given age. This exposes the market (insurance company and potential policyholder alike) to antiselection. The insurance company worries that only the healthiest people choose a life-contingent annuity and therefore adjust mortality accordingly. The potential policyholders worry that they are not being compensated for their relatively poor health and choose not to purchase what would otherwise be a very beneficial product.

This paper develops a model of underlying, unobserved health. Health is a state variable that follows a first-order Markov process. An individual reaches the state “death” either by accident from any health state or by progressively declining health state. Health state is one-dimensional, in the sense that health can either “improve” or “deteriorate” by moving farther from or close to the “death” state, respectively. The probability of death in a given year is a function of health state, not of age. Therefore, in this model a person is exactly as old as he or she feels.

I first demonstrate that a multistate, ageless Markov model can match the mortality patterns in the common annuity mortality tables. The model is extended to consider several types of mortality improvements: permanent through decreasing probability of deteriorating health, temporary through improved distribution of initial health state, and plateau through the effects of past health improvements.

I then construct an economic model of optimal policyholder behavior, assuming that the policyholder either knows his or her health state or has some limited information. the value of mortality risk transfer through purchasing a life-contingent annuity is estimated for each health state under various risk-aversion parameters. Given the economic model for optimal purchasing of annuities, the value of underwriting (limited information about policyholder health state) is demonstrated.     

The Value of Deposit Insurance in the Presence of Interest Rate and Credit Risk

In this paper we employ the theory of the term structure of interest rates and the pricing of interest contingent contracts to determine the fair value of insurance for depository institutions. The balance sheet of a bank is taken to consist of long and short positions in various fixed income securities. Deposit insurance for the bank is a put option on the value of the assets. The value of deposits, assets, the implied exercise price of the put and the value of the put are all determined simultaneously as part of the same valuation solution. The approach is developed initially for a single‐state term structure. It is extended to incorporate credit risk on bank assets.
The most important policy implication is that for a bank whose assets are longer term than its liabilities and whose borrowers are not excessively leveraged the properly calculated, risk‐adjusted deposit insurance premia are increasing functions of the level of interest rates. Sensitivity analyses also treat such factors as the bank's deposit to asset ratio, duration gap, interest volatility, the volatility of assets backing the bank loans, and the bank's borrowers' debt to equity ratio.     

The systematic pricing of market sentiment shock

ABSTRACT

We show that market sentiment shocks create demand shocks for risky assets and a systematic risk for assets. We measure a market sentiment shock as the unexpected portion of the University of Michigan Consumer Sentiment Index’s growth. This shock prices stock returns in arbitrage pricing theory framework at 1% after controlling for market, size, value, momentum, and liquidity risk factors. Its premium lowered the implied risk aversion by 97.9% to 11.46 between 1978 and 2009 in our sentiment consumption-based capital-asset-pricing model. Merton’s [1973. “An Intertemporal Capital Asset Pricing Model.” Econometrica 41: 867–887]. intertemporal capital-asset-pricing model reconfirms our finding that this market sentiment shock is a systematic risk factor that provides investment opportunities.     

Cash-Flow Valuation and Value at Risk

The cash-flow valuation method (CFVM) has been developed in Canada for the valuation of insurance company annuity products. Its range of application is expected to be extended shortly to the valuation of most other life insurance company products. The CFVM is based on the use of “best-guess” assumptions, supplemented by specific provisions for adverse deviations. In this paper, special attention is paid to the calculation of the provision for adverse deviations with respect to the interest rate risk. We show that the determination of this provision is the analog for life insurance and annuity policy liabilities of the calculation by banks of Value at Risk (VaR) with respect to portfolios of securities held for trading.     

Valuing an Early‐Stage Biotechnology Investment as a Rainbow Option

In an article published in this journal in 2003, Richard Shockley and three of his students presented a detailed valuation of an early‐stage biotechnology investment using a binomial lattice option pricing model. The article demonstrates how investments with multiple stages can be treated as “compound sequential options”—that is, as series of options in which investments in one option provide the opportunity to invest in the next in the series. In this article, the author uses the same business case analyzed by Shockley et al. to demonstrate how to value this early‐stage biotechnology investment by separately modeling the two types of risks: technology and product market. An option that has two distinct kinds of risk that develop differently over time is known as a “rainbow option.” The key adjustment to the option pricing model required to value such an option is that, instead of the standard binomial option pricing model with two outcomes at each point in time, the author uses a “quadranomial” option pricing model with four outcomes at each point in time. By distinguishing technology risks from product market risks and allowing them to develop differently over time, the author's analysis leads to a very different valuation and, indeed, a different decision about the initial investment than the one produced by Shockley's model.     

Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option

In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American‐style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature (“participation option,” henceforth). Then this price is split into the value of three components: the basic contract, the participation option, and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.     

Economic growth potential creating a real put and the resulting valuation of the firm

What do innovative new firms in our dynamic economy do to the value of existing firms? Using Schumpeter’s creative destruction idea, we expand the valuation model to incorporate these dynamics. Our model shows that these dynamics should have a greater effect on smaller firms, those in closer to perfect product market competition and those with less financial market following, as they get less market feedback for warning of new competition. This additional consideration in valuation is named the “real put” as it is an optionagainst value. Simply stated, it is an amount subtracted from a firm’s market value of capitalized earnings, plus any growth potential (that might create destructive competition against other producers) to get its net value. Following Schumpeter, new entrepreneurs and larger firms that mimic existing entrepreneurs are the innovators of new products and services. They create the real put against value in their potential competitors. We empirically test this using Morningstar’s “moat” classification of firms. We find firms with “wider moats” meaning greater product market power have much lower delisting rates that indicate smaller puts against value being exercised. While we are not the first in finance to view Schumpeter’s ideas, this is the first paper to consider its direct effect on valuation.