Determinants of Actuarial Valuation Method Changes for Pension Funding and Reporting: Evidence from the UK

This study examines various factors that potentially explain cross‐sectional variations in UK corporate managerial discretion to switch towards a market‐based actuarial pension valuation method for pension funding and reporting purposes. Evidence is based on accounting, actuarial and share market data for an industry‐matched pair sample of 90 UK firms. Consistent with our hypotheses we find that companies have a greater propensity to switch actuarial methods if they use lower discount rates, lower flow funding ratios and sponsor larger pension plans in the pre‐switch valuation year. These findings are consistent with the traditional perspective, which implies that UK corporate switching decisions are explained by characteristics of their defined benefit pension funds. The results run contrary to the findings of earlier US based studies that find that such choices can be explained from an alternative corporate financial perspective.     

A data and digital-contracts driven method for pricing complex derivatives

Abstract

In this paper, we propose a data and digital-contracts driven (DDCD) method for pricing various complex options. The DDCD method is a combination of nonparametric and parametric methods. In general, nonparametric data driven methods use observed data as training data of a learning network directly. Different from these, in the proposed DDCD method, some European-style digital contracts (DCs) of the underlying assets are added as auxiliary information to guide the learning process of the pricing formula. The DCs can be obtained by using the observed data according to parametric methods. Thus, the DCs are actually used as the hints of the pricing formula, and then the DDCD method has superior pricing accuracy to the common data driven method in practical applications. Some Monte Carlo simulation experiments are performed and the results demonstrate that the proposed method not only has the advantages of generalization and superior accuracy, as the non-parametric method has, but also has the property of robustness to financial data with noise, as the parametric method has.     

Calculating Funding Premiums for Universal Life Insurance

Abstract

This paper provides a brief overview of the most commonly used methods for calculating the level gross premium required to achieve a specific funding target under a typical universal life product design. The first method described utilizes summation techniques from numerical analysis to derive a general accumulation formula. Manipulating this formula leads to an expression for the modal gross funding premium. The second method uses a partial Taylor series expansion to derive a variant of the Newton-Raphson iteration formula, which can be shown to provide second-order convergence to the funding premium. Other iteration methods providing first-order convergence are also described. A more detailed discussion of these methods and their applicability can be found in the author’s paper “Calculating Funding Premiums for Universal Life Insurance, with Examples,” scheduled to be published in the 1999–2000 volume of the TSA Reports.     

“Understanding Relationships Using Copulas,” Edward Frees and Emiliano Valdez,January 1998

Abstract

The problem of how to fund a defined-benefit pension plan is detached from the problem of how the cost of such a plan should be recognized. An approach to funding based on the projection of aggregate cash flows and the explicit modeling of new entrants is presented. It is shown that commonly used funding methods can be derived from the cash-flow approach. A generalized funding method for a plan subject to a stationary distribution of new entrants is derived. It is concluded that plan actuaries might need to modify existing funding methods to incorporate useful information about the expected number and distribution of future entrants.     

Fair Valuation of Equity-Linked Policies under Insurer Default Risk

Abstract

We consider the problem of computing the fair value of equity-linked policies with an interestrate guarantee when the insurer is subject to credit risk. The framework is developed based on modern financial theory using the no-arbitrage principle. In this context, an equity-linked policy is considered as a vulnerable contingent claim that expires before maturity if the firm asset value reaches a prespecified default threshold depending on the firm’s liabilities. We derive a closedform formula in a continuous-time environment to compute the fair value of the contract. We also develop a discrete-time model that allows us to address fair evaluation when the policy embeds a surrender option.     

Market-Consistent Valuation and Funding of Cash Balance Pensions

Cash balance pension benefits are accumulated at guaranteed crediting rates, usually based on yields on government securities. Viewed as a financial liability, the benefit is a form of interest rate derivative, which can be valued using financial models and theory. In this article, we derive the market value for a range of commonly used crediting rates, assuming the accrued benefit liability comprises the past contributions, allowing for full interest credits up to a known future retirement date. We use the Hull-White interest rate model to determine crediting rates and to determine the market value. We explore the risks associated with different crediting rate choices by evaluating the liability using market data from 1998 to 2013. We propose two other approaches to the accrued benefit. The first approach assumes the accrued benefit comprises past contributions with interest up to the valuation date, but no future interest credits. Future credits on past contributions are assumed funded through future contributions. The second method projects all contributions and interest to retirement and assumes equal units of accrual of this projected benefit in each year of service. We compare the three approaches through numerical examples.     

Loan collateral and financial reporting conservatism: Chinese evidence

We examine the relation between the use of collateral and financial reporting conservatism for a sample of Chinese firms. In the absence of flexibility in risk pricing through interest rates and strong contract enforcement in China, we find that lenders reduce collateral requirements from more conservative borrowers and that this negative relation is significantly moderated by borrowers’ poor credit quality and low asset tangibility. Our finding that conservatism can result in a tangible benefit in the form of lower collateral requirements indicates that lenders value financial reporting conservatism. However, the benefit from financial reporting conservatism is muted as lenders become more concerned about borrowers’ default risk or ability to pledge tangible assets as collateral against loans.     

新时期农户金融需求：现状、特点及对策——基于浙江的实证

通过对浙江省农户金融需求状况调查发现,农户的借贷需求呈现多样化特征,生活性资金需求比例较高;农户对信用社的了解和认知程度不高,民间借贷是农户融资的主要渠道;农户对其它金融需求的了解意愿比较强烈。因此,地方政府和金融监管部门对民间金融应积极引导,加强监管,使其成为正规金融的有益补充。而作为担当＂支农主力军＂角色的农村信用社应深化改革,开发多样性信贷产品,满足农户多样化的金融需求。最后还要通过金融知识下乡等方式,让农户了解金融常识。     

Do Macro-economic Crises Determine Accounting Value Relevance?

Abstract

We investigate whether the value relevance of earnings and book values in Turkey significantly changed across periods of financial uncertainty. Our enquiry differs from the mainstream literature that posits a unidirectional association determined by the ‘quality’ of individual firm accounts towards price. We find divergence in accounting value relevance components across the 1997–2012 period. Dominant value relevance shifts from earnings and negative interest rates in hyper-inflation, to the balance sheet after IFRS in 2005. On the other hand, the global financial crisis (GFC) is associated with diminished accounting value relevance for all variables. Policy issues are raised about value relevance consistency, the use of negative (low) interest rates as fiscal policies and the asymmetric application of market based valuations in emerging economies.     

The emergence of temporal correlations in a study of global economic interdependence

Abstract

We develop a simple firm-based automaton model for global economic interdependence of countries using modern notions of self-organized criticality and recently developed dynamical renormalization-group methods. We demonstrate how extremely strong statistical correlations can naturally develop between two countries even if the financial interconnections between those countries remain very weak. Potential policy implications of this result are also discussed.     

Financial Economics and Actuarial Practice

Abstract

Starting in the United Kingdom and continuing through the U.S. and Canadian actuarial professions, proponents of financial economics have been forcefully promoting a review of traditional actuarial practices and training. In particular, the financial theories first proposed by Modigliani and Miller and subsequently developed by others have been used to highlight serious weaknesses in typical actuarial thinking. In summary, it is claimed that much actuarial advice wrongly specifies value, that guidelines and standards need radical revision, and that traditional actuarial intuition suffers in comparison to newer modes of thought adopted by other professions.

This paper examines concepts from both financial economics and actuarial science as applied to defined benefit schemes using a simple discounted cash-flow framework as a reference point. The general finding is that many standard modes of actuarial thought are, in fact, indefensible when examined with the tools and techniques of financial economics. The call for revision of actuarial training and practices is credible and necessary.

However, the paper also touches upon areas where a heavy-handed application of finance theory could be misguided due to limitations in the simple financial economic models presented. It concludes that financial economics should be carefully integrated into actuarial thought rather than appended to existing actuarial theory or inserted as a wholesale replacement.     

Social Security

Abstract

The U.S. Social Security program (Old-Age, Survivors, and Disability Insurance) was enacted in 1935, long after many European nations had instituted similar ones. The driving force for such action was the Great Depression of the early 1930s, which had pushed many persons into poverty. The program was not intended to solve the immediate problem (which instead was handled by federal funding of state public assistance plans), but rather as an initial step of preventive action for the long run.

The current financial status of the Social Security program is excellent over the short range, but very likely a significant, although not overwhelming, problem is present as to the long range. Various proposals to remedy the situation are examined, some merely maintaining the existing character of the program but reducing benefit costs and/or increasing its income, and others reducing its scope by partially or wholly privatizing it.     

Long guarantees with short duration: the rolling annuity

We present a new type of with-profits annuities which offer lifelong, yet hedgeable, guarantees. The rolling annuity gives a minimum lifelong guarantee at the time of contribution complemented with a series of guaranteed increases prior to retirement. Importantly, the initial guarantee and the subsequent increases are all set at prevailing market rates and hence are not known in advance. The structure of the guarantee implies that, prior to the last increase, the liability is equivalent to a zero-coupon bond maturing at the next increase and can therefore easily be hedged in the financial markets. Furthermore, the short duration implies that the financial and regulatory value will (essentially) coincide. We show financial fairness and we derive the reserve and thereby the hedging strategy. We also consider longevity risk, the duration profile, and report on a simulation study of the real value of the final payout.     

The Iterated Cte

Abstract

In this paper we present a method for defining a dynamic risk measure from a static risk measure, by backwards iteration. We apply the method to the conditional tail expectation (CTE) risk measure to construct a new, dynamic risk measure, the iterated CTE (ICTE). We show that the ICTE is coherent, consistent, and relevant according to the definitions of Riedel (2003), and we derive formulae for the ICTE for the case where the loss process is lognormal. Finally, we demonstrate the practical implementation of the ICTE to an equity-linked insurance contract with maturity and death benefit guarantees.     

The impact of terrorism on financial markets: An empirical study

The main focus of this paper is to study empirically the impact of terrorism on the behavior of stock, bond and commodity markets. We consider terrorist events that took place in 25 countries over an 11-year time period and implement our analysis using different methods: an event-study approach, a non-parametric methodology, and a filtered GARCH-EVT approach. In addition, we compare the effect of terrorist attacks on financial markets with the impact of other extreme events such as financial crashes and natural catastrophes. The results of our analysis show that a non-parametric approach is the most appropriate method among the three for analyzing the impact of terrorism on financial markets. We demonstrate the robustness of this method when interest rates, equity market integration, spillover and contemporaneous effects are controlled. We show how the results of this approach can be used for investors’ portfolio diversification strategies against terrorism risk.     

Minimum Rate of Return Guarantees: The Danish Case

We analyze minimum rate of return guarantees for life-insurance (investment) contracts and pension plans with a smooth surplus distribution mechanism. We specifically model the smoothing mechanism used by most Danish life-insurance companies and pension funds. The annual distribution of bonus will be based on this smoothing mechanism after taking the minimum rate of return guarantee into account. In addition, based on the contribution method the customer will receive a final (non-negative) undistributed surplus when the contract matures. We consider two different methods that the company can use to collect payment for issuing these minimum rate of return guarantee contracts: the direct method where the company gets a fixed (percentage) fee of the customer's savings each year, e.g. 0.5% in Denmark, and the indirect method where the company gets a share of the distributed surplus. In both cases we analyze how to set the terms of the contract in order to have a fair contract between an individual customer and the company. Having analyzed the one-customer case, we turn to analyzing the case with two customers. We consider the consequences of pooling the undistributed surplus over two inhomogeneous customers. This implies setting up different mechanisms for distributing final bonus (undistributed surplus) between the customers.     

“Analysis of Incremental Returns of Canadian Mutual Funds”, J. F. Carrière; C. F. Hill,April 2001

Abstract

The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.     

“On the Merger of Two Companies,” Hans Gerber and Elias S. W. Shiu,July 2006

Abstract

Bankruptcy risk falls to pension plan participants if a plan sponsor fails when a defined benefit (DB) pension plan is underfunded. This article examines the incidence of that risk and how it changes when public policy provides a guarantee fund. Although government-based guarantee funds are in a unique position to provide pension protection, primarily because of the extent to which the risk of sponsor default is systematic in nature, a looming question is the extent to which such guarantees are exposed to moral hazard. The article focuses on that question using data from four Canadian provinces, including one (Ontario) that operates a guarantee fund for pensions. The findings show that plan assets per DB-plan participant increase with the earnings of workers and decrease with higher unemployment, and that level of assets also is moderated by the influence of taxes, with higher plan assets observed when and where tax rates are higher. Plans in Ontario had on average $20,035 less in asset value per participant, and Ontario plans covered by the guarantee fund had an average of $16,497 less per participant than other Canadian DB plans not backed by a guarantee fund. A separate model finds the presence of a guarantee fund to be one of a very small number of variables significant in explaining variability in the plans’ funded ratios. These empirical results are consistent with the existence of moral hazard.     

Computation of Multivariate Barrier Crossing Probability and its Applications in Credit Risk Models

Abstract

In this paper we consider computational methods of finding exit probabilities for a class of multivariate diffusion processes. Although there is an abundance of results for one-dimensional diffusion processes, for multivariate processes one has to rely on approximations or simulation methods. We adopt a Large Deviations approach to approximate barrier crossing probabilities of a multivariate Brownian Bridge. We use this approach in conjunction with simulation methods to develop an efficient method of obtaining barrier crossing probabilities of a multivariate Brownian motion. Using numerical examples, we demonstrate that our method works better than other existing methods. We mainly focus on a three-dimensional process, but our framework can be extended to higher dimensions. We present two applications of the proposed method in credit risk modeling. First, we show that we can efficiently estimate the default probabilities of several correlated credit risky entities. Second, we use this method to efficiently price a credit default swap (CDS) with several correlated reference entities. In a conventional approach one normally adopts an arbitrary copula to capture dependency among counterparties. The method we propose allows us to incorporate the instantaneous variance-covariance structure of the underlying process into the CDS prices.     

Pricing Dynamic Investment Fund Protection

Abstract

We consider an investment fund whose unit value is modeled by a geometric Brownian motion. Different forms of dynamic investment fund protection are examined. The basic form is a guarantee that instantaneously provides the necessary payments so that the upgraded fund unit value does not fall below a protected level. A closed form expression for the price of such a guarantee is derived. This result can also be applied to price a guarantee where the protected level is an exponential function of time. Moreover, it is explicitly shown how the protection can be generated by construction of the replicating portfolio. The dynamic investment fund protection is compared with the corresponding put option, and it is shown that for short time intervals the ratio of the prices approaches 2. Finally, a more exotic guarantee is considered, where the protected level is a given percentage of the maximal observed fund unit value. Assuming that the protected level remains constant once the payments have started, we obtain a surprisingly simple formula for the price of a perpetual guarantee. Several numerical and graphical illustrations show how the theoretical results can be implemented in practice.