This study investigates the benefits and drawbacks of pension plan consolidation by quantifying the impact of mergers of heterogeneous plans on different stakeholders in a unique Canadian implementation of defined benefit plans. Using a comprehensive framework that combines a realistic economic scenario generator, a stochastic mortality model that captures differences among subpopulations, a cost model with economies of scale, and a dynamic asset allocation methodology, we evaluate the combined effect of asset- and liability-side changes on three groups of measures: plan-related risk measures assessing profits from an economic capital perspective, consumption-based metrics to understand the impact on members, and contribution risk measures capturing the risk from the employer’s viewpoint. We apply the framework to a hypothetical and empirically relevant merger and find that consolidation is favorable under most circumstances: the positive impacts of better diversification and economies of scale continue to outweigh the negative effects of heterogeneity even when the merging plans have different mortality expectations, different maturity levels, or modest differences in initial funded ratios.

We examine the impact of asset allocation and contribution rates on the risk of defined benefit (DB) pension schemes, using both a run-off and a shorter 3-year time horizon. Using the 3-year horizon, which is typically preferred by regulators, a high bond allocation reduces the spread of the distribution of surplus. However, this result is reversed when examined on a run-off basis. Furthermore, under both the 3-year horizon and the run-off, the higher bond allocation reduces the median level of surplus. Pressure on the affordability of DB schemes has led to widespread implementation of the so-called de-risking strategies, such as moving away from predominantly equity investments to greater bond investments. If the incentives produced by shorter term risk assessments are contributing to this shift, they might be harming the long-term financial health of the schemes. Contribution rates have relatively lower impact on the risk.

Insurance companies make extensive use of Monte Carlo simulations in their capital and solvency models. To overcome the computational problems associated with Monte Carlo simulations, most large life insurance companies use proxy models such as replicating portfolios (RPs). In this paper, we present an example based on a variable annuity guarantee, showing the main challenges faced by practitioners in the construction of RPs: the feature engineering step and subsequent basis function selection problem. We describe how neural networks can be used as a proxy model and how to apply risk-neutral pricing on a neural network to integrate such a model into a market risk framework. The proposed model naturally solves the feature engineering and feature selection problems of RPs.

The relationship between sex workers and their clients is generally characterized as being based entirely on the direct exchange of sexual favours for money. However, this received wisdom cannot account for a nation such as China which attaches significant value to “face,” social status and interpersonal dignity. This paper draws parallels with high-end sex workers elsewhere in Asia as well as globally. With a focus on the high-end sector, I examine how workers and their clients engage not only in pecuniary transactions but also in genuinely intimate and non-remunerative relationships. High-end sex workers make use of their earned economic capital to acquire cultural capital, and use online apps as marketing tools to target local elites and expats to forge longer-term intimate relationships. Male clients in more commercialized, post-industrial cities in China continue to seek diverse types of sexual experiences, with some clients seeking genuine intimacy. Furthermore, I explore how Chinese and foreign clients overcome social barriers to develop such relationships with sex workers. Building on this sociocultural perspective, this paper analyses ethnographically both sides of the female sex worker–client relationship in high-end karaoke lounges and bars in Dongguan, southern China.

With the advent of formal regulatory requirements for rigorous risk-based, or economic, capital quantification for the financial risk management of banking and insurance sectors, regulators and policy-makers are turning their attention to the pension sector, the other integral player in the financial markets. In this paper, we analyse the impact of applying economic capital techniques to defined benefit pension schemes in the United Kingdom. We propose two alternative economic capital quantification approaches, first, for individual defined benefit pension schemes on a stand-alone basis and then for the pension sector as a whole by quantifying economic capital of the UK’s Pension Protection Fund, which takes over eligible schemes with deficit, in the event of sponsor insolvency. We find that economic capital requirements for individual schemes are significantly high. However, we show that sharing risks through the Pension Protection Fund reduces the aggregate economic capital requirement of the entire sector.

The UK Pension Protection Fund (PPF) was established in April 2005 to protect the pensions of members of UK private sector defined benefit pension schemes which have insufficient assets and whose corporate sponsor fails. The Fund takes over the pension scheme assets and assumes responsibility for the payment of compensation to the former members of the scheme. The PPF is funded by a levy on the population of eligible schemes. This paper discusses the application of Enterprise Risk Management principles and techniques to the unique situation of the PPF. The elements of the financial management of the Fund have been developed by reference to practice within proprietary insurance institutions and within pension funds. The paper will be of interest and, we hope, of some value to students, researchers and analysts and also to the PPF's own stakeholder groups that have a stake in an effective pension protection regime.

We undertake a mathematical clarification of the QIS5 proposal for the calculation of the Motor Third Party Liability (MTPL) man-made catastrophe risk capital in terms of two more general models. The QIS5 model assumption implies that the total loss consists of a single catastrophe claim in case it occurs during the next one-year insurance time period. However, the total loss should instead be dynamically modelled by a sequence of claims of varying size that follow a compound Poisson Pareto model, which is our first alternative model. A second possibility also takes into account the effect of investments, whose financial return process follows a Black-Scholes-Merton model. If one excludes limits of coverage, then asymptotically as the total loss increases without limits the first model is equivalent to the model assumption obtained from the QIS5 assumption by replacing a single catastrophe claim by the total loss. In other words, the QIS5 simple model is justified as limiting asymptotic approximation to the classical compound Poisson Pareto model. Conversely, an asymptotic approximation to the VaR economic capital from this model identifies with a modified QIS5 CAT formula. The inclusion of limits of coverage is also analyzed. In this situation we obtain new simple closed-form implementations of the economic capital formulas.

This article considers the amount of economic capital that defined benefit (DB) pension schemes potentially need to cover the risks they are running. A real open scheme, the Universities Superannuation Scheme, is modelled and used to illustrate our results and, as expected, economic capital requirements are large. We discuss the appropriateness of these results and what they mean for the DB pension scheme industry and their sponsors. The article is particularly pertinent following the recent European Commission Green Paper on the future of European pensions systems, its call for advice on reviewing the Institutions for Occupational Retirement Provision Directive and the introduction of the Basel 2 and Solvency 2 risk-based regulatory regimes for banking and insurance, respectively.

This paper covers a number of different topics related to the measurement and modelling of dependency within economic capital models. The scope of the paper is relatively wide. We address in some detail the different approaches to modelling dependencies ranging from the more common variance-covariance matrix approach, to the consideration of the use of copulas and the more sophisticated causal models that feature feedback loops and other systems design ideas.

There are many data and model uncertainties in modelling dependency and so we have also endeavoured to cover topics such as spurious relationships and wrong-way risk to highlight some of the uncertainties involved.

With the advent of the internal model approval process under Solvency II, senior management needs to have a greater understanding of dependency methodology. We have devoted a section of this paper to a discussion of possible different ways to communicate the results of modelling to the board, senior management and other interested parties within an insurance company.

We have endeavoured throughout this paper to include as many numerical examples as possible to help in the understanding of the key points, including our discussion of model parameterisation and the communication to an insurance executive of the impact of dependency on economic capital modelling results.

The economic capital model can be seen as a combination of two key components: the marginal risk distribution of each risk and the aggregation methodology which combines these into a single aggregate distribution or capital number. This paper is concerned with the aggregation part, the methods and assumptions employed and the issues arising, and not the determination of the marginal risk distributions which is equally of importance and in many cases equally as complex.

The draft paper sets out the authors' views of what good practice for the actuarial aspects of internal models will look like in 2012, the year Solvency II is expected to be implemented. Actuaries working on internal models can expect to have to follow such practices if their internal models are to be approved for use in calculating regulatory capital. The paper is therefore relevant for actuaries who plan to work on internal model implementation for Solvency II.

Moreover, the risk quantification techniques discussed in the paper can also be used in the Own Risk Solvency Assessment (ORSA) process also required by Solvency II. The paper is therefore relevant to actuaries working in companies that are not planning to apply to use an internal model.

The paper covers both life and non-life insurance and reinsurance, and reviews current practice as well as setting out possible future practice. This leads to identification of areas for research by the Profession to prepare for 2012 and an indication of the directions this work might take.

The paper is effectively a work in progress, and readers should ask themselves what they should do in response to the ideas discussed.

The focus of the paper is non-profit lifetime annuities in the UK. Annuity insurers have been faced with, or have initiated, an unprecedented amount of change during the last decade, and rapid change is still continuing. We draw out implications for the actuarial management of the business, arising from the evolution of: longevity risk assessment and management, investment strategy and operations, financial reporting, and enterprise risk management. We discuss Solvency II in some technical depth, analysing the proposed rules for technical provisions and solvency capital requirement.

It is known that the partial stop-loss contract is an optimal reinsurance form under the VaR risk measure. Assuming that market premiums are set according to the expected value principle with varying loading factors, the optimal reinsurance parameters of this contract are obtained under three alternative single and joint party reinsurance criteria: (i) strong minimum of the total retained loss VaR measure; (ii) weak minimum of the total retained loss VaR measure and maximum of the reinsurer's expected profit; (iii) weak minimum of the total retained loss VaR measure and minimum of the total variance risk measure. New conditions for financing in the mean simultaneously the cedent's and the reinsurer's required VaR economic capital are revealed for situations of pure risk transfer (classical reinsurance) or risk and profit transfer (design of internal reinsurance or reinsurance captive owned by the captive of a corporate firm).

Capital and cost of capital form a bridge between the insurance firm and the financial markets. The term capital is used in various ways. In current parlance, economic capital is frequently used to mean capital calculated using a risk-based measure which is independent of the regulatory requirements. In this paper we discuss the concept of target capital, where the firm takes account of three different approaches to risk appetite: regulatory capital plus a buffer; rating agency views; and the views of shareholders, where they make commitments to customers and wish to protect franchise value. We describe how, when blending these views, the firm needs to understand the trade-offs between too high and too low amounts of capital, with reference to the double taxation burden, insurance gearing (leverage of premiums to capital ratio), and the impact of the firm's credit rating on maximising franchise value. We then discuss the main drivers of the cost of capital, which we define as the required total return on the market value of the firm, as determined by reference to the opportunity cost of alternative investments of equivalent risk. We explain that, because the stock market value of the firm is not the same as the capital held inside the firm, the cost of capital derived from external studies cannot be directly applied to internal measures of target return such as return on equity (ROE); it is necessary to translate between the two measures. We separate the risk of the firm between the investment risk and the insurance risk. We describe the frictional costs of investing in an insurance firm, and explain the role of parameter and model risk arising from the uncertainty of the future claim costs of the firm. We describe the findings of two studies of the actual historical stock market returns of United States P&C companies. One of them suggests that applying the Fama-French model produces higher and more accurate cost of capital estimates than the capital asset pricing model (CAPM) method. This is explained by linking the price to book ratio to the costs of financial distress, which are particularly important for general insurance firms, given the influence of insurance strength ratings from the rating agencies. Finally, we attempt to estimate the risk load required in premiums to compensate investors for the elements of cost of capital which we have described, in a way that combines the financial economic approaches to insurance target returns with the traditional actuarial approaches to assessing the risks in the insurance business.

The Solvency II Directive mandates insurance firms to value their assets and liabilities using market consistent valuation. For many types of insurance business Economic Scenario Generators (ESGs) are the only practical way to determine the market consistent value of liabilities. The directive also allows insurance companies to use an internal model to calculate their solvency capital requirement. In particular, this includes use of ESG models. Regardless of whether an insurer chooses to use an internal model, Economic Scenario Generators will be the only practical way of valuing many life insurance contracts. Draft advice published by the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS) requires that insurance firms who intend to use an internal model to calculate their capital requirements under Solvency II need to comply with a number of tests regardless of whether the model (or data) is produced internally or is externally sourced. In particular the tests include a ‘use test’, mandating the use of the model for important decision making within the insurer. This means that Economic Scenario Generators will need to subject themselves to the governance processes and that senior managers and boards will need to understand what ESG models do and what they don't do. In general, few senior managers are keen practitioners of stochastic calculus, the building blocks of ESG models. The paper therefore seeks to explain Economic Scenario Generator models from a non-technical perspective as far as possible and to give senior management some guidance of the main issues surrounding these models from an ERM/Solvency II perspective.

The impact that asset allocation has on the economic capital and the risk adjusted performance of financial services firms is considered in this article. A stochastic modelling approach is used in conjunction with a life insurance annuity firm illustrative example. It is shown that traditional solvency driven deterministic approaches to financial services firm asset allocation can yield sub optimal results in terms of minimising economic capital or maximising risk adjusted performance. Our results challenge the conventional wisdom that the assets backing life insurance annuities and financial services firm capital should be invested in low risk, bond type, assets. Implications for firms, customers, capital providers and regulators are discussed.

The impact that capital structure and capital asset allocation have on financial services firm economic capital and risk adjusted performance is considered. A stochastic modelling approach is used in conjunction with banking and insurance examples. It is demonstrated that gearing up Tier 1 capital with Tier 2 capital can be in the interests of bank Tier 1 capital providers, but may not always be so for insurance Tier 1 capital providers. It is also shown that, by allocating a bank or insurance firm’s Tier 1 and Tier 2 capital to higher yielding, more risky assets, risk adjusted performance can be enhanced. These results are particularly pertinent with the advent of the new Basel 2 and Solvency 2 risk based capital initiatives, for banks and insurers respectively.