Financial models are fast becoming an essential tool of the modern reinsurance company, spurred on by the demands of shareholders and regulators. By Dr Peter England.

Insurers and reinsurers are in the business of accepting the risk of others for a suitable fee. It is perverse, therefore, that they often fail to understand their own risk profiles, sometimes setting aside insufficient capital to withstand losses to their exposures. This irony has not been lost on regulators and shareholders, who are increasingly losing patience with the industry and demanding a more professional and scientific approach to risk management. It is a global trend, aided partly by the gradual convergence of insurance and banking and, with it, a corresponding coming together of regulation. Put simply, the authorities have more faith in a risk-based approach applied to assessing the security of banks than in the solvency methods traditionally used for insurance and reinsurance. As a result, the rules are being rewritten, placing more demands on risk carriers.

Examples of this trend include:

  • the US-based National Association of Insurance Commissioners' (NAIC) risk-based capital system used as a benchmark for regulatory minimums;

  • the Lloyd's risk-based capital system for setting the capital requirements of Lloyd's members;

  • Canada's Dynamic Capital Adequacy Testing;

  • Australia's new risk-based Prudential Standards (where `the bar is now set much higher for insurers'); and

  • the UK's proposals for risk-based regulation focusing on financial strength and risk systems and controls, due to come into force early in 2004.

    The European Union, meanwhile, appears to be moving in the same direction as a result of its Solvency 2 review, which is expected to come to fruition in 2005 or after.

    Once the decision has been taken to go down the risk-based route, it leads inevitably to a greater use of stochastic models - that is to say, financial models that enable an insurer or reinsurer to analyse the full range of possible outcomes, both favourable and unfavourable. To quote the UK's Financial Services Authority, "stochastic models are fundamental to regulatory reform."

    Risk and capital
    Essentially, insurers have three choices when it comes to risk: mitigate it, transfer it or capitalise against it. Mitigating risk means trying to remove it completely, which might be possible for some elements of risk, such as identified operational risks. Risk transfer is self-explanatory, and a variety of mechanisms exist to help insurers transfer their risks to another party, such as traditional reinsurance or securitisation. Risks that cannot be mitigated or transferred must be capitalised against, and corporate governance dictates that company directors have ultimate responsibility for risk management.

    With a tougher line on corporate governance following the spectacular failure of several high-profile companies, the analysis of risk is firmly on the board's agenda at insurance companies. Questions such as, "How much capital is sufficient?" and "How should capital be allocated?" should be commonplace. Those questions are, easy to ask, but obtaining answers is not always straightforward in the absence of a sound risk analysis framework. Additional questions such as, "How much capital is released by reinsurance?" and, "What is an adequate price for risk transfer?" are also challenging.

    Modern risk analysis techniques tackle such problems by building financial models that simulate outcomes of specified risk factors that might occur in practice, from good to bad. Thousands of possible scenarios are considered, including the kind of extreme events that may never have occurred in the past. Possible risk factors might be standard insurance losses, catastrophe and large losses, asset returns, economic factors, operational risk losses and so on.

    It is also important to consider the dependence between these risk factors, where, for example, extreme results in several risk factors might occur at the same time. September 11 demonstrated, of course, a situation where extreme results in several types of risk occurred simultaneously. And indeed, the event has focused attention on the need to understand this type of dependency.

    This kind of analysis is called `stochastic modeling', and the risk profiles generated by these financial models can be used to answer the questions posed above. In fact, simulation modeling is not new - it is routinely used for modeling potential exposures to natural catastrophes - but its usefulness is increasingly being recognised for the analysis of other areas of risk.

    Simple answers to complex questions
    Apart from helping to satisfy the regulators, financial risk modeling can have profound business benefits, encouraging better informed management decisions. When carried out appropriately, it can lead to improvements in a number of areas, including:

  • capital adequacy and allocation;

  • reinsurance purchasing;

  • product and pricing strategy;

  • security ratings;

  • business expansion; and

  • mergers and acquisitions.

    Some of the larger reinsurers are taking this a step further, providing financial risk modeling services to their customers. Apart from increasing the stability of their client base, it gives them a better understanding of the risks they are accepting.

    Lloyd's - a case study
    As a case study, consider the risk profile of a large Lloyd's syndicate with four main business divisions: UK motor, worldwide commercial property, marine and aviation. Each business division has its own outwards reinsurance programme, and there is umbrella cover protecting against losses breaching the business division level programmes. The syndicate was interested in its risk profile in relation to its mix of business, and the efficacy of its reinsurance programme. The syndicate also wanted to be able to demonstrate a good understanding of its risks, and capital adequacy, in discussions with ratings agencies.

    To satisfy the syndicate's requirements, an internal risk model was built which simulated gross attritional, large and catastrophe losses to each line of business within each division. These were then passed through a model of the reinsurance programme for each division, then through the umbrella cover before finally being aggregated to provide an overall net risk profile to assess capital requirements and financial strength.

    Having determined the global risk profile and capital requirements, capital could be allocated back to divisional level. Table 1 shows the total capital required and allocation of capital by business division. Notice that the allocation methodology highlights the commercial property division as the key risk area. This reflects the fact that inwards catastrophe XL reinsurance formed the largest line of business. Also notice that the capital released by the umbrella reinsurance programme is shown as a negative capital requirement.

    The overall risk profile showed that the probability of capital being insufficient was less than 1%, but also showed the full extent of the potential downside.

    A by-product of the analysis was the ability to assess reinsurance efficacy by studying the risk profile of simulated losses to the various reinsurance programmes. Table 2 shows the average simulated cost (including reinstatements) and the average reinsurance recoveries for each layer of the aviation whole account XL programme.

    Notice that, as expected, the average cost is higher than the average recoveries, reflecting the cost of risk transfer, and that the highest layer is essentially sleep-easy cover. In this case, the profile of simulated losses to the reinsurance programme can be viewed from the perspective of the insured or the insurer, and can be used to calculate a suitable price for the risk transfer.

    Apart from studying capital requirements and allocation on a sound technical basis, and assessing reinsurance efficacy, the analysis had many other benefits.

    Simply thinking about the model structure required collecting information on the various reinsurance programmes, and obtaining suitable data to study large losses provided valuable information relating to the `big picture', the key risk areas and the methods used to control them. This highlighted areas where improvements could be made (for example, in modeling catastrophes), and areas where the reinsurance programme might need to be re-evaluated. It also aided communication between functions that hitherto had been largely independent.

    Understanding your risk profile
    In the case study, a complex financial simulation model was used to provide relatively straightforward answers to some difficult questions. It succeeded because the insurer gained a thorough understanding of its risk profile. The aim of this kind of analysis might be to keep regulators happy, but ideally it should underpin all of the key strategic decisions of an insurance or reinsurance company, particularly those relating to the deployment of resources. However, simulation modeling need not be reserved solely for such challenging problems; it is equally effective for smaller-scale problems, such as pricing individual contracts.

    Trying to understand a company's financial strengths and weaknesses without a suitable risk analysis framework is virtually impossible, particularly when dependencies between classes of business and key risk factors need to be considered. As a result, stochastic modeling is rapidly becoming the methodology of choice in quantifying risk management decisions. In 1995, the UK Government Actuary stated: "I believe that stochastic modeling is fundamental to our profession. How else can we seriously advise our clients and our wider public on the consequences of managing uncertainty in the different areas in which we work?"

    We are increasingly seeing his words come true.

    By Dr Peter England
    Dr Peter England is a senior consultant at Paratus Consulting, a jointly owned subsidiary of EMB and Miller Herbers Lehmann. He is a Visiting Fellow at City University's Department of Actuarial Science and Statistics in London.