Wind derivatives are financial instruments designed to mitigate losses caused by adverse wind conditions. With the rapid growth of wind power capacity due to efforts to reduce carbon emissions, the demand for wind derivatives to manage uncertainty in wind power production is expected to increase. However, existing wind derivative literature often assumes normally distributed wind speed, despite the presence of skewness and leptokurtosis in historical wind speed data. This paper investigates how the misspecification of wind speed models affects wind derivative prices and proposes the use of the generalized hyperbolic distribution to account for non-normality. The study develops risk-neutral approaches for pricing wind derivatives using the conditional Esscher transform, which can accommodate stochastic processes with any distribution, provided the moment-generating function exists. The analysis demonstrates that model risk varies depending on the choice of the underlying index and the derivative’s payoff structure. Therefore, caution should be exercised when choosing wind speed models. Essentially, model risk cannot be ignored in pricing wind speed derivatives.

Conventional diagnoses of the 2007/8 Global Financial Crisis see it as “abnormal”, and then resort to explanations in terms of “irrational exuberance”, “animal spirits”, “herding behaviour” and so on. The prescription – “better regulation” – then follows automatically, as it has done after every such crisis, all the way back to tulipmania 400 years ago. But if there are different “seasons of risk”, and if financial sector actors are able to latch onto different risk-handling strategies, each appropriate to one of those seasons and inappropriate to the others, then we have a very different explanation: one in which, in contrast to both neoclassical and behavioural economics, rationality is no longer singular. This “anthropological” hypothesis has its roots in Mary Douglas’s book “How Institutions Think”, and the paper shows how it is well supported by historical evidence, agent-based modelling, and fieldwork among both financial sector firms and their regulators, as well as by parallels from ecology, organisation theory and evolutionary (i.e. Schumpeterian) economics.

This paper presents latest thinking from the Institute and Faculty of Actuaries’ Model Risk Working Party and follows on from their Phase I work, Model Risk: Daring to Open the Black Box. This is a more practical paper and presents the contributors’ experiences of model risk gained from a wide range of financial and non-financial organisations with suggestions for good practice and proven methods to reduce model risk. After a recap of the Phase I work, examples of model risk communication are given covering communication: to the Board; to the regulator; and to external stakeholders. We present a practical framework for model risk management and quantification with examples of the key actors, processes and cultural challenge. Lessons learned are then presented from other industries that make extensive use of models and include the weather forecasting, software and aerospace industries. Finally, a series of case studies in practical model risk management and mitigation are presented from the contributors’ own experiences covering primarily financial services.

A deep-deferred annuity is a deferred annuity where payments start very late in life, i.e. well after the normal retirement age. This annuity has received much attention lately as it was made accessible to 401(k) plans in the United States in 2014. By transferring the risk of outliving retirement savings at high ages to annuity providers, deep-deferred annuities provide annuitants with enhanced later-life financial security. However, the valuation of this annuity suffers from high uncertainty because the mortality data at high ages are sparse and possibly unreliable. In this paper, we use risk ratio to measure demographic risk in the valuation. Demographic risk is decomposed into the following four components: (1) mortality tail curve risk, (2) mortality improvement model risk, (3) parameter risk in mortality tail curves, and (4) parameter risk in mortality improvement rate models. Our quantitative analysis aims to provide insights into the development and risk management of deep-deferred annuities.

Taming the beast of uncertainty has been the grand project to which actuaries have dedicated much of their energy and skill over at least the last 50 years – roughly the time since, in Hans Bühlmann's (1989) famous term, “Actuaries of the Second Kind” emerged.

With the increasing use of complex quantitative models in applications throughout the financial world, model risk has become a major concern. Such risk is generated by the potential inaccuracy and inappropriate use of models in business applications, which can lead to substantial financial losses and reputational damage. In this paper, we deal with the management and measurement of model risk. First, a model risk framework is developed, adapting concepts such as risk appetite, monitoring, and mitigation to the particular case of model risk. The usefulness of such a framework for preventing losses associated with model risk is demonstrated through case studies. Second, we investigate the ways in which different ways of using and perceiving models within an organisation both lead to different model risks. We identify four distinct model cultures and argue that in conditions of deep model uncertainty, each of those cultures makes a valuable contribution to model risk governance. Thus, the space of legitimate challenges to models is expanded, such that, in addition to a technical critique, operational and commercial concerns are also addressed. Third, we discuss through the examples of proxy modelling, longevity risk, and investment advice, common methods and challenges for quantifying model risk. Difficulties arise in mapping model errors to actual financial impact. In the case of irreducible model uncertainty, it is necessary to employ a variety of measurement approaches, based on statistical inference, fitting multiple models, and stress and scenario analysis.

Longevity risk faced by annuity portfolios and defined-benefit pension schemes is typically long-term, i.e. the risk is of an adverse trend which unfolds over a long period of time. However, there are circumstances when it is useful to know by how much expectations of future mortality rates might change over a single year. Such an approach lies at the heart of the one-year, value-at-risk view of reserves, and also for the pending Solvency II regime for insurers in the European Union. This paper describes a framework for determining how much a longevity liability might change based on new information over the course of one year. It is a general framework and can accommodate a wide choice of stochastic projection models, thus allowing the user to explore the importance of model risk. A further benefit of the framework is that it also provides a robustness test for projection models, which is useful in selecting an internal model for management purposes.

Several important classes of liability are sensitive to the direction of future mortality trends, and this paper presents some recent developments in fitting smooth models to historical mortality-experience data. We demonstrate the impact these models have on mortality projections, and the resulting impact which these projections have on financial products. We base our work round the Lee-Carter family of models. We find that each model fit, while using the same data and staying within the Lee-Carter family, can change the direction of the mortality projections. The main focus of the paper is to demonstrate the impact of these projections on various financial calculations, and we provide a number of ways of quantifying, both graphically and numerically, the model risk in such calculations. We conclude that the impact of our modelling assumptions is financially material. In short, there is a need for awareness of model risk when assessing longevity-related liabilities, especially for annuities and pensions.

We analyze different types of guaranteed withdrawal benefits for life, the latest guarantee feature within variable annuities. Besides an analysis of the impact of different product features on the clients' payoff profile, we focus on pricing and hedging of the guarantees. In particular, we investigate the impact of stochastic equity volatility on pricing and hedging. We consider different dynamic hedging strategies for delta and vega risks and compare their performance. We also examine the effects if the hedging model (with deterministic volatility) differs from the data-generating model (with stochastic volatility). This is an indication for the model risk an insurer takes by assuming constant equity volatilities for risk management purposes, whereas in the real world volatilities are stochastic.

A major outcome of ERM activities in insurance companies has been the bringing together of all of the key risks in the company, to be managed collectively in a holistic fashion. The authors of this paper believe that an ERM framework also needs to look beyond the company, and have regard to the risk management needs of investors, from the point of view of the contribution of the insurance company to the overall risk and reward of their total investment portfolios. To meet these needs, the ERM framework needs to provide sufficient information on topics such as systematic risk, potential correlations of earnings from future new business with macroeconomic trends, other risks to franchise value, and sources of model risk within the company. The paper does not provide solutions for the issues described above; but limits itself to describing and discussing the direction for some important new initiatives in ERM activities.

All UK insurers exposed to longevity risk need to perform stress tests for their Individual Capital Assessment (ICA). Some have put in place deterministic models which are arguably too simple; others have developed stochastic models that can be demanding and complex.

This paper presents a simple model to turn any deterministic mortality scenario into a stochastic model. We propose a simple model of stochastic variation that is easy to explain and to implement, which could be an alternative to and/or complete some of the well known models. The model can be applied to any best estimates of future mortality rates, as it aims to describe how longevity behaves around the projected expected values.

The paper proposes a possible calibration on the England and Wales population mortality that produces a minimum indication of possible future variation and uses the results to validate the model's assumptions. Using sample portfolios and the stochastic model, we can simulate cash flows to determine the distribution of the net present values (NPV) of annuity outgo.

The three annual 2¼% interest coupons of the Winterthur Insurance convertible bond (face value Chf 4 700) will only be paid out if during their corresponding observation periods no major storm or hail storm on one single day damages at least 6 000 motor vehicles insured with Winterthur Insurance. Data for events, where storm or hail damaged more than 1 000 insured vehicles, are available for the last ten years. Using a constant-parameter model, the estimated discounted value of the three Wincat coupons together is Chf 263.29. A conservative evaluation, which accounts for the standard deviation of the estimate, gives a coupon value of Chf 238.25. However, fitting models which admit a trend or a change-point, leads to substantially higher knock-out probabilities of the coupons. The estimated discounted values of the coupons can drop below the above conservative value; a conservative evaluation as above leads to substantially lower values. Hence, already the model uncertainty is higher than the standard deviations of the used estimators. This shows the dominance of the model risk. Consistency, dispersion, robustness and sensitivity of the models are analysed by a simulation study.