For some time now, Solvency II requires that insurance companies calculate minimum capital requirements to face the risk of insolvency, either in accordance with the Standard Formula or using a full or partial Internal Model. An Internal Model must be based on a market-consistent valuation of assets and liabilities at a 1-year time span, where a real-world probabilistic structure is used for the first year of projection. In this paper, we describe the major risks of a non-life insurance company, i.e. the non-life underwriting risk and market risk, and their interactions, focusing on the non-life premium risk, equity risk, and interest rate risk. This analysis is made using some well-known stochastic models in the financial-actuarial literature and practical insurance business, i.e. the Collective Risk Model for non-life premium risk, the Geometric Brownian Motion for equity risk, and a real-world version of the G2++ Model for interest rate risk, where parameters are calibrated on current and real market data. Finally, we illustrate a case study on a single-line and a multi-line insurance company in order to see how the risk drivers behave in both a stand-alone and an aggregate framework.

Defined benefit pension funds invest in illiquid asset classes for return, diversification or liability hedging reasons. So far, little is known about factors influencing how much they invest in illiquid assets. We conjecture that liquidity and capital requirements are pivotal in this decision. Short-term pension payments and margining on derivative contracts generate liquidity requirements, while regulations impose capital requirements. Consistent with our model we empirically find that these requirements create a hump-shaped impact of liability duration on the fraction of risky assets invested in illiquid assets. Further, we report that pension fund size, type, and funding ratio impact illiquid assets allocations.

For insurance companies in Europe, the introduction of Solvency II leads to a tightening of rules for solvency capital provision. In life insurance, this especially affects retirement products that contain a significant portion of longevity risk (e.g., conventional annuities). Insurance companies might react by price increases for those products, and, at the same time, might think of alternatives that shift longevity risk (at least partially) to policyholders. In the extreme case, this leads to so-called tontine products where the insurance company’s role is merely administrative and longevity risk is shared within a pool of policyholders. From the policyholder’s viewpoint, such products are, however, not desirable as they lead to a high uncertainty of retirement income at old ages. In this article, we alternatively suggest a so-called tonuity that combines the appealing features of tontine and conventional annuity. Until some fixed age (the switching time), a tonuity’s payoff is tontine-like, afterwards the policyholder receives a secure payment of a (deferred) annuity. A tonuity is attractive for both the retiree (who benefits from a secure income at old ages) and the insurance company (whose capital requirements are reduced compared to conventional annuities). The tonuity is a possibility to offer tailor-made retirement products: using risk capital charges linked to Solvency II, we show that retirees with very low or very high risk aversion prefer a tontine or conventional annuity, respectively. Retirees with medium risk aversion, however, prefer a tonuity. In a utility-based framework, we therefore determine the optimal tonuity characterized by the critical switching time that maximizes the policyholder’s lifetime utility.

This paper focusses on some practical issues that can arise when developing methodologies for calculating benchmark figures for extreme market events, particularly in the context of the Financial Services Authority's ICAS regime. The paper limits discussion to equity and interest rate risks. Whilst not intended to constitute formal guidance, it is hoped that the material contained within the paper will be useful to practitioners. The paper acknowledges the role of prior beliefs in the choice of data to be used for modelling and its influence upon the ensuing results.

Advances in risk management capabilities should make it profitable for major banks to rely on internal credit ratings to calculate Basel II capital requirements (IRB approach). Firms and, more generally, market participants would benefit from the disclosure of these ratings. Banks, however, have no incentives to make their rating data publicly available. This paper proposes a regulatory framework to efficiently solve this incentive issue. It first shows that there are benefits in requiring the disclosure of internal ratings. In particular, it would reduce the cost of capital for both large and small borrowers while facilitating investor diversification.

To be sure, internal rating disclosure would also have its costs. For example, market volatility may increase, whereas lender-borrower relationships may suffer. This paper argues that it is possible to design a regulatory framework under which the benefits of mandatory rating disclosure clearly outweigh its costs. Banks opting for the IRB approach would have to provide their internal ratings to one of several regional entities. The latter would consolidate the data collected and give each borrower a rating equal to the average of the ratings it gets from its lenders. The average rating would be disclosed to the public unless the borrower has opted for non-disclosure. Relying upon multiple regional entities may cause some uncertainty (a given firm may get diverging average ratings), but it would also reduce moral hazard effects and foster competition in the rating industry.