Mortality-Indexed Annuities

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries, and especially its aggregate form, i.e. the risk of unsystematic changes to general mortality patterns, bears a large potential for accumulative losses for insurers. As obvious risk management tools such as (re)insurance or hedging are less suited to manage an annuity provider’s exposure to aggregate longevity risk, the current paper proposes a new type of life annuities with benefits contingent on actual mortality experience, and it also details actuarial aspects of implementation. Similar adaptations to conventional product design exist in investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience is found in German private health insurance so that the idea is not novel in general, but it is in the context of longevity risk. By not or re-transferring the systematic longevity risk insurers may avoid accumulative losses so that the primary focus in an extensive Monte-Carlo simulation is on the question of whether and to what extent such products are also advantageous for policyholders in contrast to a comparable conventional annuity product

Hedging Brevity Risk with Mortality-based Securities

In 2003, Swiss Re introduced a mortality-based security designed to hedge excessive mortality changes for its life book of business. The concern was apparently brevity risk, i.e., the risk of premature death. The brevity risk due to a pandemic is similar to the property risk associated with catastrophic events such as earthquakes and hurricanes and the security used to hedge the risk is similar to a CAT bond. This work looks at the incentives associated with insurance-linked securities. It considers the trade-offs an insurer or reinsurer faces in selecting a hedging strategy. We compare index and indemnity-based hedging as alternative design choices and ask which is capable of creating the greater value for shareholders. Additionally, we model an insurer or reinsurer that is subject to insolvency risk, which creates an incentive problem known as the judgment proof problem. The corporate manager is assumed to act in the interests of shareholders and so the judgment proof problem yields a conflict of interest between shareholders and other stakeholders. Given the fact that hedging may improve the situation, the analysis addresses what type of hedging tool would be best to use. We show that an indemnity-based security tends to worsen the situation, as it introduces an additional incentive problem. Index-based hedging, on the other hand, under certain conditions turns out to be beneficial and therefore clearly dominates indemnity-based strategies. This result is further supported by showing that for the same strike prices the current shareholder value is greater with the index-based security than the indemnity-based security

Vertical information content of nadir measurements of tropospheric NO2 from satellite

Poster presented at the EGU General Assembly 2014 in Vienna/Austria

Marshall-Peierls sign rule in frustrated Heisenberg chains

We consider the frustrated antiferromagnetic s=1 Heisenberg quantum spin chain with regard to the Marshall-Peierls sign rule (MPSR). By using exact diagonalization data we investigate the breakdown of the MPSR in dependence on frustration and compare our findings with data for s=1/2. We calculate a critical value of frustration J_2(crit) where the MPSR is violated. The extrapolation of this value to the infinite chain limit holds J_2(crit) approx. 0.016, lower than in the case of s=1/2 (J_2(crit) approx. 0.027). This points to a stronger influence of frustration in the case of s=1. Nevertheless the calculation of the weight of the Ising-states violating the MPSR shows that the MPSR holds approximately even for quite large frustration and may be used for numerical techniques.Comment: 4 pages (Latex), 2 Postscript figures, to be published in acta physica polonica A (European Conference 'Physics of Magnetism 99'

Catastrophe index-linked securities and reinsurance as substituties

The use of catastrophe bonds (cat bonds) implies the problem of the so called basis risk, resulting from the fact that, in contrast to traditional reinsurance, this kind of coverage cannot be a perfect hedge for the primary’s insured portfolio. On the other hand cat bonds offer some very attractive economic features: Besides their usefulness as a solution to the problems of moral hazard and default risk, an important advantage of cat bonds can be seen in the presumably lower transaction costs compared to (re)insurance products. Insurance coverage usually incurs costs of acquisition, monitoring and loss adjustment, all of which can be reduced by making use of the financial markets. Additionally, cat bonds are only weakly correlated with market risk, implying that in perfect financial markets these securities could be traded at a price including just small risk premiums. Although these aspects have been identified in economic literature, to our knowledge there has been no publication so far that formally addresses the trade-off between basis risk and transaction cost. In this paper, therefore, we introduce a simple model that enables us to analyze cat bonds and reinsurance as substitutional risk management tools in a standard insurance demand theory environment. We concentrate on the problem of basis risk versus transaction cost, and show that the availability of cat bonds affects the structure of optimal reinsurance contract design in an interesting way, as it leads to an increase of indemnity for small losses and a decrease of indemnity for large losses

Hedging Brevity Risk with Mortality-based Securities

In 2003, Swiss Re introduced a mortality-based security designed to hedge excessive mortality changes for its life book of business. The concern was apparently brevity risk, i.e., the risk of premature death. The brevity risk due to a pandemic is similar to the property risk associated with catastrophic events such as earthquakes and hurricanes and the security used to hedge the risk is similar to a CAT bond. This work looks at the incentives associated with insurance-linked securities. It considers the trade-offs an insurer or reinsurer faces in selecting a hedging strategy. We compare index and indemnity-based hedging as alternative design choices and ask which is capable of creating the greater value for shareholders. Additionally, we model an insurer or reinsurer that is subject to insolvency risk, which creates an incentive problem known as the judgment proof problem. The corporate manager is assumed to act in the interests of shareholders and so the judgment proof problem yields a conflict of interest between shareholders and other stakeholders. Given the fact that hedging may improve the situation, the analysis addresses what type of hedging tool would be best to use. We show that an indemnity-based security tends to worsen the situation, as it introduces an additional incentive problem. Index-based hedging, on the other hand, under certain conditions turns out to be beneficial and therefore clearly dominates indemnity-based strategies. This result is further supported by showing that for the same strike prices the current shareholder value is greater with the index-based security than the indemnity-based security.alternative risk transfer; insurance; default risk

Catastrophic events as threats to society: Private and public risk management strategies

Dramatic events in the recent past have drawn attention to catastrophe risk management problems. The devastating terrorist attacks of September 11th, 2001 incurred the highest insured losses to date. Furthermore, a trend of increasing losses from natural catastrophes appears to be observable since the late 1980s. The increase in catastrophe losses triggered intensive discussion about risk management of catastrophic risk, focusing on three issues. First, considering the loss potential of certain catastrophic events, the insurance markets' capacity does not seem to be sufficient. An approach to address this capacity issue can be seen in passing certain catastrophic risks to investors via securitization. Second, after the events of September 11, 2001, the government's role as a bearer of risk became an increasingly important issue. Finally, as has been recently demonstrated by the floods in Europe of August 2002, problems of protecting against catastrophic threats do not only exist on the supply side but also on the demand side. Thus policymakers are considering the establishment of mandatory insurance for fundamental risks such as flood and windstorm. This paper will address aspects of these three issues. In particular, we are concerned with the extent to which state or government involvement in the management of catastrophic risk is reasonable. --catastrophic risk,risk management,public-private partnership

Tax arbitrage in the German insurance market

In this paper we analyze the attractiveness of a so called mortality swap, which combines an immediate annuity and a whole life insurance contract, in the German insurance market. The analysis follows a methodology introduced by Charupat and Milevsky (2001). Using theoretical products based on actuarially fair calculation, we find that depending on the level of interest rates there exist significant arbitrage opportunities in particular for elderly and high income people which can mainly be explained by an inadequate and unsatisfactory tax legislation. Empirical results based on products offered in the market confirm these findings. --

Mortality-Indexed Annuities

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries, and especially its aggregate form, i.e. the risk of unsystematic changes to general mortality patterns, bears a large potential for accumulative losses for insurers. As obvious risk management tools such as (re)insurance or hedging are less suited to manage an annuity provider’s exposure to aggregate longevity risk, the current paper proposes a new type of life annuities with benefits contingent on actual mortality experience, and it also details actuarial aspects of implementation. Similar adaptations to conventional product design exist in investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience is found in German private health insurance so that the idea is not novel in general, but it is in the context of longevity risk. By not or re-transferring the systematic longevity risk insurers may avoid accumulative losses so that the primary focus in an extensive Monte-Carlo simulation is on the question of whether and to what extent such products are also advantageous for policyholders in contrast to a comparable conventional annuity product.Longevity risk; systematic risk; risk avoidance; mortality-indexed annuities

Improving risk allocation through cat bonds

Catastrophe bonds (cat bonds) often use index triggers, such as, for instance, parametric descriptions of a catastrophe. This implies the problem of the so-called basis risk, resulting from the fact that, in contrast to traditional reinsurance, this kind of coverage cannot be a perfect hedge for the primary's insured portfolio. On the other hand, cat bonds offer some very attractive economic features: Besides their usefulness as a solution to the problems of moral hazard and default risk, an important advantage of cat bonds can be seen in presumably lower risk premiums compared to (re)insurance products. Cat bonds are only weakly correlated with market risk, implying that in perfect financial markets these securities could be traded at a price including just small risk premiums. Furthermore, there is empirical evidence that risk aversion of reinsurers is an important reason for high reinsurance prices. In this paper we introduce a simple model that enables us to analyze cat bonds and reinsurance as substitutional risk management tools in a standard insurance demand theory environment. We concentrate on the problem of basis risk versus reinsurers' risk aversion and show that the availability of cat bonds affects the structure of an optimal reinsurance contract as well as the reinsurance budget. Primarily, reinsurance is substituted by index-linked coverage for large losses. --Insurance,Financial Markets,Decision Making and Risk