Portfolio optimization in the catastrophe space (original) (raw)

Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks

A catastrophe may affect different locations and produce losses that are rare and highly correlated in space and time. It may ruin many insurers if their risk exposures are not properly diversified among locations. The multidimentional distribution of claims from different locations depends on decision variables such as the insurer's coverage at different locations, on spatial and temporal characteristics of possible catastrophes and the vulnerability of insured values. As this distribution is analytically intractable, the most promising approach for managing the exposure of insurance portfolios to catastrophic risks requires geographically explicit simulations of catastrophes. The straightforward use of so-called catastrophe modeling runs quickly into an extremely large number of "what-if" evaluations. The aim of this paper is to develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision making on coverages of losses, profits, stability, and survival of insurers. We establish connections between ruin probability and the maximization of concave risk functions and we outline numerical experiments.

The risk implications of insurance securitization: The case of catastrophe bonds

Journal of Corporate Finance, 2014

Catastrophe (Cat) bonds are insurance securitization vehicles which are supposed to transfer catastrophe-related underwriting risk from issuers to capital markets. This paper addresses key, unanswered questions concerning Cat bonds and offers the following results. First, our findings show firms that issue Cat bonds exhibit less risky underwriting portfolios with less exposure to catastrophe risks and overall less need to hedge catastrophe risk. These results show that the access to the market for insurance securitization is easiest for firms with less risky portfolios. Second, firms that issue Cat bonds are found to experience a reduction in their default risk relative to non-issuing firms and our results, therefore, demonstrate that Cat bonds provide effective catastrophe hedging for issuing firms. T h i r d , firms with less catastrophe exposure, increase their catastrophe exposure following an issue. Therefore, our paper cautions that the ability to hedge catastrophe risk causes some firms to seek additional catastrophe risk.

Catastrophe risk management with counterparty risk using alternative instruments

Insurance Mathematics & Economics, 2010

Since weather-related disasters have an upward trend-cycle movement and the global financial crisis has revealed the severity of counterparty risk, this study reinvestigates and incorporates the catastrophe characteristics and counterparty risk into the valuation of catastrophe products. First, the excess of loss reinsurance is traditionally used to reduce catastrophe risk. Its premium is estimated under these catastrophe characteristics. Second, this paper looks into the price of catastrophe futures and spread option contracts that are based on a catastrophe index. The (re)insurer can apply these exchange-traded derivatives to reduce catastrophe risk without counterparty risk. Third, this paper takes counterparty risk into account to value catastrophe bonds and catastrophe equity puts. Thus, the fair valuations of these two instruments are revealed to the buyer.

Reinsurance versus securitization of catastrophe risk

Insurance: Mathematics and Economics, 2018

We provide a novel explanation for the low volume of securitization in catastrophe risk transfer using a signaling model. Relative to securitization, reinsurance features lower adverse selection costs because reinsurers possess superior underwriting resources than ordinary capital market investors. Reinsurance premia, however, reflect markups over actuarially fair premia due to the additional costs of underwriting. Insurers' risk transfer choices trade off the costs and benefits of reinsurance relative to securitization. In equilibrium, low risks are transferred via reinsurance, while intermediate and high risks are transferred via partial and full securitization, respectively. An increase in the loss size increases the trigger risk level above which securitization is chosen. Hence, catastrophe exposures, which are characterized by lower probabilities and higher severities, are more likely to be retained or reinsured rather than securitized.

Reinsurance or securitization: The case of natural catastrophe risk

Journal of Mathematical Economics, 2014

We investigate the suitability of securitization as an alternative to reinsurance for the purpose of transferring natural catastrophe risk. We characterize the conditions under which one or the other form of risk transfer dominates using a setting in which reinsurers and traders in financial markets produce costly information about catastrophes. Such information is useful to insurers: along with the information produced by insurers themselves, it reduces insurers' costly capital requirements. However, traderswho seek to benefit from trading in financial markets may produce 'too much' information,thereby making risk transfer through securitization prohibitively costly.

Valuation of catastrophe reinsurance with catastrophe bonds

Insurance: Mathematics and Economics, 2007

This study develops a contingent-claim framework for valuing a reinsurance contract and examines how a reinsurance company can increase the value of a reinsurance contract and reduce its default risk by issuing catastrophe (CAT) bonds. The results also show how the changes in contract values and default risk premium are related to basis risk, trigger level, catastrophe risk, interest rate risk, and the reinsurer's capital position.

Securitization of Catastrophe Risk: New Developments in Insurance Linked Securities and Derivatives

2009

This paper discusses the most recent developments in insurance securitization and assesses the potential for growth in the insurance-linked securities (ILS) market and in insurance-linked derivatives. In particular, the authors analyze the motivations of security sponsors and investors to participate in the catastrophe (CAT)– linked capital market, and identify the key components of growth and its impediments. Finally, this article

Catastrophe Bonds and Reinsurance: The Competitive Effect of Information-Insensitive Triggers

Social Science Research Network, 2005

We identify a new benefit of index or parametric triggers. Asymmetric information between reinsurers on an insurer's risk affects competition in the reinsurance market: reinsurers are subject to adverse selection, since only high-risk insurers may find it optimal to change reinsurers. The result is high reinsurance premiums and crosssubsidization of high-risk insurers by low-risk insurers. A contract with a parametric or index trigger (such as a catastrophe bond) is insensitive to information asymmetry and therefore alters the equilibrium in the reinsurance market. Provided that basis risk is not too high, the introduction of contracts with parametric or index triggers

The allocation of catastrophe risk

Journal of Banking & Finance, 2002

The potential losses from catastrophes have led financial researchers to address the following questions: (1) to what extent is catastrophe risk being shared (insured) and is the allocation of catastrophe risk consistent with notions of optimal risk sharing? if not, what market imperfections hinder the efficient allocation of catastrophe risk? and (3) are there government policies or private market solutions that could lead to a more efficient allocation of catastrophe risk? This paper summarizes the research that has been conducted on these questions. Ó

Catastrophe Derivatives and Reinsurance Contracts: An Incomplete Markets Approach

SSRN Electronic Journal, 2000

We apply a recently developed new approach to the pricing of catastrophe derivatives to the valuation of a reinsurance contract. Since the payoff of that contract has the form of a vertical spread, our methodology is also applicable to the valuation of such spreads in other markets. We do not assume a fully diversifiable CAT event risk, but we assume, instead, that there exists a class of investors whose diversified portfolios return is negatively affected by the occurrence of the CAT event. We derive bounds for a reinsurance contract with a non-convex payoff using recent results from the option pricing literature; we also show that these bounds are tighter than the ones arising from a combination of the bounds of the options forming the spread. We adopt a recursive discrete time approach as more realistic for the class of problems that we examine, and we value numerically the reinsurance contract with real data from hurricane landings in Florida. Last, we show that the limiting pricing kernels defining the bounds for derivative assets of this type are crucially dependent on the shape of the derivatives payoff function and do not have a closed form expression.