# 1 Introduction

All countries are exposed and vulnerable to natural disasters.<sup>1</sup> Exposure is mostly determined by geographic characteristics, vulnerability by policies, and depends on levels of economic development. Indeed, richer countries have more resources to finance risk mitigation activities in preparation for, or reconstruction activities in the aftermath of, a shock. This may well explain why the cost of the recent terrible earthquake (both in terms of human lives and economic costs) was much larger in Haiti than in Chile and this despite the fact that the latter earthquake was stronger.

If countries differ in their exposure and vulnerability to natural disasters, should they deal with them differently? What are the pros and cons of purchasing catastrophe insurance versus doing nothing and/or relying on ex-post lending facilities such as the ones offered by international financial institutions? To answer these important questions, this paper presents a simple model that sheds some new light on the main tradeoffs that countries face in making such diffi cult choices.

It is well known<sup>2</sup> that market insurance, if reasonably priced, is the most effective way for risk adverse agents to cope with large and rare events. This is true for individuals as well as for sovereigns. Indeed, there are a few recent examples of countries that insured themselves against natural catastrophes:<sup>3</sup> In May 2006, the Mexican government issued a US 160 million dollar parametric catastrophe bond to finance rescue and rebuilding in the case a major earthquake hits some densely populated areas of the country;<sup>4</sup> in 2007, a pool of Caribbean countries developed a Caribbean Catastrophe Risk Insurance Facility (CCRICF) that facilitates their access to the insurance market. However, catastrophe insurance is expensive and even in the most successful cases, such as the two we just discussed, the cost of coverage turned out to be a multiple of the fair price (around three times in either case).<sup>5</sup> Why is insurance so costly? Several reasons are invoked, including supply-side constraints induced by either agency costs or adverse selection, problems of information opacity of tail events, coordination failures,<sup>6</sup> and oligopolistic practices. While the securitization<sup>7</sup> of catastrophic risk through the issuance of catastrophe bonds may in the future induce greater market discipline, until now it has fallen short of reducing the costs of insurance to actuarially fair levels.<sup>8</sup> If insurance is so expensive, why do countries still buy it? One reason could be risk aversion; another could be the presence of concavities in the production function and/or convexities in the borrowing cost function that create hedging opportunities as in Froot et al. (1993). While both these assumptions may play an important role for the demand of insurance, nonetheless we think that they only partially justify why a

> 1 By exposure we denote the probability of being hit by a natural disaster and by vulnerabilty the expected loss associated with any of such disasters.

> 2 See Elrich and Becker (1972).

> 3 See Hofman and Brukoff (2006) for a survey of the insurance opportunities available to developing countries against natural disasters.

> 4 This was the the first tranch of a 450 milion US dollars insurage coverge plan. Payment are triggered if a earthquake of magnitude 7.5 or 8 hits some predefined zones of the country. See Nell and Richter (2004) for a discussion of the of parametric insurance, that is of insurance policies with payments linked to measurable events such as the magnitude of an earthquake, or the wind-speed of an hurricane.

> 5 Note that a loading equal to two to three times the fair price is considerably lower than industry averages that range from 5 to 6 times expected outlays.

> 6 See Ibragimov et al. (2008)

> 7 For a comprehensive discussion of the market for catastrophe risk, see Froot (2001).

> 8 For a discussion of the securitization of catastrophe risk and the development of a catastrophe bond market, see Doherty (1997).

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