Academic journal article Journal of Risk and Insurance

Pricing Mortality Securities with Correlated Mortality Indexes

Academic journal article Journal of Risk and Insurance

Pricing Mortality Securities with Correlated Mortality Indexes

Article excerpt

ABSTRACT

This article proposes a stochastic model, which captures mortality correlations across countries and common mortality shocks, for analyzing catastrophe mortality contingent claims. To estimate our model, we apply particle filtering, a general technique that has wide applications in non-Gaussian and multivariate jump-diffusion models and models with nonanalytic observation equations. In addition, we illustrate how to price mortality securities with normalized multivariate exponential titling based on the estimated mortality correlations and jump parameters. Our results show the significance of modeling mortality correlations and transient jumps in mortality security pricing.

INTRODUCTION

Over the last century, populations of different countries have been increasingly linked by flows of information, goods, transportation, and communication, and as a consequence the world has become more closely connected and interdependent. While the trend of globalization has substantially driven market growth and international trade, it has also helped to spread some of the deadliest infectious diseases across borders (Daulaire, 1999). Thus, it seems improper to forecast mortality for an individual national population in isolation from others. Indeed, in practice, intercountry mortality correlation has long been a serious concern for insurers that underwrite life insurance business.

Mortality forecast that takes into account a country's linkage to others is important in the sense that not only does it facilitate better understanding of mortality risk, but it also has enormous implications for pricing mortality securities. Recent financial innovation makes mortality securitization a viable option for insurers or reinsurers to transfer catastrophe mortality risk arising from the possible occurrence of pandemics or large-scale terrorist attacks. By segregating its cash flows linked to extreme mortality risk, an insurance firm is able to repackage them into securities that are traded in capital markets (Blake and Burrows, 2001; Lin and Cox, 2005; Cox and Lin, 2007). Since the first publicly traded mortality security issued by Swiss Re in 2003, almost all mortality transactions determine the coupons and principals based on three or more population mortality indexes, with the only exception--the Tartan mortality bond sold in 2006. This indicates that insurers or reinsurers are keenly interested in transferring potential country-correlated mortality risk embedded in their business. For instance, the mortality risk of the 2003 Swiss Re mortality bond was defined in terms of an index based on the weighted average annual population death rates in the United States, the United Kingdom, France, Italy, and Switzerland (Lin and Cox, 2008). As another example, the mortality bond issued by the Nathan Ltd. in 2008 depended on the annual population death rates of four countries, namely, the United States, the United Kingdom, Canada, and Germany. Given that the existing (and possible future) mortality securities bundle multination mortality risks, mortality correlation among countries merits serious consideration in mortality securitization pricing.

In the recent literature, a number of stochastic mortality models have been proposed. Despite the importance of mortality correlation, surprisingly very few papers treat correlation as an indispensable element. For example, in order to account for catastrophic mortality death shocks, Chen and Cox (2009) incorporate a jump-diffusion process into the original Lee-Carter model to forecast mortality rates and price the 2003 Swiss Re mortality bond. Yet, while the Swiss Re bond payments depended on five-country weighted mortality index, the authors price this bond only based on the U.S. mortality rates. Hence, it is not clear how to extend their method to multipopulation correlated mortality scenarios.

Beelders and Colarossi (2004) and Chen and Cummins (2010), on the other hand, use the extreme value theory to measure mortality risk of the 2003 Swiss Re bond. …

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