Academic journal article Journal of Risk and Insurance

Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

Academic journal article Journal of Risk and Insurance

Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

Article excerpt

ABSTRACT

Normalized exponential tilting is an extension of classical theories, including the Capital Asset Pricing Model (CAPM) and the Black-Merton-Scholes model, to price risks with general-shaped distributions. The need for changing multivariate probability measures arises in pricing contingent claims on multiple underlying assets or liabilities. In this article, we apply it to valuation of mortality-based securities written on mortality indices of several countries. We show how to use multivariate exponential tilting to price the first pure mortality security, the Swiss Re bond. The same technique can be applied in other mortality securitization pricing.

INTRODUCTION

Life insurance securitization has been an important life insurance financial innovation since 1988. Securitization may increase a firm's value by reducing transaction costs, agency costs, informational asymmetries, taxation, and regulation (Cowley and Cummins, 2005). In these transactions, positive future net cash flow from the policies is dedicated to pay the bondholders. Therefore, they are similar to asset securitizations (Lin and Cox, 2006).

The complexity of life insurance securitization impedes its development because underlying cash flows of life insurance securitization are determined by numerous contingencies including mortality, persistency, regulatory risk, insurer policy dividend decisions, and other factors. Cowley and Cummins (2005) conclude that "each layer of complexity increases the degree of informational asymmetries between the investor and the issuer, reducing credit ratings and adding to costs." The Swiss Re bond issued in December 2003 is a breakthrough in life insurance securitization--it is the first pure mortality security. It stripped out pure mortality risks and thus increased the transparency of the deal. Moreover, pure mortality securities may provide a diversification benefit since mortality may have no or low correlation with an investor's existing portfolio (Lin and Cox, 2005). According to MorganStanley (2003), "the appetite for this security [the Swiss Re bonds] from investors was strong."

However, mortality securities will not achieve the level of success of mortgage-backed securities and other types of asset-backed securities until a substantial volume of transactions reaches the public markets (Cowley and Cummins, 2005). Among all factors, correct transaction price is an indispensable part of their success. However, like mortality securities, mortality securitization modeling is in an early stage of development. We note there are relatively few preliminary papers in this area. Developing asset pricing theory in this area is important since it will help market participants better understand these new financial instruments. Most of the existing mortality securitization pricing and modeling papers have two major shortcomings: first, they ignore mortality jumps (Lee and Carter, 1992; Renshaw, Haberman, and Hatzoupoulos, 1996; Lee, 2000; Sithole, Haberman, and Verrall, 2000; Milevsky and Promislow, 2001; Olivieri and Pitacco, 2002; Dahl, 2003; Cairns, Blake, and Dowd, 2006) and/or correlation between reference risks. Mortality jumps should not be ignored in mortality securitization modeling since the rationale behind selling or buying mortality securities is to hedge or take catastrophe mortality risks (i.e., more death than expected). Moreover, we should take into account correlation of mortality risks if the security is based on several reference risks (e.g., population mortality indices of several countries). Second, the complete market pricing methodology may not be appropriate. Pure mortality risk bonds may not be spanned with traded securities. Therefore, we propose to price mortality bonds in an incomplete market framework with the jump processes, using multivariate exponential tilting.

Change of probability measure is a common theme in pricing and valuation of risks and contingent claims. …

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