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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 2000

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Valuation of catastrophe bonds

Kulikowski R., Jakubowski A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2000

Vol. 48, nr 2

182-211

A new approach to valuation of bonds under the default risk conditions, based on the concept of the investors' two-factor utility function is proposed. The first factor describes the expected average return from the risky investments, while the second - the worst case return. As a class of risky securities the so called catastrophe bonds are considered. It is assumed that depending on the structure of the security contract, the investor who buys the bond issued by a local authority governing the risky region - will lose his interest payments and/or the principal value, if a catastrophic event occurs. In the paper, the problem of pricing the catastrophe bonds is thoroughly analysed. The answer to one main question is given. It is how much of the default risk premium should be paid to an investor in order to compensate for risk, attached to the consequences of a catastrophe which can occur wit h same estimated probability. For the purpose of the valuation procedure, the new notions of the security safety level, the safety index, as well as a two rules decision model are successively introduced. The subjective scale as a measure of the degree of individuals' risk aversion is proposed. The idea of objective and subjective risk components is investigated. The new methodology proposed is illustrated by a series of computational examples. The results obtained, in the assumed conditions closed to a real life practice, are widely interpreted and discussed.