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Application of the one-factor CIR interest rate model to catastrophe bond pricing under uncertainty

Nowak P., Romaniuk M.

Journal of Automation Mobile Robotics and Intelligent Systems

2014

Vol. 8, No. 3

19--27

The number and amount of losses caused by natural catastrophes are important problems for insurance industry. New financial instruments were introduce to transfer risks from insurance to financial market. In this paper we consider the problem of pricing such instruments, called the catastrophe bonds (CAT bonds). We derive valuation formulas using stochastic analysis and fuzzy sets theory. As model of short interest rate we apply the one-factor Cox–Ingersoll–Ross (CIR) model. In this paper we treat the volatility of the interest rate as a fuzzy number to describe uncertainty of the market. We also apply the Monte Carlo approach to analyze the obtained cat bond fuzzy prices.

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.