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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.

Approximation of market valuations on the set of risk measures

Tkaliński T.

Demonstratio Mathematica

2009

Vol. 42, nr 2

441-452

In this work we introduce the problem of choice of a risk measure providing best approximation of risk estimates derived from market valuations. We begin with a brief overview of connections between pricing and risk measurement issues which reveal importance of the problem we consider and lead to the mathematical formulation. In the main result under fairly general assumptions we establish the existence of the solution. In the second part we define a problem of finding a risk measure optimal with respect to the capital requirements. We impose additional assumptions, all of which have strong practical justification and in this particular setting we show that a solution exists and is a spectral measure of risk. As an example of application we show that there is some optimal spectral measure of risk for speculative position created in a market model with CIR short rate dynamics.