Contents
Contributors 6
Preface 9
I Finance 13
1 Stable Distributions 15
Szymon Borak, Wolfgang Hardle, and Rafa l Weron
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2 De nitions and Basic Characteristic . . . . . . . . . . . . . . . 16
1.2.1 Characteristic Function Representation . . . . . . . . . 18
1.2.2 Stable Density and Distribution Functions . . . . . . . . 20
1.3 Simulation of -stable Variables . . . . . . . . . . . . . . . . . . 22
1.4 Estimation of Parameters . . . . . . . . . . . . . . . . . . . . . 24
1.4.1 Tail Exponent Estimation . . . . . . . . . . . . . . . . . 25
1.4.2 Quantile Estimation . . . . . . . . . . . . . . . . . . . . 27
1.4.3 Characteristic Function Approaches . . . . . . . . . . . 28
1.4.4 Maximum Likelihood Method . . . . . . . . . . . . . . . 29
1.5 Financial Applications of Stable Laws . . . . . . . . . . . . . . 30

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4 Pricing of Catastrophe Bonds 87
Krzysztof Burnecki, Grzegorz Kukla, and David Taylor
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1.1 The Emergence of CAT Bonds . . . . . . . . . . . . . . 88
4.1.2 Insurance Securitization . . . . . . . . . . . . . . . . . . 90
4.1.3 CAT Bond Pricing Methodology . . . . . . . . . . . . . 91
4.2 Compound Doubly Stochastic Poisson Pricing Model . . . . . . 93
4.3 Calibration of the Pricing Model . . . . . . . . . . . . . . . . . 94
4.4 Dynamics of the CAT Bond Price . . . . . . . . . . . . . . . . . 98