E-Book Overview
Statistical Tools for Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field of quantitative finance and insurance, this book offers a unique combination of topics from which every market analyst and risk manager will benefit. Covering topics such as heavy tailed distributions, implied trinomial trees, pricing of CAT bonds, simulation of risk processes and ruin probability approximation, the book does not only offer practitioners insight into new methods for their applications, but it also gives theoreticians insight into the applicability of the stochastic technology. Additionally, the book provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations.
E-Book Content
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Statistical Tools in Finance and Insurance ˇ ıˇ Pavel C´ zek, Wolfgang H¨ ardle, Rafal Weron
November 25, 2003
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Contents
I
Finance
9
1 Stable distributions in finance
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Szymon Borak, Wolfgang H¨ ardle, Rafal Weron 1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.2
α-stable distributions . . . . . . . . . . . . . . . . . . . . . . . .
12
1.2.1
Characteristic function representation . . . . . . . . . .
14
1.2.2
Simulation of α-stable variables . . . . . . . . . . . . . .
16
1.2.3
Tail behavior . . . . . . . . . . . . . . . . . . . . . . . .
18
Estimation of parameters . . . . . . . . . . . . . . . . . . . . .
18
1.3.1
Tail exponent estimation
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