This book is designed for students, researchers and practitioners who want to be introduced to modern statistical tools applied in finance and insurance. It is the result of a joint effort of the Center for Economic Research (CentER), Center for Applied Statistics and Economics (C.A.S.E.) and Hugo Steinhaus Center for Stochastic Methods (HSC). All three institutions brought in their specific profiles and created with this book a wide-angle view on and solutions to up-to-date practical problems.
The text is comprehensible for a graduate student in financial engineering as well as for an inexperienced newcomer to quantitative finance and insurance who wants to get a grip on advanced statistical tools applied in these fields. An experienced reader with a bright knowledge of financial and actuarial mathematics will probably skip some sections but will hopefully enjoy the various computational tools. Finally, a practitioner might be familiar with some of the methods. However, the statistical techniques related to modern financial products, like MBS or CAT bonds, will certainly attract him.
``Statistical Tools for Finance and Insurance'' consists naturally of two main parts. Each part contains chapters with high focus on practical applications. The book starts with an introduction to stable distributions, which are the standard model for heavy tailed phenomena. Their numerical implementation is thoroughly discussed and applications to finance are given. The second chapter presents the ideas of extreme value and copula analysis as applied to multivariate financial data. This topic is extended in the subsequent chapter which deals with tail dependence, a concept describing the limiting proportion that one margin exceeds a certain threshold given that the other margin has already exceeded that threshold. The fourth chapter reviews the market in catastrophe insurance risk, which emerged in order to facilitate the direct transfer of reinsurance risk associated with natural catastrophes from corporations, insurers, and reinsurers to capital market investors. The next contribution employs functional data analysis for the estimation of smooth implied volatility surfaces. These surfaces are a result of using an oversimplified market benchmark model - the Black-Scholes formula - to real data. An attractive approach to overcome this problem is discussed in chapter six, where implied trinomial trees are applied to modeling implied volatilities and the corresponding state-price densities. An alternative route to tackling the implied volatility smile has led researchers to develop stochastic volatility models. The relative simplicity and the direct link of model parameters to the market makes Heston's model very attractive to front office users. Its application to FX option markets is covered in chapter seven. The following chapter shows how the computational complexity of stochastic volatility models can be overcome with the help of the Fast Fourier Transform. In chapter nine the valuation of Mortgage Backed Securities is discussed. The optimal prepayment policy is obtained via optimal stopping techniques. It is followed by a very innovative topic of predicting corporate bankruptcy with Support Vector Machines. Chapter eleven presents a novel approach to money-demand modeling using fuzzy clustering techniques. The first part of the book closes with productivity analysis for cost and frontier estimation. The nonparametric Data Envelopment Analysis is applied to efficiency issues of insurance agencies.
The insurance part of the book starts with a chapter on loss distributions. The basic models for claim severities are introduced and their statistical properties are thoroughly explained. In chapter fourteen, the methods of simulating and visualizing the risk process are discussed. This topic is followed by an overview of the approaches to approximating the ruin probability of an insurer. Both finite and infinite time approximations are presented. Some of these methods are extended in chapters sixteen and seventeen, where classical and anomalous diffusion approximations to ruin probability are discussed and extended to cases when the risk process exhibits good and bad periods. The last three chapters are related to one of the most important aspects of the insurance business - premium calculation. Chapter eighteen introduces the basic concepts including the pure risk premium and various safety loadings under different loss distributions. Calculation of a joint premium for a portfolio of insurance policies in the individual and collective risk models is discussed as well. The inclusion of deductibles into premium calculation is the topic of the following contribution. The last chapter of the insurance part deals with setting the appropriate level of insurance premium within a broader context of business decisions, including risk transfer through reinsurance and the rate of return on capital required to ensure solvability.
Our e-book offers a complete PDF version of this text and the corresponding HTML files with links to algorithms and quantlets. The reader of this book may therefore easily reconfigure and recalculate all the presented examples and methods via the enclosed XploRe Quantlet Server (XQS), which is also available from www.xplore-stat.de and www.quantlet.com. A tutorial chapter explaining how to setup and use XQS can be found in the third and final part of the book.
We gratefully acknowledge the support of Deutsche Forschungsgemeinschaft (SFB 373 Quantifikation und Simulation Ökonomischer Prozesse, SFB 649 Ökonomisches Risiko) and Komitet Badan Naukowych (PBZ-KBN 016/P03/99 Mathematical models in analysis of financial instruments and markets in
Poland).
A book of this kind would not have been possible without the help of many friends, colleagues,
and students. For the technical production of the e-book platform and quantlets we would like
to thank Zdenek Hlávka, Sigbert Klinke, Heiko Lehmann, Adam Misiorek, Piotr Uniejewski, Qingwei Wang, and Rodrigo Witzel.
Special thanks for careful proofreading and supervision of the insurance part go to Krzysztof Burnecki.
Pavel Cízek, Wolfgang Härdle, and Rafa Weron
Tilburg, Berlin, and Wrocaw, February 2005