Statistical tools for finance and insurance.

*(English)*Zbl 1078.62112
Berlin: Springer (ISBN 3-540-22189-1/pbk). 517 p. (2005).

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 for Applied Statistics and Economics and Hugo Steinhaus Center for Stochastic Methods. 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 broad 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.

It consists naturally of two main parts. Each part contains chapters with high focus on practical applications. The finance part of 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 foreign exchange 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, 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.

The 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 \[ \text{www.xplore-stat.de}\quad \text{and} \quad \text{www.quantlet.com}. \] A tutorial chapter explaining how to setup and use XQS can be found in the third and final part of the book.

It consists naturally of two main parts. Each part contains chapters with high focus on practical applications. The finance part of 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 foreign exchange 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, 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.

The 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 \[ \text{www.xplore-stat.de}\quad \text{and} \quad \text{www.quantlet.com}. \] A tutorial chapter explaining how to setup and use XQS can be found in the third and final part of the book.

Reviewer: Edward M. Psyadlo (Odessa)

##### MSC:

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

91G70 | Statistical methods; risk measures |

91B30 | Risk theory, insurance (MSC2010) |

91B26 | Auctions, bargaining, bidding and selling, and other market models |