Stable Paretian models in finance (Q2709279)

The monograph is an important contribution to contemporary attempts on relaxation of normality assumptions common in continuous time stochastic financial models. It promotes the use of stable models as the right approach to capturing heavy-tails, asymmetries and complicated dependence structures. It is based on a large part of authors' work in stable finance modeling, contains both the theoretical results and empirical applications. It explains and generalizes several concepts of contemporary theoretical and empirical finance and shows how to approach them in case of stable non-Gaussian distributions of returns.NEWLINENEWLINENEWLINEA background material on univariate stable distributions and on estimation and testing their form is included in Chapters 2 and 3, multivariate stable models are introduced in Chapter 7. Complemented by two chapters devoted to modeling dynamic structure of financial return processes (temporal movements of the first moments of returns, evolution of volatilities and comparisons of stable return distribution models with ARCH-type ones) and by applications and empirical comparisons in Chapters 1 and 4, the first part of the book addresses problems of asset return processes modeling in their complexity.NEWLINENEWLINENEWLINEThe rest of the book centres around theory and empirical applications of stable models in finance: Chapters 8-10 deal with asset pricing (e.g., CAPM and APT models), portfolio theory and risk management (Value-at-Risk) under Gaussian and stable non-Gaussian distributions. Option pricing under alternative stable models is treated in Chapters 11 and 12 and is complemented by a chapter on related numerical results. Chapters 14 and 15 indicate possible exploitation of stable models in econometrics in the presence of heavy-tailed innovations.NEWLINENEWLINENEWLINEFor the most part, the chapters include material both on the theory and applications, with numerical illustrations on real data accompanied by explanations how to implement the models. An extensive list of references amounts 1157 entries.NEWLINENEWLINENEWLINEThe text requires the reader familiar with probability and statistics and with some of financial mathematics. The book is partly written at the level of advanced research papers and is primarily intended for researchers and advanced graduate students in mathematical finance. Nevertheless, numerous described real life examples and the shared experience in their numerical treatment give a guarantee that the book will attract attention of a broader group of practitioners looking for new models with a better fit to real data.