Copula functions are a very popular tool for applications in finance. However, most of these applications (and all of them as far as pricing and risk management are concerned), are referred to cross-section dynamics (what is called spatial dependence in statistics). Standard examples are the evaluation of multivariate equity and credit derivatives, and aggregation of Value-at-Risk figures on different risk factors over a common investment horizon period. This book will introduce readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications. The first part of the book will briefly introduce the standard the theory of copula functions, before examining the link between copulas and Markov processes. It will then introduce new techniques to design Markov processes that are suited to represent the dynamics of market risk factors and their co-movement, providing techniques to both estimate and simulate such dynamics. The second part of the book will show readers how to apply these methods to the evaluation of pricing of multivariate derivative contracts in the equity and credit markets. It will then move on to explore the applications of joint temporal and cross-section aggregation to the problem of risk integration which is paramount in risk management. Like Copula Methods in Finance, this book is a first in bringing the latest tools and techniques for pricing and risk management to the practitioner.
