The book offers an overview of credit risk modeling and management. A three-step approach is adopted with the contents, after introducing the essential concepts of both mathematics and finance.Initially the focus is on the modeling of credit risk parameters mainly at the level of individual debtor and transaction, after which the book delves into counterparty credit risk, thus providing the link between credit and market risks. The second part is aimed at the portfolio level when multiple loans are pooled and default correlation becomes an important factor to consider and model. In this respect, the book explains how copulas help in modeling. The final stage is the macro perspective when the combination of credit risks related to financial institutions produces systemic risk and affects overall financial stability.The entire approach is two-dimensional as well. First, all modeling steps have replicable programming codes both in R and Matlab. In this way, the reader can experience the impact of changing the default probabilities of a given borrower or the weights of a sector. Second, at each stage, the book discusses the regulatory environment. This is because, at times, regulation can have stricter constraints than the outcome of internal models. In summary, the book guides the reader in modeling and managing credit risk by providing both the theoretical framework and the empirical tools necessary for a modern finance professional. In this sense, the book is aimed at a wide audience in all fields of study: from quants who want to engage in finance to economists who want to learn about coding and modern financial engineering.

In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics.The aims of this book are as follows:

In the early 1980s, the late luminary Tito Arecchi was the first to highlight the existence of chaos in a laser model. Since then, along with several colleagues, he developed many important lines of research in this field, such as generalized multistability, laser with injected signal, laser with delayed feedback and the worldwide accepted classification of lasers of A, B and C, depending on their typical relaxation rates. Later, chaos control and synchronization were investigated in lasers and other systems, providing innovative schemes. Very recently, in his last contribution to laser physics, the model of the laser with feedback demonstrating its universal features was revisited.This book aims to present the research activity of Prof. Arecchi and his colleagues in the domain of nonlinear dynamics of lasers, since his seminal works of 1982 till the latest. Also included is our last contribution on jerk dynamics of laser's minimal universal model and a brief history of the discovery of laser where the reader will discover or rediscover many anecdotes about it.

Risk control, capital allocation, and realistic derivative pricing and hedging are critical concerns for major financial institutions and individual traders alike. Events from the collapse of Lehman Brothers to the Greek sovereign debt crisis demonstrate the urgent and abiding need for statistical tools adequate to measure and anticipate the amplitude of potential swings in the financial markets—from ordinary stock price and interest rate moves, to defaults, to those increasingly frequent "rare events" fashionably called black swan events. Yet many on Wall Street continue to rely on standard models based on artificially simplified assumptions that can lead to systematic (and sometimes catastrophic) underestimation of real risks. In Practical Methods of Financial Engineering and Risk Management, Dr. Rupak Chatterjee— former director of the multi-asset quantitative research group at Citi—introduces finance professionals and advanced students to the latest concepts, tools, valuation techniques, and analytic measures being deployed by the more discerning and responsive Wall Street practitioners, on all operational scales from day trading to institutional strategy, to model and analyze more faithfully the real behavior and risk exposure of financial markets in the cold light of the post-2008 realities. Until one masters this modern skill set, one cannot allocate risk capital properly, price and hedge derivative securities realistically, or risk-manage positions from the multiple perspectives of market risk, credit risk, counterparty risk, and systemic risk. The book assumes a working knowledge of calculus, statistics, and Excel, but it teaches techniques from statistical analysis, probability, and stochastic processes sufficient to enable the reader to calibrate probability distributions and create the simulations that are used on Wall Street to valuate various financial instruments correctly, model the risk dimensions of trading strategies, and perform the numerically intensive analysis of risk measures required by various regulatory agencies.

Features Uses an in-depth case study to illustrate multiple factors in counterparty credit risk exposures Suitable for quantitative risk managers at banks, as well as students of finance, financial mathematics, and software engineering Provides the reader with numerous examples and applications

The recent global financial crisis has caused massive upheavals worldwide. The papers in this volume analyze whether financial principles seem to have shifted in recent years, and what that may mean for international financial markets and regulation. What “broke” in the current crisis? Is there no “playbook” on how to respond to systemic crises? What is the optimal role of the state in dealing with crises? How should asset bubbles be addressed in the future? Do we need a major overhaul of governance in the industry? What means exist to address systemic crises? What reforms are needed? These and related issues are discussed by an impressive list of well-known scholars, policymakers and practitioners, with an emphasis on the implications for public policy.

State-of-the-art techniques and tools needed to facilitate effective credit portfolio management and robust quantitative credit analysis Filled with in-depth insights and expert advice, Active Credit Portfolio Management in Practice serves as a comprehensive introduction to both the theory and real-world practice of credit portfolio management. The authors have written a text that is technical enough both in terms of background and implementation to cover what practitioners and researchers need for actually applying these types of risk management tools in large organizations but which at the same time, avoids technical proofs in favor of real applications. Throughout this book, readers will be introduced to the theoretical foundations of this discipline, and learn about structural, reduced-form, and econometric models successfully used in the market today. The book is full of hands-on examples and anecdotes. Theory is illustrated with practical application. The authors' Website provides additional software tools in the form of Excel spreadsheets, Matlab code and S-Plus code. Each section of the book concludes with review questions designed to spark further discussion and reflection on the concepts presented.

It was the end of 2005 when our employer, a major European Investment Bank, gave our team the mandate to compute in an accurate way the counterparty credit exposure arising from exotic derivatives traded by the ?rm. As often happens, - posure of products such as, for example, exotic interest-rate, or credit derivatives were modelled under conservative assumptions and credit of?cers were struggling to assess the real risk. We started with a few models written on spreadsheets, t- lored to very speci?c instruments, and soon it became clear that a more systematic approach was needed. So we wrote some tools that could be used for some classes of relatively simple products. A couple of years later we are now in the process of building a system that will be used to trade and hedge counterparty credit ex- sure in an accurate way, for all types of derivative products in all asset classes. We had to overcome problems ranging from modelling in a consistent manner different products booked in different systems and building the appropriate architecture that would allow the computation and pricing of credit exposure for all types of pr- ucts, to ?nding the appropriate management structure across Business, Risk, and IT divisions of the ?rm. In this book we describe some of our experience in modelling counterparty credit exposure, computing credit valuation adjustments, determining appropriate hedges, and building a reliable system.

Contains Nearly 100 Pages of New MaterialThe recent financial crisis has shown that credit risk in particular and finance in general remain important fields for the application of mathematical concepts to real-life situations. While continuing to focus on common mathematical approaches to model credit portfolios, Introduction to Credit Risk Modelin

This paper discusses the impact of the rapid adoption of artificial intelligence (AI) and machine learning (ML) in the financial sector. It highlights the benefits these technologies bring in terms of financial deepening and efficiency, while raising concerns about its potential in widening the digital divide between advanced and developing economies. The paper advances the discussion on the impact of this technology by distilling and categorizing the unique risks that it could pose to the integrity and stability of the financial system, policy challenges, and potential regulatory approaches. The evolving nature of this technology and its application in finance means that the full extent of its strengths and weaknesses is yet to be fully understood. Given the risk of unexpected pitfalls, countries will need to strengthen prudential oversight.