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Author: Stephane Crepey Publisher: Springer Science & Business Media ISBN: 3642371132 Category : Computers Languages : en Pages : 464
Book Description
Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time". Damiano Brigo, Chair of Mathematical Finance, Imperial College London While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance
Author: Stephane Crepey Publisher: Springer Science & Business Media ISBN: 3642371132 Category : Computers Languages : en Pages : 464
Book Description
Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time". Damiano Brigo, Chair of Mathematical Finance, Imperial College London While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance
Author: Tomasz R. Bielecki Publisher: Springer Science & Business Media ISBN: 9783540675938 Category : Business & Economics Languages : en Pages : 524
Book Description
The motivation for the mathematical modeling studied in this text on developments in credit risk research is the bridging of the gap between mathematical theory of credit risk and the financial practice. Mathematical developments are covered thoroughly and give the structural and reduced-form approaches to credit risk modeling. Included is a detailed study of various arbitrage-free models of default term structures with several rating grades.
Author: Frédéric Vrins Publisher: MDPI ISBN: 3039287605 Category : Business & Economics Languages : en Pages : 190
Book Description
Credit risk remains one of the major risks faced by most financial and credit institutions. It is deeply connected to the real economy due to the systemic nature of some banks, but also because well-managed lending facilities are key for wealth creation and technological innovation. This book is a collection of innovative papers in the field of credit risk management. Besides the probability of default (PD), the major driver of credit risk is the loss given default (LGD). In spite of its central importance, LGD modeling remains largely unexplored in the academic literature. This book proposes three contributions in the field. Ye & Bellotti exploit a large private dataset featuring non-performing loans to design a beta mixture model. Their model can be used to improve recovery rate forecasts and, therefore, to enhance capital requirement mechanisms. François uses instead the price of defaultable instruments to infer the determinants of market-implied recovery rates and finds that macroeconomic and long-term issuer specific factors are the main determinants of market-implied LGDs. Cheng & Cirillo address the problem of modeling the dependency between PD and LGD using an original, urn-based statistical model. Fadina & Schmidt propose an improvement of intensity-based default models by accounting for ambiguity around both the intensity process and the recovery rate. Another topic deserving more attention is trade credit, which consists of the supplier providing credit facilities to his customers. Whereas this is likely to stimulate exchanges in general, it also magnifies credit risk. This is a difficult problem that remains largely unexplored. Kanapickiene & Spicas propose a simple but yet practical model to assess trade credit risk associated with SMEs and microenterprises operating in Lithuania. Another topical area in credit risk is counterparty risk and all other adjustments (such as liquidity and capital adjustments), known as XVA. Chataignier & Crépey propose a genetic algorithm to compress CVA and to obtain affordable incremental figures. Anagnostou & Kandhai introduce a hidden Markov model to simulate exchange rate scenarios for counterparty risk. Eventually, Boursicot et al. analyzes CoCo bonds, and find that they reduce the total cost of debt, which is positive for shareholders. In a nutshell, all the featured papers contribute to shedding light on various aspects of credit risk management that have, so far, largely remained unexplored.
Author: Tomasz R. Bielecki Publisher: Springer Science & Business Media ISBN: 3662048213 Category : Business & Economics Languages : en Pages : 517
Book Description
The motivation for the mathematical modeling studied in this text on developments in credit risk research is the bridging of the gap between mathematical theory of credit risk and the financial practice. Mathematical developments are covered thoroughly and give the structural and reduced-form approaches to credit risk modeling. Included is a detailed study of various arbitrage-free models of default term structures with several rating grades.
Author: David Lando Publisher: Princeton University Press ISBN: 1400829194 Category : Business & Economics Languages : en Pages : 328
Book Description
Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk. David Lando considers the two broad approaches to credit risk analysis: that based on classical option pricing models on the one hand, and on a direct modeling of the default probability of issuers on the other. He offers insights that can be drawn from each approach and demonstrates that the distinction between the two approaches is not at all clear-cut. The book strikes a fruitful balance between quickly presenting the basic ideas of the models and offering enough detail so readers can derive and implement the models themselves. The discussion of the models and their limitations and five technical appendixes help readers expand and generalize the models themselves or to understand existing generalizations. The book emphasizes models for pricing as well as statistical techniques for estimating their parameters. Applications include rating-based modeling, modeling of dependent defaults, swap- and corporate-yield curve dynamics, credit default swaps, and collateralized debt obligations.
Author: Kerry Back Publisher: Springer ISBN: 3540446443 Category : Mathematics Languages : en Pages : 317
Book Description
This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and insurance: the theory of stochastic processes, optimal and stochastic control, stochastic differential equations, convex analysis and duality theory. Five topics are treated in detail: Utility maximization in incomplete markets; the theory of nonlinear expectations and its relationship with the theory of risk measures in a dynamic setting; credit risk modelling; the interplay between finance and insurance; incomplete information in the context of economic equilibrium and insider trading.
Author: Łukasz Delong Publisher: Springer Science & Business Media ISBN: 1447153316 Category : Mathematics Languages : en Pages : 285
Book Description
Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Author: Hans Föllmer Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110463458 Category : Mathematics Languages : en Pages : 608
Book Description
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Author: Darrell Duffie Publisher: Princeton University Press ISBN: 1400829178 Category : Business & Economics Languages : en Pages : 415
Book Description
In this book, two of America's leading economists provide the first integrated treatment of the conceptual, practical, and empirical foundations for credit risk pricing and risk measurement. Masterfully applying theory to practice, Darrell Duffie and Kenneth Singleton model credit risk for the purpose of measuring portfolio risk and pricing defaultable bonds, credit derivatives, and other securities exposed to credit risk. The methodological rigor, scope, and sophistication of their state-of-the-art account is unparalleled, and its singularly in-depth treatment of pricing and credit derivatives further illuminates a problem that has drawn much attention in an era when financial institutions the world over are revising their credit management strategies. Duffie and Singleton offer critical assessments of alternative approaches to credit-risk modeling, while highlighting the strengths and weaknesses of current practice. Their approach blends in-depth discussions of the conceptual foundations of modeling with extensive analyses of the empirical properties of such credit-related time series as default probabilities, recoveries, ratings transitions, and yield spreads. Both the "structura" and "reduced-form" approaches to pricing defaultable securities are presented, and their comparative fits to historical data are assessed. The authors also provide a comprehensive treatment of the pricing of credit derivatives, including credit swaps, collateralized debt obligations, credit guarantees, lines of credit, and spread options. Not least, they describe certain enhancements to current pricing and management practices that, they argue, will better position financial institutions for future changes in the financial markets. Credit Risk is an indispensable resource for risk managers, traders or regulators dealing with financial products with a significant credit risk component, as well as for academic researchers and students.
Author: Stephane Crepey
Author: Stephane Crepey
Author: Tomasz R. Bielecki
Author: Frédéric Vrins
Author: Tomasz R. Bielecki
Author: David Lando
Author: Kerry Back
Author: Łukasz Delong
Author: Rasul, Mohammad
Author: Hans Föllmer
Author: Darrell Duffie