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This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice. In the 2nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. In the 3rd printing of the 2nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility. Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk. This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on the practical rather than the theoretical aspects of financial modelling.

Derivative securities --- Finance --- Fixed-income securities --- Interest rates --- Options (Finance) --- Mathematical models. --- Finance. --- Economics, Mathematical. --- Probabilities. --- Statistics. --- Econometrics. --- Public finance. --- Economics. --- Public Economics. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Finance, general. --- Options (Finances) --- Instruments dérivés (Finances) --- Taux d'intérêt --- Valeurs mobilières à revenus fixes --- Finances --- Modèles mathématiques --- EPUB-LIV-FT SPRINGER-B LIVMATHE --- Distribution (Probability theory. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Cameralistics --- Public finance --- Currency question --- Economics, Mathematical --- Statistics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Funding --- Funds --- Economics --- AA / International- internationaal --- 305.91 --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Public finances --- Economics, Mathematical . --- Statistics . --- Mathematical economics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Options (Finance) - Mathematical models - Mathematical models. --- Derivative securities - Mathematical models. --- Interest rates - Mathematical models. --- Fixed-income securities - Mathematical models. --- Finance - Mathematical models.

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Mathematical finance and financial engineering have been rapidly expanding fields of science over the past three decades. The main reason behind this phenomenon has been the success of sophisticated quantitative methodologies in helping professionals to manage financial risks. The newly developed credit derivatives industry has grown around the need to handle credit risk, which is one of the fundamental factors of financial risk. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better apprehending, modeling and hedging of this kind of risk. One of the objectives has been to understand links between credit risk and other major sources of uncertainty, such as the market risk or the liquidity risk. The main objective of this monograph is to present a comprehensive survey ofthe past developments in the area of credit risk research, as well as put forth the most recent advancements in this field. An important aspect of this text is that it attempts to bridge the gap between the mathematical theory of credit risk and the financial practice, which serves as the motivation for the mathematical modeling studied in the book. Mahtematical developments are presented in a thorough manner and cover the structural (value-of-the-firm) and the reduced-form (intensity-based) approaches to credit risk modeling, applied both to single and to multiple defaults. In particular, the book offers a detailed study of various arbitrage-free models of defaultable term structures with several rating grades. This book will serve as a valuable reference for financial analysts and traders involved with credit derivatives. Some aspects of the book may also be useful for market practitioners with managing credit-risk sensitives portfolios. Graduate students and researchers in areas such as finance theory, mathematical finance, financial engineering and probability theory will benefit from the book as well. On the technical side, readers are assumed to be familiar with graduate level probability theory, theory of stochastic processes, and elements of stochastic analysis and PDEs; some acquaintance with arbitrage pricing theory is also.

AA / International- internationaal --- 333.130.2 --- 305.7 --- 333.605 --- 333.70 --- 333.109 --- Bankliquiditeit. Verplichte reserves. Solvabiliteit. --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente. --- Nieuwe financiële instrumenten. --- Theorie en organisatie van het bankkrediet. --- Veiligheid. Bankovervallen. Bankrisico's. --- -Risk management --- Risk management --- Credit --- Mathematical models --- Mathematical models. --- Crédit --- Gestion du risque --- Modèles mathématiques --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Veiligheid. Bankovervallen. Bankrisico's --- Bankliquiditeit. Verplichte reserves. Solvabiliteit --- Nieuwe financiële instrumenten --- Theorie en organisatie van het bankkrediet --- Public finance. --- Economics, Mathematical . --- Probabilities. --- Public Economics. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Econometrics --- Cameralistics --- Public finance --- Public finances --- Currency question --- Methodology --- Risk management - Mathematical models --- Credit - Mathematical models

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This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice. In the 2nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. In the 3rd printing of the 2nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility. Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk. This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on the practical rather than the theoretical aspects of financial modelling.

Quantitative methods (economics) --- Finance --- Operational research. Game theory --- Mathematical statistics --- Financial analysis --- Business economics --- stochastische analyse --- statistiek --- financiën --- financiële analyse --- econometrie --- kansrekening

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