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Record Nr. |
UNINA9910829940203321 |
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Autore |
Fries Christian <1970-> |
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Titolo |
Mathematical finance [[electronic resource] ] : theory, modeling, implementation / / Christian Fries |
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Pubbl/distr/stampa |
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Hoboken, N.J., : Wiley-Interscience, c2007 |
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ISBN |
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1-280-97434-6 |
9786610974344 |
0-470-17978-3 |
0-470-17977-5 |
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Descrizione fisica |
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1 online resource (544 p.) |
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Disciplina |
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Soggetti |
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Derivative securities - Prices - Mathematical models |
Securities - Mathematical models |
Investments - Mathematical models |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 503-510) and index. |
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Nota di contenuto |
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Mathematical Finance: Theory, Modeling, Implementation; Contents; 1 Introduction; 1.1 Theory, Modeling, and Implementation; 1.2 Interest Rate Models and Interest Rate Derivatives; 1.3 About This Book; 1.3.1 How to Read This Book; 1.3.2 Abridged Versions; 1.3.3 Special Sections; 1.3.4 Notation; 1.3.5 Feedback; 1.3.6 Resources; I Foundations; 2 Foundations; 2.1 Probability Theory; 2.2 Stochastic Processes; 2.3 Filtration; 2.4 Brownian Motion; 2.5 Wiener Measure, Canonical Setup; 2.6 Itô Calculus; 2.6.1 Itô Integral; 2.6.2 Itô Process; 2.6.3 Itô Lemma and Product Rule |
2.7 Brownian Motion with Instantaneous Correlation2.8 Martingales; 2.8.1 Martingale Representation Theorem; 2.9 Change of Measure; 2.10 Stochastic Integration; 2.11 Partial Differential Equations (PDEs); 2.11.1 Feynman-Kač Theorem; 2.12 List of Symbols; 3 Replication; 3.1 Replication Strategies; 3.1.1 Introduction; 3.1.2 Replication in a Discrete Model; 3.2 Foundations: Equivalent Martingale Measure; 3.2.1 Challenge and Solution Outline; 3.2.2 Steps toward the Universal Pricing Theorem; 3.3 Excursus: Relative Prices and Risk-Neutral |
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Measures; 3.3.1 Why relative prices? |
3.3.2 Risk-Neutral MeasureII First Applications; 4 Pricing of a European Stock Option under the Black-Scholes Model; 5 Excursus: The Density of the Underlying of a European Call Option; 6 Excursus: Interpolation of European Option Prices; 6.1 No-Arbitrage Conditions for Interpolated Prices; 6.2 Arbitrage Violations through Interpolation; 6.2.1 Example 1 : Interpolation of Four Prices; 6.2.2 Example 2: Interpolation of Two Prices; 6.3 Arbitrage- Free Interpolation of European Option Prices; 7 Hedging in Continuous and Discrete Time and the Greeks; 7.1 Introduction |
7.2 Deriving the Replications Strategy from Pricing Theory7.2.1 Deriving the Replication Strategy under the Assumption of a Locally Riskless Product; 7.2.2 Black-Scholes Differential Equation; 7.2.3 Derivative V(t) as a Function of Its Underlyings S i(t); 7.2.4 Example: Replication Portfolio and PDE under a Black-Scholes Model; 7.3 Greeks; 7.3.1 Greeks of a European Call-Option under the Black-Scholes Model; 7.4 Hedging in Discrete Time: Delta and Delta-Gamma Hedging; 7.4.1 Delta Hedging; 7.4.2 Error Propagation; 7.4.3 Delta-Gamma Hedging; 7.4.4 Vega Hedging |
7.5 Hedging in Discrete Time: Minimizing the Residual Error (Bouchaud-Sornette Method)7.5.1 Minimizing the Residual Error at Maturity T; 7.5.2 Minimizing the Residual Error in Each Time Step; III Interest Rate Structures, Interest Rate Products, and Analytic Pricing Formulas; Motivation and Overview; 8 Interest Rate Structures; 8.1 Introduction; 8.1.1 Fixing Times and Tenor Times; 8.2 Definitions; 8.3 Interest Rate Curve Bootstrapping; 8.4 Interpolation of Interest Rate Curves; 8.5 Implementation; 9 Simple Interest Rate Products; 9.1 Interest Rate Products Part 1: Products without Optionality |
9.1.1 Fix, Floating, and Swap |
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Sommario/riassunto |
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A balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pri |
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