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Mathematical finance [[electronic resource] ] : theory, modeling, implementation / / Christian Fries
| Mathematical finance [[electronic resource] ] : theory, modeling, implementation / / Christian Fries |
| Autore | Fries Christian <1970-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2007 |
| Descrizione fisica | 1 online resource (544 p.) |
| Disciplina |
332.601
332.6015195 |
| Soggetto topico |
Derivative securities - Prices - Mathematical models
Securities - Mathematical models Investments - Mathematical models |
| ISBN |
1-280-97434-6
9786610974344 0-470-17978-3 0-470-17977-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910829940203321 |
Fries Christian <1970->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical finance [[electronic resource] ] : theory, modeling, implementation / / Christian Fries
| Mathematical finance [[electronic resource] ] : theory, modeling, implementation / / Christian Fries |
| Autore | Fries Christian <1970-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2007 |
| Descrizione fisica | 1 online resource (544 p.) |
| Disciplina |
332.601
332.6015195 |
| Soggetto topico |
Derivative securities - Prices - Mathematical models
Securities - Mathematical models Investments - Mathematical models |
| ISBN |
1-280-97434-6
9786610974344 0-470-17978-3 0-470-17977-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910841724103321 |
|
Fries Christian <1970->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
