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The LIBOR market model in practice [[electronic resource] /] / Dariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk
| The LIBOR market model in practice [[electronic resource] /] / Dariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk |
| Autore | Gatarek Dariusz |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 |
| Descrizione fisica | 1 online resource (292 p.) |
| Disciplina |
332.64570151
332.8011 |
| Altri autori (Persone) |
BachertPrzemyslaw
MaksymiukRobert |
| Collana | Wiley finance series |
| Soggetto topico |
Interest rates - Mathematical models
Interest rate futures - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-67334-4
1-280-74002-7 9786610740024 0-470-06041-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The LIBOR Market Model in Practice; Contents; Acknowledgments; About the Authors; Introduction; Part I THEORY; 1 Mathematics in a Pill; 1.1 Probability Space and Random Variables; 1.2 Normal Distributions; 1.3 Stochastic Processes; 1.4 Wiener Processes; 1.5 Geometric Wiener Processes; 1.6 Markov Processes; 1.7 Stochastic Integrals and Stochastic Differential Equations; 1.8 Ito's Formula; 1.9 Martingales; 1.10 Girsanov's Theorem; 1.11 Black's Formula (1976); 1.12 Pricing Derivatives and Changing of Numeraire; 1.13 Pricing of Interest Rate Derivatives and the Forward Measure
2 Heath-Jarrow-Morton and Brace-Gatarek-Musiela Models2.1 HJM and BGM Models Under the Spot Measure; 2.2 Vasicek Model; 2.3 Cox-Ingersoll-Ross Model; 2.4 Black-Karasinski Model; 2.5 HJM and BGM Models under the Forward Measures; 3 Simulation; 3.1 Simulation of HJM and BGM Models under the Forward Measure; 3.2 Monte Carlo Simulation of Multidimensional Gaussian Variables; Random numbers generation; Principal Components Analysis (PCA); Cholesky decomposition; 3.3 Trinomial Tree Simulation of Multidimensional Gaussian Variables; 4 Swaption Pricing and Calibration 4.1 Linear Pricing in the BGM Model4.2 Linear Pricing of Swaptions in the HJM Model; 4.3 Universal Volatility Function; 4.4 Time Homogeneous Volatility; 4.5 Separated Volatility; Example of Separated Calibration; 4.6 Parametrized Volatility; 4.7 Parametric Calibration to Caps and Swaptions Based on Rebonato Approach; 4.8 Semilinear Pricing of Swaptions in the BGM Model; 4.9 Semilinear Pricing of Swaptions in the HJM Model; 4.10 Nonlinear Pricing of Swaptions; 4.11 Examples; 5 Smile Modelling in the BGM Model; 5.1 The Shifted BGM Model; 5.2 Stochastic Volatility for Long Term Options 5.3 The Uncertain Volatility Displaced LIBOR Market Model5.4 Mixing the BGM and HJM Models; 6 Simplified BGM and HJM Models; 6.1 CMS Rate Dynamics in Single-Factor HJM Model; 6.2 CMS Rate Dynamics in a Single Factor BGM Model; 6.3 Calibration; 6.4 Smile; Part II CALIBRATION; 7 Calibration Algorithms to Caps and Floors; 7.1 Introduction; 7.2 Market Data; Interpretation of ATM Swaption Quotes; 7.3 Calibration to Caps; 7.3.1 Caplet Values; 7.3.2 ATM Strikes for Caps; 7.3.3 Stripping Caplet Volatilities from Cap Quotes; 7.4 Non-Parametric Calibration Algorithms 7.4.1 Piecewise Constant Instantaneous Volatilities Depending on the Time to Maturity7.4.2 Piecewise Constant Instantaneous Volatilities Depending on the Maturity of the Underlying Forward Rate; 7.5 Conclusions; 8 Non-Parametric Calibration Algorithms to Caps and Swaptions; 8.1 Introduction; 8.2 The Separated Approach; 8.3 The Separated Approach with Optimization; 8.4 The Locally Single Factor Approach; 8.5 Calibration with Historical Correlations of Forward Rates; 8.6 Calibration to Co-Terminal Swaptions; 8.7 Conclusions 9 Calibration Algorithms to Caps and Swaptions Based on Optimization Techniques |
| Record Nr. | UNINA-9910143707703321 |
Gatarek Dariusz
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The LIBOR market model in practice [[electronic resource] /] / Dariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk
| The LIBOR market model in practice [[electronic resource] /] / Dariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk |
| Autore | Gatarek Dariusz |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 |
| Descrizione fisica | 1 online resource (292 p.) |
| Disciplina |
332.64570151
332.8011 |
| Altri autori (Persone) |
BachertPrzemyslaw
MaksymiukRobert |
| Collana | Wiley finance series |
| Soggetto topico |
Interest rates - Mathematical models
Interest rate futures - Mathematical models |
| ISBN |
1-118-67334-4
1-280-74002-7 9786610740024 0-470-06041-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The LIBOR Market Model in Practice; Contents; Acknowledgments; About the Authors; Introduction; Part I THEORY; 1 Mathematics in a Pill; 1.1 Probability Space and Random Variables; 1.2 Normal Distributions; 1.3 Stochastic Processes; 1.4 Wiener Processes; 1.5 Geometric Wiener Processes; 1.6 Markov Processes; 1.7 Stochastic Integrals and Stochastic Differential Equations; 1.8 Ito's Formula; 1.9 Martingales; 1.10 Girsanov's Theorem; 1.11 Black's Formula (1976); 1.12 Pricing Derivatives and Changing of Numeraire; 1.13 Pricing of Interest Rate Derivatives and the Forward Measure
2 Heath-Jarrow-Morton and Brace-Gatarek-Musiela Models2.1 HJM and BGM Models Under the Spot Measure; 2.2 Vasicek Model; 2.3 Cox-Ingersoll-Ross Model; 2.4 Black-Karasinski Model; 2.5 HJM and BGM Models under the Forward Measures; 3 Simulation; 3.1 Simulation of HJM and BGM Models under the Forward Measure; 3.2 Monte Carlo Simulation of Multidimensional Gaussian Variables; Random numbers generation; Principal Components Analysis (PCA); Cholesky decomposition; 3.3 Trinomial Tree Simulation of Multidimensional Gaussian Variables; 4 Swaption Pricing and Calibration 4.1 Linear Pricing in the BGM Model4.2 Linear Pricing of Swaptions in the HJM Model; 4.3 Universal Volatility Function; 4.4 Time Homogeneous Volatility; 4.5 Separated Volatility; Example of Separated Calibration; 4.6 Parametrized Volatility; 4.7 Parametric Calibration to Caps and Swaptions Based on Rebonato Approach; 4.8 Semilinear Pricing of Swaptions in the BGM Model; 4.9 Semilinear Pricing of Swaptions in the HJM Model; 4.10 Nonlinear Pricing of Swaptions; 4.11 Examples; 5 Smile Modelling in the BGM Model; 5.1 The Shifted BGM Model; 5.2 Stochastic Volatility for Long Term Options 5.3 The Uncertain Volatility Displaced LIBOR Market Model5.4 Mixing the BGM and HJM Models; 6 Simplified BGM and HJM Models; 6.1 CMS Rate Dynamics in Single-Factor HJM Model; 6.2 CMS Rate Dynamics in a Single Factor BGM Model; 6.3 Calibration; 6.4 Smile; Part II CALIBRATION; 7 Calibration Algorithms to Caps and Floors; 7.1 Introduction; 7.2 Market Data; Interpretation of ATM Swaption Quotes; 7.3 Calibration to Caps; 7.3.1 Caplet Values; 7.3.2 ATM Strikes for Caps; 7.3.3 Stripping Caplet Volatilities from Cap Quotes; 7.4 Non-Parametric Calibration Algorithms 7.4.1 Piecewise Constant Instantaneous Volatilities Depending on the Time to Maturity7.4.2 Piecewise Constant Instantaneous Volatilities Depending on the Maturity of the Underlying Forward Rate; 7.5 Conclusions; 8 Non-Parametric Calibration Algorithms to Caps and Swaptions; 8.1 Introduction; 8.2 The Separated Approach; 8.3 The Separated Approach with Optimization; 8.4 The Locally Single Factor Approach; 8.5 Calibration with Historical Correlations of Forward Rates; 8.6 Calibration to Co-Terminal Swaptions; 8.7 Conclusions 9 Calibration Algorithms to Caps and Swaptions Based on Optimization Techniques |
| Record Nr. | UNINA-9910830441703321 |
|
Gatarek Dariusz
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The LIBOR market model in practice / / Dariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk
| The LIBOR market model in practice / / Dariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk |
| Autore | Gatarek Dariusz |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 |
| Descrizione fisica | 1 online resource (292 p.) |
| Disciplina | 332.1/13 |
| Altri autori (Persone) |
BachertPrzemyslaw
MaksymiukRobert |
| Collana | Wiley finance series |
| Soggetto topico |
Interest rates - Mathematical models
Interest rate futures - Mathematical models |
| ISBN |
9786610740024
9781118673348 1118673344 9781280740022 1280740027 9780470060414 0470060417 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The LIBOR Market Model in Practice; Contents; Acknowledgments; About the Authors; Introduction; Part I THEORY; 1 Mathematics in a Pill; 1.1 Probability Space and Random Variables; 1.2 Normal Distributions; 1.3 Stochastic Processes; 1.4 Wiener Processes; 1.5 Geometric Wiener Processes; 1.6 Markov Processes; 1.7 Stochastic Integrals and Stochastic Differential Equations; 1.8 Ito's Formula; 1.9 Martingales; 1.10 Girsanov's Theorem; 1.11 Black's Formula (1976); 1.12 Pricing Derivatives and Changing of Numeraire; 1.13 Pricing of Interest Rate Derivatives and the Forward Measure
2 Heath-Jarrow-Morton and Brace-Gatarek-Musiela Models2.1 HJM and BGM Models Under the Spot Measure; 2.2 Vasicek Model; 2.3 Cox-Ingersoll-Ross Model; 2.4 Black-Karasinski Model; 2.5 HJM and BGM Models under the Forward Measures; 3 Simulation; 3.1 Simulation of HJM and BGM Models under the Forward Measure; 3.2 Monte Carlo Simulation of Multidimensional Gaussian Variables; Random numbers generation; Principal Components Analysis (PCA); Cholesky decomposition; 3.3 Trinomial Tree Simulation of Multidimensional Gaussian Variables; 4 Swaption Pricing and Calibration 4.1 Linear Pricing in the BGM Model4.2 Linear Pricing of Swaptions in the HJM Model; 4.3 Universal Volatility Function; 4.4 Time Homogeneous Volatility; 4.5 Separated Volatility; Example of Separated Calibration; 4.6 Parametrized Volatility; 4.7 Parametric Calibration to Caps and Swaptions Based on Rebonato Approach; 4.8 Semilinear Pricing of Swaptions in the BGM Model; 4.9 Semilinear Pricing of Swaptions in the HJM Model; 4.10 Nonlinear Pricing of Swaptions; 4.11 Examples; 5 Smile Modelling in the BGM Model; 5.1 The Shifted BGM Model; 5.2 Stochastic Volatility for Long Term Options 5.3 The Uncertain Volatility Displaced LIBOR Market Model5.4 Mixing the BGM and HJM Models; 6 Simplified BGM and HJM Models; 6.1 CMS Rate Dynamics in Single-Factor HJM Model; 6.2 CMS Rate Dynamics in a Single Factor BGM Model; 6.3 Calibration; 6.4 Smile; Part II CALIBRATION; 7 Calibration Algorithms to Caps and Floors; 7.1 Introduction; 7.2 Market Data; Interpretation of ATM Swaption Quotes; 7.3 Calibration to Caps; 7.3.1 Caplet Values; 7.3.2 ATM Strikes for Caps; 7.3.3 Stripping Caplet Volatilities from Cap Quotes; 7.4 Non-Parametric Calibration Algorithms 7.4.1 Piecewise Constant Instantaneous Volatilities Depending on the Time to Maturity7.4.2 Piecewise Constant Instantaneous Volatilities Depending on the Maturity of the Underlying Forward Rate; 7.5 Conclusions; 8 Non-Parametric Calibration Algorithms to Caps and Swaptions; 8.1 Introduction; 8.2 The Separated Approach; 8.3 The Separated Approach with Optimization; 8.4 The Locally Single Factor Approach; 8.5 Calibration with Historical Correlations of Forward Rates; 8.6 Calibration to Co-Terminal Swaptions; 8.7 Conclusions 9 Calibration Algorithms to Caps and Swaptions Based on Optimization Techniques |
| Altri titoli varianti | London Interbank Offer Rate market model in practice |
| Record Nr. | UNINA-9911019556503321 |
|
Gatarek Dariusz
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||