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An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault
| An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (243 p.) |
| Disciplina |
332.8
332.80151922 |
| Collana | Advanced series on statistical science & applied probability |
| Soggetto topico |
Interest rate futures - Mathematical models
Stochastic models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-60363-5
9786613784322 981-4390-86-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. A Review of Stochastic Calculus; 1.1 Brownian Motion; 1.2 Stochastic Integration; 1.3 Quadratic Variation; 1.4 Ito's Formula; 1.5 Exercises; 2. A Review of Black-Scholes Pricing and Hedging; 2.1 Call and Put Options; 2.2 Market Model and Portfolio; 2.3 PDE Method; 2.4 The Girsanov Theorem; 2.5 Martingale Method; 2.6 Exercises; 3. Short Term Interest Rate Models; 3.1 Mean-Reverting Models; 3.2 Constant Elasticity of Variance (CEV) Models; 3.3 Time-Dependent Models; 3.4 Exercises; 4. Pricing of Zero-Coupon Bonds; 4.1 Definition and Basic Properties
4.2 Absence of Arbitrage and the Markov Property4.3 Absence of Arbitrage and the Martingale Property; 4.4 PDE Solution: Probabilistic Method; 4.5 PDE Solution: Analytical Method; 4.6 Numerical Simulations; 4.7 Exercises; 5. Forward Rate Modeling; 5.1 Forward Contracts; 5.2 Instantaneous Forward Rate; 5.3 Short Rates; 5.4 Parametrization of Forward Rates; Nelson-Siegel parametrization; Svensson parametrization; 5.5 Curve Estimation; 5.6 Exercises; 6. The Heath-Jarrow-Morton (HJM) Model; 6.1 Restatement of Objectives; 6.2 Forward Vasicek Rates; 6.3 Spot Forward Rate Dynamics 6.4 The HJM Condition6.5 Markov Property of Short Rates; 6.6 The Hull-White Model; 6.7 Exercises; 7. The Forward Measure and Derivative Pricing; 7.1 Forward Measure; 7.2 Dynamics under the Forward Measure; 7.3 Derivative Pricing; 7.4 Inverse Change of Measure; 7.5 Exercises; 8. Curve Fitting and a Two-Factor Model; 8.1 Curve Fitting; 8.2 Deterministic Shifts; 8.3 The Correlation Problem; 8.4 Two-Factor Model; 8.5 Exercises; 9. A Credit Default Model; 9.1 Survival Probabilities; 9.2 Stochastic Default; 9.3 Defaultable Bonds; 9.4 Credit Default Swaps; 9.5 Exercises 10. Pricing of Caps and Swaptions on the LIBOR10.1 Pricing of Caplets and Caps; 10.2 Forward Rate Measure and Tenor Structure; 10.3 Swaps and Swaptions; 10.4 The London InterBank Offered Rates (LIBOR) Model; 10.5 Swap Rates on the LIBOR Market; 10.6 Forward Swap Measures; 10.7 Swaption Pricing on the LIBOR Market; 10.8 Exercises; 11. The Brace-Gatarek-Musiela (BGM) Model; 11.1 The BGM Model; 11.2 Cap Pricing; 11.3 Swaption Pricing; 11.4 Calibration of the BGM Model; 11.5 Exercises; 12. Appendix A: Mathematical Tools; Measurability; Covariance and Correlation; Gaussian Random Variables Conditional ExpectationMartingales in Discrete Time; Martingales in Continuous Time; Markov Processes; 13. Appendix B: Some Recent Developments; Infinite dimensional analysis; Extended interest rate models; Exotic and path-dependent options on interest rates; Sensitivity analysis and the Malliavin calculus; Longevity and mortality risk; 14. Solutions to the Exercises; Bibliography; Index; Author Index |
| Record Nr. | UNINA-9910462558603321 |
Privault Nicolas
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault
| An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (243 p.) |
| Disciplina |
332.8
332.80151922 |
| Collana | Advanced series on statistical science & applied probability |
| Soggetto topico |
Interest rate futures - Mathematical models
Stochastic models |
| ISBN |
1-281-60363-5
9786613784322 981-4390-86-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. A Review of Stochastic Calculus; 1.1 Brownian Motion; 1.2 Stochastic Integration; 1.3 Quadratic Variation; 1.4 Ito's Formula; 1.5 Exercises; 2. A Review of Black-Scholes Pricing and Hedging; 2.1 Call and Put Options; 2.2 Market Model and Portfolio; 2.3 PDE Method; 2.4 The Girsanov Theorem; 2.5 Martingale Method; 2.6 Exercises; 3. Short Term Interest Rate Models; 3.1 Mean-Reverting Models; 3.2 Constant Elasticity of Variance (CEV) Models; 3.3 Time-Dependent Models; 3.4 Exercises; 4. Pricing of Zero-Coupon Bonds; 4.1 Definition and Basic Properties
4.2 Absence of Arbitrage and the Markov Property4.3 Absence of Arbitrage and the Martingale Property; 4.4 PDE Solution: Probabilistic Method; 4.5 PDE Solution: Analytical Method; 4.6 Numerical Simulations; 4.7 Exercises; 5. Forward Rate Modeling; 5.1 Forward Contracts; 5.2 Instantaneous Forward Rate; 5.3 Short Rates; 5.4 Parametrization of Forward Rates; Nelson-Siegel parametrization; Svensson parametrization; 5.5 Curve Estimation; 5.6 Exercises; 6. The Heath-Jarrow-Morton (HJM) Model; 6.1 Restatement of Objectives; 6.2 Forward Vasicek Rates; 6.3 Spot Forward Rate Dynamics 6.4 The HJM Condition6.5 Markov Property of Short Rates; 6.6 The Hull-White Model; 6.7 Exercises; 7. The Forward Measure and Derivative Pricing; 7.1 Forward Measure; 7.2 Dynamics under the Forward Measure; 7.3 Derivative Pricing; 7.4 Inverse Change of Measure; 7.5 Exercises; 8. Curve Fitting and a Two-Factor Model; 8.1 Curve Fitting; 8.2 Deterministic Shifts; 8.3 The Correlation Problem; 8.4 Two-Factor Model; 8.5 Exercises; 9. A Credit Default Model; 9.1 Survival Probabilities; 9.2 Stochastic Default; 9.3 Defaultable Bonds; 9.4 Credit Default Swaps; 9.5 Exercises 10. Pricing of Caps and Swaptions on the LIBOR10.1 Pricing of Caplets and Caps; 10.2 Forward Rate Measure and Tenor Structure; 10.3 Swaps and Swaptions; 10.4 The London InterBank Offered Rates (LIBOR) Model; 10.5 Swap Rates on the LIBOR Market; 10.6 Forward Swap Measures; 10.7 Swaption Pricing on the LIBOR Market; 10.8 Exercises; 11. The Brace-Gatarek-Musiela (BGM) Model; 11.1 The BGM Model; 11.2 Cap Pricing; 11.3 Swaption Pricing; 11.4 Calibration of the BGM Model; 11.5 Exercises; 12. Appendix A: Mathematical Tools; Measurability; Covariance and Correlation; Gaussian Random Variables Conditional ExpectationMartingales in Discrete Time; Martingales in Continuous Time; Markov Processes; 13. Appendix B: Some Recent Developments; Infinite dimensional analysis; Extended interest rate models; Exotic and path-dependent options on interest rates; Sensitivity analysis and the Malliavin calculus; Longevity and mortality risk; 14. Solutions to the Exercises; Bibliography; Index; Author Index |
| Record Nr. | UNINA-9910790318703321 |
|
Privault Nicolas
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An elementary introduction to stochastic interest rate modeling / / Nicolas Privault
| An elementary introduction to stochastic interest rate modeling / / Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (243 p.) |
| Disciplina |
332.8
332.80151922 |
| Collana | Advanced series on statistical science & applied probability |
| Soggetto topico |
Interest rate futures - Mathematical models
Stochastic models |
| ISBN |
1-281-60363-5
9786613784322 981-4390-86-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. A Review of Stochastic Calculus; 1.1 Brownian Motion; 1.2 Stochastic Integration; 1.3 Quadratic Variation; 1.4 Ito's Formula; 1.5 Exercises; 2. A Review of Black-Scholes Pricing and Hedging; 2.1 Call and Put Options; 2.2 Market Model and Portfolio; 2.3 PDE Method; 2.4 The Girsanov Theorem; 2.5 Martingale Method; 2.6 Exercises; 3. Short Term Interest Rate Models; 3.1 Mean-Reverting Models; 3.2 Constant Elasticity of Variance (CEV) Models; 3.3 Time-Dependent Models; 3.4 Exercises; 4. Pricing of Zero-Coupon Bonds; 4.1 Definition and Basic Properties
4.2 Absence of Arbitrage and the Markov Property4.3 Absence of Arbitrage and the Martingale Property; 4.4 PDE Solution: Probabilistic Method; 4.5 PDE Solution: Analytical Method; 4.6 Numerical Simulations; 4.7 Exercises; 5. Forward Rate Modeling; 5.1 Forward Contracts; 5.2 Instantaneous Forward Rate; 5.3 Short Rates; 5.4 Parametrization of Forward Rates; Nelson-Siegel parametrization; Svensson parametrization; 5.5 Curve Estimation; 5.6 Exercises; 6. The Heath-Jarrow-Morton (HJM) Model; 6.1 Restatement of Objectives; 6.2 Forward Vasicek Rates; 6.3 Spot Forward Rate Dynamics 6.4 The HJM Condition6.5 Markov Property of Short Rates; 6.6 The Hull-White Model; 6.7 Exercises; 7. The Forward Measure and Derivative Pricing; 7.1 Forward Measure; 7.2 Dynamics under the Forward Measure; 7.3 Derivative Pricing; 7.4 Inverse Change of Measure; 7.5 Exercises; 8. Curve Fitting and a Two-Factor Model; 8.1 Curve Fitting; 8.2 Deterministic Shifts; 8.3 The Correlation Problem; 8.4 Two-Factor Model; 8.5 Exercises; 9. A Credit Default Model; 9.1 Survival Probabilities; 9.2 Stochastic Default; 9.3 Defaultable Bonds; 9.4 Credit Default Swaps; 9.5 Exercises 10. Pricing of Caps and Swaptions on the LIBOR10.1 Pricing of Caplets and Caps; 10.2 Forward Rate Measure and Tenor Structure; 10.3 Swaps and Swaptions; 10.4 The London InterBank Offered Rates (LIBOR) Model; 10.5 Swap Rates on the LIBOR Market; 10.6 Forward Swap Measures; 10.7 Swaption Pricing on the LIBOR Market; 10.8 Exercises; 11. The Brace-Gatarek-Musiela (BGM) Model; 11.1 The BGM Model; 11.2 Cap Pricing; 11.3 Swaption Pricing; 11.4 Calibration of the BGM Model; 11.5 Exercises; 12. Appendix A: Mathematical Tools; Measurability; Covariance and Correlation; Gaussian Random Variables Conditional ExpectationMartingales in Discrete Time; Martingales in Continuous Time; Markov Processes; 13. Appendix B: Some Recent Developments; Infinite dimensional analysis; Extended interest rate models; Exotic and path-dependent options on interest rates; Sensitivity analysis and the Malliavin calculus; Longevity and mortality risk; 14. Solutions to the Exercises; Bibliography; Index; Author Index |
| Record Nr. | UNINA-9910821107503321 |
|
Privault Nicolas
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| 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 |
| 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 |
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 |
| Altri titoli varianti | London Interbank Offer Rate market model in practice |
| Record Nr. | UNINA-9910877172703321 |
|
Gatarek Dariusz
|
||
| Chichester, England ; ; Hoboken, NJ, : John Wiley & Sons, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical interest theory [[electronic resource] /] / Leslie Jane Federer Vaaler, James W. Daniel
| Mathematical interest theory [[electronic resource] /] / Leslie Jane Federer Vaaler, James W. Daniel |
| Autore | Vaaler Leslie Jane Federer |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Washington, D.C., : Mathematical Association of America, 2009 |
| Descrizione fisica | 1 online resource (493 p.) |
| Disciplina | 332.801/513 |
| Altri autori (Persone) | DanielJames W |
| Collana | MAA textbooks |
| Soggetto topico |
Interest rates - Mathematical models
Interest rate futures - Mathematical models Risk management - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-61444-600-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""cover ""; ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""To students""; ""Examples""; ""Problems""; ""Special Features""; ""Coverage""; ""Second edition""; ""Financial transactions""; ""Acknowledgments""; ""Contacting the authors""; ""0 An introduction to the Texas Instruments BA II Plus""; ""0.1 CHOOSING A CALCULATOR""; ""0.2 FONT CONVENTION""; ""0.3 BA II PLUS BASICS""; ""0.4 PROBLEMS, CHAPTER 0""; ""1 The growth of money""; ""1.1 INTRODUCTION""; ""1.2 WHAT IS INTEREST ?""; ""1.3 ACCUMULATION AND AMOUNT FUNCTIONS""
""1.4 SIMPLE INTEREST / LINEAR ACCUMULATION FUNCTIONS""""1.5 COMPOUND INTEREST (THE USUAL CASE!)""; ""1.6 INTEREST IN ADVANCE / THE EFFECTIVE DISCOUNT RATE""; ""1.7 DISCOUNT FUNCTIONS / THE TIME VALUE OF MONEY""; ""1.8 SIMPLE DISCOUNT""; ""1.9 COMPOUND DISCOUNT""; ""1.10 NOMINAL RATES OF INTEREST AND DISCOUNT""; ""1.11 A FRIENDLY COMPETITION (CONSTANT FORCE OF INTEREST)""; ""1.12 FORCE OF INTEREST""; ""1.13 NOTE FOR THOSE WHO SKIPPED SECTIONS (1.11) AND (1.12)""; ""1.14 INFLATION""; ""1.15 PROBLEMS, CHAPTER 1""; ""1.3) Accumulation and amount functions""; ""(1.4) Simple interest"" ""(1.5) Compound interest""""(1.6) Effective discount rates/ Interest in advance""; ""(1.7) Discount functions/ The time value of money""; ""(1.8) Simple discount""; ""(1.9) Compound discount""; ""(1.10) Nominal rates of interest and discount""; ""(1.11) A friendly competition (Constant force of interest)""; ""(1.12) Force of interest""; ""(1.13) Note for those who skipped Section (1.11) and (1.12)""; ""(1.14) Inflation""; ""Chapter 1 review problems""; ""2 Equations of value and yield rates""; ""2.1 INTRODUCTION"" ""2.2 EQUATIONS OF VALUE FOR INVESTMENTS INVOLVING A SINGLE DEPOSIT MADE UNDER COMPOUND INTEREST""""2.3 EQUATIONS OF VALUE FOR INVESTMENTS WITH MULTIPLE CONTRIBUTIONS""; ""2.4 INVESTMENT RETURN""; ""2.5 REINVESTMENT CONSIDERATIONS""; ""2.6 APPROXIMATE DOLLAR-WEIGHTED YIELD RATES""; ""2.7 FUND PERFORMANCE""; ""2.8 PROBLEMS, CHAPTER 2""; ""(2.0) Chapter 2 writing problems""; ""(2.2) Equations of value for investments involving a single deposit made under compound interest""; ""2.3) Equations of value for investments with multiple contributions""; ""(2.4) Investment return"" ""(2.5) Reinvestment considerations""""(2.6) Approximate dollar-weighted yield rates""; ""(2.7) Fund performance""; ""Chapter 2 review problems""; ""3 Annuities (annuities certain)""; ""3.1 INTRODUCTION""; ""3.2 ANNUITIES - IMMEDIATE""; ""3.3 ANNUITIES -DUE""; ""3.4 PERPETUITIES""; ""3.5 DEFERRED ANNUITIES AND VALUES ON ANY DATE""; ""3.6 OUTSTANDING LOAN BALANCES""; ""3.7 NONLEVEL ANNUITIES""; ""3.8 ANNUITIES WITH PAYMENTS IN GEOMETRIC PROGRESSION""; ""3.9 ANNUITIES WITH PAYMENTS IN ARITHMETIC PROGRESSION""; ""3.10 YIELD RATE EXAMPLES INVOLVING ANNUITIES"" ""3.11 ANNUITY SYMBOLS FOR NONINTEGRAL TERMS"" |
| Record Nr. | UNINA-9910465220903321 |
|
Vaaler Leslie Jane Federer
|
||
| Washington, D.C., : Mathematical Association of America, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical interest theory [[electronic resource] /] / Leslie Jane Federer Vaaler, James W. Daniel
| Mathematical interest theory [[electronic resource] /] / Leslie Jane Federer Vaaler, James W. Daniel |
| Autore | Vaaler Leslie Jane Federer |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Washington, D.C., : Mathematical Association of America, 2009 |
| Descrizione fisica | 1 online resource (493 p.) |
| Disciplina | 332.801/513 |
| Altri autori (Persone) | DanielJames W |
| Collana |
AMS/MAA Textbooks
MAA textbooks |
| Soggetto topico |
Interest rates - Mathematical models
Interest rate futures - Mathematical models Risk management - Mathematical models |
| ISBN | 1-61444-600-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""cover ""; ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""To students""; ""Examples""; ""Problems""; ""Special Features""; ""Coverage""; ""Second edition""; ""Financial transactions""; ""Acknowledgments""; ""Contacting the authors""; ""0 An introduction to the Texas Instruments BA II Plus""; ""0.1 CHOOSING A CALCULATOR""; ""0.2 FONT CONVENTION""; ""0.3 BA II PLUS BASICS""; ""0.4 PROBLEMS, CHAPTER 0""; ""1 The growth of money""; ""1.1 INTRODUCTION""; ""1.2 WHAT IS INTEREST ?""; ""1.3 ACCUMULATION AND AMOUNT FUNCTIONS""
""1.4 SIMPLE INTEREST / LINEAR ACCUMULATION FUNCTIONS""""1.5 COMPOUND INTEREST (THE USUAL CASE!)""; ""1.6 INTEREST IN ADVANCE / THE EFFECTIVE DISCOUNT RATE""; ""1.7 DISCOUNT FUNCTIONS / THE TIME VALUE OF MONEY""; ""1.8 SIMPLE DISCOUNT""; ""1.9 COMPOUND DISCOUNT""; ""1.10 NOMINAL RATES OF INTEREST AND DISCOUNT""; ""1.11 A FRIENDLY COMPETITION (CONSTANT FORCE OF INTEREST)""; ""1.12 FORCE OF INTEREST""; ""1.13 NOTE FOR THOSE WHO SKIPPED SECTIONS (1.11) AND (1.12)""; ""1.14 INFLATION""; ""1.15 PROBLEMS, CHAPTER 1""; ""1.3) Accumulation and amount functions""; ""(1.4) Simple interest"" ""(1.5) Compound interest""""(1.6) Effective discount rates/ Interest in advance""; ""(1.7) Discount functions/ The time value of money""; ""(1.8) Simple discount""; ""(1.9) Compound discount""; ""(1.10) Nominal rates of interest and discount""; ""(1.11) A friendly competition (Constant force of interest)""; ""(1.12) Force of interest""; ""(1.13) Note for those who skipped Section (1.11) and (1.12)""; ""(1.14) Inflation""; ""Chapter 1 review problems""; ""2 Equations of value and yield rates""; ""2.1 INTRODUCTION"" ""2.2 EQUATIONS OF VALUE FOR INVESTMENTS INVOLVING A SINGLE DEPOSIT MADE UNDER COMPOUND INTEREST""""2.3 EQUATIONS OF VALUE FOR INVESTMENTS WITH MULTIPLE CONTRIBUTIONS""; ""2.4 INVESTMENT RETURN""; ""2.5 REINVESTMENT CONSIDERATIONS""; ""2.6 APPROXIMATE DOLLAR-WEIGHTED YIELD RATES""; ""2.7 FUND PERFORMANCE""; ""2.8 PROBLEMS, CHAPTER 2""; ""(2.0) Chapter 2 writing problems""; ""(2.2) Equations of value for investments involving a single deposit made under compound interest""; ""2.3) Equations of value for investments with multiple contributions""; ""(2.4) Investment return"" ""(2.5) Reinvestment considerations""""(2.6) Approximate dollar-weighted yield rates""; ""(2.7) Fund performance""; ""Chapter 2 review problems""; ""3 Annuities (annuities certain)""; ""3.1 INTRODUCTION""; ""3.2 ANNUITIES - IMMEDIATE""; ""3.3 ANNUITIES -DUE""; ""3.4 PERPETUITIES""; ""3.5 DEFERRED ANNUITIES AND VALUES ON ANY DATE""; ""3.6 OUTSTANDING LOAN BALANCES""; ""3.7 NONLEVEL ANNUITIES""; ""3.8 ANNUITIES WITH PAYMENTS IN GEOMETRIC PROGRESSION""; ""3.9 ANNUITIES WITH PAYMENTS IN ARITHMETIC PROGRESSION""; ""3.10 YIELD RATE EXAMPLES INVOLVING ANNUITIES"" ""3.11 ANNUITY SYMBOLS FOR NONINTEGRAL TERMS"" |
| Record Nr. | UNINA-9910791743603321 |
|
Vaaler Leslie Jane Federer
|
||
| Washington, D.C., : Mathematical Association of America, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical interest theory / / Leslie Jane Federer Vaaler, James W. Daniel
| Mathematical interest theory / / Leslie Jane Federer Vaaler, James W. Daniel |
| Autore | Vaaler Leslie Jane Federer |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Washington, D.C., : Mathematical Association of America, 2009 |
| Descrizione fisica | 1 online resource (493 p.) |
| Disciplina | 332.801/513 |
| Altri autori (Persone) | DanielJames W |
| Collana |
AMS/MAA Textbooks
MAA textbooks |
| Soggetto topico |
Interest rates - Mathematical models
Interest rate futures - Mathematical models Risk management - Mathematical models |
| ISBN | 1-61444-600-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""cover ""; ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""To students""; ""Examples""; ""Problems""; ""Special Features""; ""Coverage""; ""Second edition""; ""Financial transactions""; ""Acknowledgments""; ""Contacting the authors""; ""0 An introduction to the Texas Instruments BA II Plus""; ""0.1 CHOOSING A CALCULATOR""; ""0.2 FONT CONVENTION""; ""0.3 BA II PLUS BASICS""; ""0.4 PROBLEMS, CHAPTER 0""; ""1 The growth of money""; ""1.1 INTRODUCTION""; ""1.2 WHAT IS INTEREST ?""; ""1.3 ACCUMULATION AND AMOUNT FUNCTIONS""
""1.4 SIMPLE INTEREST / LINEAR ACCUMULATION FUNCTIONS""""1.5 COMPOUND INTEREST (THE USUAL CASE!)""; ""1.6 INTEREST IN ADVANCE / THE EFFECTIVE DISCOUNT RATE""; ""1.7 DISCOUNT FUNCTIONS / THE TIME VALUE OF MONEY""; ""1.8 SIMPLE DISCOUNT""; ""1.9 COMPOUND DISCOUNT""; ""1.10 NOMINAL RATES OF INTEREST AND DISCOUNT""; ""1.11 A FRIENDLY COMPETITION (CONSTANT FORCE OF INTEREST)""; ""1.12 FORCE OF INTEREST""; ""1.13 NOTE FOR THOSE WHO SKIPPED SECTIONS (1.11) AND (1.12)""; ""1.14 INFLATION""; ""1.15 PROBLEMS, CHAPTER 1""; ""1.3) Accumulation and amount functions""; ""(1.4) Simple interest"" ""(1.5) Compound interest""""(1.6) Effective discount rates/ Interest in advance""; ""(1.7) Discount functions/ The time value of money""; ""(1.8) Simple discount""; ""(1.9) Compound discount""; ""(1.10) Nominal rates of interest and discount""; ""(1.11) A friendly competition (Constant force of interest)""; ""(1.12) Force of interest""; ""(1.13) Note for those who skipped Section (1.11) and (1.12)""; ""(1.14) Inflation""; ""Chapter 1 review problems""; ""2 Equations of value and yield rates""; ""2.1 INTRODUCTION"" ""2.2 EQUATIONS OF VALUE FOR INVESTMENTS INVOLVING A SINGLE DEPOSIT MADE UNDER COMPOUND INTEREST""""2.3 EQUATIONS OF VALUE FOR INVESTMENTS WITH MULTIPLE CONTRIBUTIONS""; ""2.4 INVESTMENT RETURN""; ""2.5 REINVESTMENT CONSIDERATIONS""; ""2.6 APPROXIMATE DOLLAR-WEIGHTED YIELD RATES""; ""2.7 FUND PERFORMANCE""; ""2.8 PROBLEMS, CHAPTER 2""; ""(2.0) Chapter 2 writing problems""; ""(2.2) Equations of value for investments involving a single deposit made under compound interest""; ""2.3) Equations of value for investments with multiple contributions""; ""(2.4) Investment return"" ""(2.5) Reinvestment considerations""""(2.6) Approximate dollar-weighted yield rates""; ""(2.7) Fund performance""; ""Chapter 2 review problems""; ""3 Annuities (annuities certain)""; ""3.1 INTRODUCTION""; ""3.2 ANNUITIES - IMMEDIATE""; ""3.3 ANNUITIES -DUE""; ""3.4 PERPETUITIES""; ""3.5 DEFERRED ANNUITIES AND VALUES ON ANY DATE""; ""3.6 OUTSTANDING LOAN BALANCES""; ""3.7 NONLEVEL ANNUITIES""; ""3.8 ANNUITIES WITH PAYMENTS IN GEOMETRIC PROGRESSION""; ""3.9 ANNUITIES WITH PAYMENTS IN ARITHMETIC PROGRESSION""; ""3.10 YIELD RATE EXAMPLES INVOLVING ANNUITIES"" ""3.11 ANNUITY SYMBOLS FOR NONINTEGRAL TERMS"" |
| Record Nr. | UNINA-9910822032003321 |
|
Vaaler Leslie Jane Federer
|
||
| Washington, D.C., : Mathematical Association of America, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Volatility and Correlation [[electronic resource] ] : The Perfect Hedger and the Fox
| Volatility and Correlation [[electronic resource] ] : The Perfect Hedger and the Fox |
| Autore | Rebonato Riccardo |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, : Wiley, 2005 |
| Descrizione fisica | 1 online resource (866 p.) |
| Disciplina |
332.6323
332.64/53 |
| Altri autori (Persone) | RebonatoRiccardo |
| Collana | The Wiley Finance Series |
| Soggetto topico |
Interest rate futures
Interest rate futures - Mathematical models Mathematical models Options (Finance) - Mathematical models Options (Finance) Prices Securities Securities - Prices - Mathematical models Investment & Speculation Finance Business & Economics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-67353-0
1-280-26910-3 9786610269105 0-470-09140-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Volatility and Correlation 2(nd) Edition; Contents; Preface; 0.1 Why a Second Edition?; 0.2 What This Book Is Not About; 0.3 Structure of the Book; 0.4 The New Subtitle; Acknowledgements; I Foundations; 1 Theory and Practice of Option Modelling; 1.1 The Role of Models in Derivatives Pricing; 1.1.1 What Are Models For?; 1.1.2 The Fundamental Approach; 1.1.3 The Instrumental Approach; 1.1.4 A Conundrum (or, 'What is Vega Hedging For?'); 1.2 The Efficient Market Hypothesis and Why It Matters for Option Pricing; 1.2.1 The Three Forms of the EMH; 1.2.2 Pseudo-Arbitrageurs in Crisis
1.2.3 Model Risk for Traders and Risk Managers1.2.4 The Parable of the Two Volatility Traders; 1.3 Market Practice; 1.3.1 Different Users of Derivatives Models; 1.3.2 In-Model and Out-of-Model Hedging; 1.4 The Calibration Debate; 1.4.1 Historical vs Implied Calibration; 1.4.2 The Logical Underpinning of the Implied Approach; 1.4.3 Are Derivatives Markets Informationally Efficient?; 1.4.4 Back to Calibration; 1.4.5 A Practical Recommendation; 1.5 Across-Markets Comparison of Pricing and Modelling Practices; 1.6 Using Models; 2 Option Replication; 2.1 The Bedrock of Option Pricing 2.2 The Analytic (PDE) Approach2.2.1 The Assumptions; 2.2.2 The Portfolio-Replication Argument (Deterministic Volatility); 2.2.3 The Market Price of Risk with Deterministic Volatility; 2.2.4 Link with Expectations - the Feynman-Kac Theorem; 2.3 Binomial Replication; 2.3.1 First Approach - Replication Strategy; 2.3.2 Second Approach - 'Naive Expectation'; 2.3.3 Third Approach - 'Market Price of Risk'; 2.3.4 A Worked-Out Example; 2.3.5 Fourth Approach - Risk-Neutral Valuation; 2.3.6 Pseudo-Probabilities; 2.3.7 Are the Quantities π(1) and π(2) Really Probabilities? 2.3.8 Introducing Relative Prices2.3.9 Moving to a Multi-Period Setting; 2.3.10 Fair Prices as Expectations; 2.3.11 Switching Numeraires and Relating Expectations Under Different Measures; 2.3.12 Another Worked-Out Example; 2.3.13 Relevance of the Results; 2.4 Justifying the Two-State Branching Procedure; 2.4.1 How To Recognize a Jump When You See One; 2.5 The Nature of the Transformation between Measures: Girsanov's Theorem; 2.5.1 An Intuitive Argument; 2.5.2 A Worked-Out Example; 2.6 Switching Between the PDE, the Expectation and the Binomial Replication Approaches; 3 The Building Blocks 3.1 Introduction and Plan of the Chapter3.2 Definition of Market Terms; 3.3 Hedging Forward Contracts Using Spot Quantities; 3.3.1 Hedging Equity Forward Contracts; 3.3.2 Hedging Interest-Rate Forward Contracts; 3.4 Hedging Options: Volatility of Spot and Forward Processes; 3.5 The Link Between Root-Mean-Squared Volatilities and the Time-Dependence of Volatility; 3.6 Admissibility of a Series of Root-Mean-Squared Volatilities; 3.6.1 The Equity/FX Case; 3.6.2 The Interest-Rate Case; 3.7 Summary of the Definitions So Far; 3.8 Hedging an Option with a Forward-Setting Strike 3.8.1 Why Is This Option Important? (And Why Is it Difficult to Hedge?) |
| Record Nr. | UNINA-9910143702803321 |
|
Rebonato Riccardo
|
||
| Hoboken, : Wiley, 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
