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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 [[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-9910821107503321 |
|
Privault Nicolas
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault
| Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [1st ed. 2009.] |
| Pubbl/distr/stampa | Berlin, Germany : , : Springer, , [2009] |
| Descrizione fisica | 1 online resource (321 p.) |
| Disciplina | 519.22 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Stochastic analysis
Space and time Martingales (Mathematics) |
| ISBN |
1-282-65581-7
9786612655814 3-642-02380-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The Discrete Time Case -- Continuous Time Normal Martingales -- Gradient and Divergence Operators -- Annihilation and Creation Operators -- Analysis on the Wiener Space -- Analysis on the Poisson Space -- Local Gradients on the Poisson Space -- Option Hedging in Continuous Time. |
| Record Nr. | UNINA-9910483837903321 |
|
Privault Nicolas
|
||
| Berlin, Germany : , : Springer, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault
| Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [1st ed. 2009.] |
| Pubbl/distr/stampa | Berlin, Germany : , : Springer, , [2009] |
| Descrizione fisica | 1 online resource (321 p.) |
| Disciplina | 519.22 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Stochastic analysis
Space and time Martingales (Mathematics) |
| ISBN |
1-282-65581-7
9786612655814 3-642-02380-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The Discrete Time Case -- Continuous Time Normal Martingales -- Gradient and Divergence Operators -- Annihilation and Creation Operators -- Analysis on the Wiener Space -- Analysis on the Poisson Space -- Local Gradients on the Poisson Space -- Option Hedging in Continuous Time. |
| Record Nr. | UNISA-996466768903316 |
|
Privault Nicolas
|
||
| Berlin, Germany : , : Springer, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Understanding Markov Chains [[electronic resource] ] : Examples and Applications / / by Nicolas Privault
| Understanding Markov Chains [[electronic resource] ] : Examples and Applications / / by Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [2nd ed. 2018.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XVII, 372 p. 44 illus.) |
| Disciplina | 519.233 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Probabilities
Statistics Probability Theory and Stochastic Processes Statistical Theory and Methods Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences |
| ISBN |
978-981-13-0659-4
981-13-0659-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Probability Background -- Gambling Problems -- Random Walks -- Discrete-Time Markov Chains -- First Step Analysis -- Classification of States -- Long-Run Behavior of Markov Chains -- Branching Processes -- Continuous-Time Markov Chains -- Discrete-Time Martingales -- Spatial Poisson Processes -- Reliability Theory. |
| Record Nr. | UNINA-9910300101903321 |
|
Privault Nicolas
|
||
| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Understanding Markov Chains [[electronic resource] ] : Examples and Applications / / by Nicolas Privault
| Understanding Markov Chains [[electronic resource] ] : Examples and Applications / / by Nicolas Privault |
| Autore | Privault Nicolas |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2013 |
| Descrizione fisica | 1 online resource (357 p.) |
| Disciplina | 519.233 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Probabilities
Statistics Probability Theory and Stochastic Processes Statistical Theory and Methods Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences |
| ISBN | 981-4451-51-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- 1) Probability Background -- 2) Gambling Problems -- 3) Random Walks -- 4) Discrete-Time Markov Chains -- 5) First Step Analysis -- 6) Classication of States -- 7) Long-Run Behavior of Markov Chains -- 8) Branching Processes -- 9) Continuous-Time Markov Chains -- 10) Discrete-Time Martingales -- 11) Spatial Poisson Processes -- 12) Reliability Theory -- Some Useful Identities -- Solutions to the Exercises -- References -- Index. |
| Record Nr. | UNINA-9910438037003321 |
|
Privault Nicolas
|
||
| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||