An elementary introduction to stochastic interest rate modeling / Nicolas Privault.

Format:

Book

Author/Creator:

Privault, Nicolas.

Series:

Advanced series on statistical science & applied probability ; v. 16.

Advanced series on statistical science & applied probability ; v. 16

Language:

English

Subjects (All):

Interest rate futures--Mathematical models.

Interest rate futures.

Stochastic models.

Physical Description:

1 online resource (243 p.)

Edition:

2nd ed.

Place of Publication:

Hackensack, N.J. : World Scientific, 2012.

Language Note:

English

Summary:

Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students. This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises wi

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

ISBN:

9786613784322

9781281603630

1281603635

9789814390866

9814390860

OCLC:

804661856