05385nam 2200685 a 450 991082110750332120230801223829.01-281-60363-59786613784322981-4390-86-0(CKB)2670000000230182(EBL)982499(OCoLC)804661856(SSID)ssj0000695374(PQKBManifestationID)12282614(PQKBTitleCode)TC0000695374(PQKBWorkID)10689231(PQKB)11561192(MiAaPQ)EBC982499(WSP)00002716(Au-PeEL)EBL982499(CaPaEBR)ebr10583617(CaONFJC)MIL378432(OCoLC)810413797(EXLCZ)99267000000023018220120810d2012 uy 0engur|n|---|||||txtccrAn elementary introduction to stochastic interest rate modeling[electronic resource] /Nicolas Privault2nd ed.Hackensack, N.J. World Scientific20121 online resource (243 p.)Advanced series on statistical science & applied probability ;v. 16Description based upon print version of record.981-4390-85-2 Includes bibliographical references and indexes.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 Properties4.2 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 Dynamics6.4 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 Exercises10. 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 VariablesConditional 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 IndexInterest 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 wiAdvanced series on statistical science & applied probability ;v. 16.Interest rate futuresMathematical modelsStochastic modelsInterest rate futuresMathematical models.Stochastic models.332.8332.80151922Privault Nicolas475313MiAaPQMiAaPQMiAaPQBOOK9910821107503321Elementary introduction to stochastic interest rate modeling1139892UNINA