LEADER 05419nam 2200697 a 450 001 9910462558603321 005 20200520144314.0 010 $a1-281-60363-5 010 $a9786613784322 010 $a981-4390-86-0 035 $a(CKB)2670000000230182 035 $a(EBL)982499 035 $a(OCoLC)804661856 035 $a(SSID)ssj0000695374 035 $a(PQKBManifestationID)12282614 035 $a(PQKBTitleCode)TC0000695374 035 $a(PQKBWorkID)10689231 035 $a(PQKB)11561192 035 $a(MiAaPQ)EBC982499 035 $a(WSP)00002716 035 $a(Au-PeEL)EBL982499 035 $a(CaPaEBR)ebr10583617 035 $a(CaONFJC)MIL378432 035 $a(OCoLC)810413797 035 $a(EXLCZ)992670000000230182 100 $a20120810d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn elementary introduction to stochastic interest rate modeling$b[electronic resource] /$fNicolas Privault 205 $a2nd ed. 210 $aHackensack, N.J. $cWorld Scientific$d2012 215 $a1 online resource (243 p.) 225 1 $aAdvanced series on statistical science & applied probability ;$vv. 16 300 $aDescription based upon print version of record. 311 $a981-4390-85-2 320 $aIncludes bibliographical references and indexes. 327 $aPreface; 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 327 $a4.2 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 327 $a6.4 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 327 $a10. 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 327 $aConditional 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 330 $aInterest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students. This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises wi 410 0$aAdvanced series on statistical science & applied probability ;$vv. 16. 606 $aInterest rate futures$xMathematical models 606 $aStochastic models 608 $aElectronic books. 615 0$aInterest rate futures$xMathematical models. 615 0$aStochastic models. 676 $a332.8 676 $a332.80151922 700 $aPrivault$b Nicolas$0475313 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462558603321 996 $aElementary introduction to stochastic interest rate modeling$91139892 997 $aUNINA