LEADER 05501nam 2200673 a 450 001 9910143707703321 005 20170815112945.0 010 $a1-118-67334-4 010 $a1-280-74002-7 010 $a9786610740024 010 $a0-470-06041-7 035 $a(CKB)1000000000357403 035 $a(EBL)284348 035 $a(OCoLC)85815261 035 $a(SSID)ssj0000191884 035 $a(PQKBManifestationID)11196937 035 $a(PQKBTitleCode)TC0000191884 035 $a(PQKBWorkID)10187159 035 $a(PQKB)10087445 035 $a(MiAaPQ)EBC284348 035 $a(EXLCZ)991000000000357403 100 $a20060823d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe LIBOR market model in practice$b[electronic resource] /$fDariusz Gatarek, Przemyslaw Bachert and Robert Maksymiuk 210 $aChichester, England ;$aHoboken, NJ $cJohn Wiley & Sons$dc2006 215 $a1 online resource (292 p.) 225 1 $aWiley finance series 300 $aDescription based upon print version of record. 311 $a0-470-01443-1 320 $aIncludes bibliographical references (p. [259]-265) and index. 327 $aThe 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 327 $a2 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 327 $a4.1 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 327 $a5.3 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 327 $a7.4.1 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 327 $a9 Calibration Algorithms to Caps and Swaptions Based on Optimization Techniques 330 $aThe LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, su 410 0$aWiley finance series. 606 $aInterest rates$xMathematical models 606 $aInterest rate futures$xMathematical models 608 $aElectronic books. 615 0$aInterest rates$xMathematical models. 615 0$aInterest rate futures$xMathematical models. 676 $a332.64570151 676 $a332.8011 700 $aGatarek$b Dariusz$0935699 701 $aBachert$b Przemyslaw$0935700 701 $aMaksymiuk$b Robert$0935701 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143707703321 996 $aThe LIBOR market model in practice$92107737 997 $aUNINA