05625nam 2200721 a 450 991101955650332120200520144314.09786610740024978111867334811186733449781280740022128074002797804700604140470060417(CKB)1000000000357403(EBL)284348(OCoLC)85815261(SSID)ssj0000191884(PQKBManifestationID)11196937(PQKBTitleCode)TC0000191884(PQKBWorkID)10187159(PQKB)10087445(MiAaPQ)EBC284348(Perlego)2784583(EXLCZ)99100000000035740320060823d2006 uy 0engur|n|---|||||txtccrThe LIBOR market model in practice /Dariusz Gatarek, Przemyslaw Bachert and Robert MaksymiukChichester, England ;Hoboken, NJ John Wiley & Sonsc20061 online resource (292 p.)Wiley finance seriesDescription based upon print version of record.9780470014431 0470014431 Includes bibliographical references (p. [259]-265) and index.The 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 Measure2 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 Calibration4.1 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 Options5.3 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 Algorithms7.4.1 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 Conclusions9 Calibration Algorithms to Caps and Swaptions Based on Optimization TechniquesThe 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, suWiley finance series.London Interbank Offer Rate market model in practiceInterest ratesMathematical modelsInterest rate futuresMathematical modelsInterest ratesMathematical models.Interest rate futuresMathematical models.332.1/13Gatarek Dariusz1842632Bachert Przemyslaw1842633Maksymiuk Robert1842634MiAaPQMiAaPQMiAaPQBOOK9911019556503321The LIBOR market model in practice4422812UNINA