Engineering BGM

Engineering BGM

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Also known as the Libor market model, the Brace-Gatarek-Musiela (BGM) model is becoming an industry standard for pricing interest rate derivatives. Written by one of its developers, Engineering BGM builds progressively from simple to more sophisticated versions of the BGM model, offering a range of methods that can be programmed into production code to suit readers' requirements. After introducing the standard lognormal flat BGM model, the book focuses on the shifted/displaced diffusion version. Using this version, the author develops basic ideas about construction, change of measure, correlation, calibration, simulation, timeslicing, pricing, delta hedging, barriers, callable exotics (Bermudans), and vega hedging. Subsequent chapters address cross-economy BGM, the adaptation of the BGM model to inflation, a simple tractable stochastic volatility version of BGM, and Brazilian options suitable for BGM analysis. An appendix provides notation and an extensive array of formulae.The straightforward presentation of various BGM models in this handy book will help promote a robust, safe, and stable environment for calibrating, simulating, pricing, and hedging interest rate more

Product details

  • Electronic book text | 240 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 1584889691
  • 9781584889694

Table of contents

PREFACEINTRODUCTIONBackground HJMThe First Correct Black CapletForward BGM ConstructionBOND AND SWAP BASICSZero Coupon Bonds-Drifts and VolatilitiesSwaps and Swap NotationSHIFTED BGMDefinition of Shifted ModelBackward ConstructionSWAPRATE DYNAMICSSplitting the SwaprateThe Shift PartThe Stochastic PartSwaption ValuesSwaprate ModelsPROPERTIES OF MEASURESChanges among Forward and Swaprate MeasuresTerminal MeasureSpot LIBOR MeasureHISTORICAL CORRELATION AND VOLATILITYFlat and Shifted BGM off ForwardsGaussian HJM off Yield-to-MaturityFlat and Shifted BGM off SwapratesCALIBRATION TECHNIQUESFitting the SkewMaturity-Only FitHomogeneous SpinesSeparable One-Factor FitSeparable Multi-Factor FitPedersen's MethodCascade FitExact Fit with Semidefinite ProgrammingINTERPOLATING BETWEEN NODESInterpolating ForwardsDead ForwardsInterpolation of Discount FactorsConsistent VolatilitySIMULATIONGlasserman-Type SimulationBig-Step SimulationTIMESLICERSTerminal Measure TimeslicerIntermediate Measure TimeslicerA Spot Measure Timeslicer Is ProblematicSome Technical PointsTwo-Dimensional TimeslicerPATHWISE DELTASPartial Derivatives of ForwardsPartial Derivatives of Zeros and SwapsDifferentiating Option PayoffsVanilla Caplets and SwaptionsBarrier Caps and FloorsBERMUDANSBackward RecursionThe Longstaff-Schwartz Lower Bound TechniqueUpper BoundsBermudan DeltasVEGA AND SHIFT HEDGINGWhen Calibrated to Coterminal SwaptionsWhen Calibrated to Liquid SwaptionsCROSS-ECONOMY BGMCross-Economy HJMForward FX ContractsCross-Economy ModelsModel with the Spot Volatility DeterministicCross-Economy CorrelationPedersen-Type Cross-Economy CalibrationINFLATIONTIPS and the CPIDynamics of the Forward Inflation CurveSTOCHASTIC VOLATILITY BGMConstructionSwaprate DynamicsShifted Heston OptionsSimulationInterpolation, Greeks, and CalibrationOPTIONS IN BRAZILOvernight DIPre-DI Swaps and SwaptionsDI Index OptionsDI Futures ContractsDI Futures OptionsAPPENDIX: NOTATION AND FORMULAESwap NotationGaussian DistributionsStochastic CalculusLinear AlgebraSome Fourier Transform TechnicalitiesThe Chi-Squared DistributionMiscellaneousREFERENCESINDEXshow more