紹介
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 instruments.
目次
PREFACE INTRODUCTION Background HJM The First Correct Black Caplet Forward BGM Construction BOND AND SWAP BASICS Zero Coupon Bonds-Drifts and Volatilities Swaps and Swap Notation SHIFTED BGM Definition of Shifted Model Backward Construction SWAPRATE DYNAMICS Splitting the Swaprate The Shift Part The Stochastic Part Swaption Values Swaprate Models PROPERTIES OF MEASURES Changes among Forward and Swaprate Measures Terminal Measure Spot LIBOR Measure HISTORICAL CORRELATION AND VOLATILITY Flat and Shifted BGM off Forwards Gaussian HJM off Yield-to-Maturity Flat and Shifted BGM off Swaprates CALIBRATION TECHNIQUES Fitting the Skew Maturity-Only Fit Homogeneous Spines Separable One-Factor Fit Separable Multi-Factor Fit Pedersen's Method Cascade Fit Exact Fit with Semidefinite Programming INTERPOLATING BETWEEN NODES Interpolating Forwards Dead Forwards Interpolation of Discount Factors Consistent Volatility SIMULATION Glasserman-Type Simulation Big-Step Simulation TIMESLICERS Terminal Measure Timeslicer Intermediate Measure Timeslicer A Spot Measure Timeslicer Is Problematic Some Technical Points Two-Dimensional Timeslicer PATHWISE DELTAS Partial Derivatives of Forwards Partial Derivatives of Zeros and Swaps Differentiating Option Payoffs Vanilla Caplets and Swaptions Barrier Caps and Floors BERMUDANS Backward Recursion The Longstaff-Schwartz Lower Bound Technique Upper Bounds Bermudan Deltas VEGA AND SHIFT HEDGING When Calibrated to Coterminal Swaptions When Calibrated to Liquid Swaptions CROSS-ECONOMY BGM Cross-Economy HJM Forward FX Contracts Cross-Economy Models Model with the Spot Volatility Deterministic Cross-Economy Correlation Pedersen-Type Cross-Economy Calibration INFLATION TIPS and the CPI Dynamics of the Forward Inflation Curve STOCHASTIC VOLATILITY BGM Construction Swaprate Dynamics Shifted Heston Options Simulation Interpolation, Greeks, and Calibration OPTIONS IN BRAZIL Overnight DI Pre-DI Swaps and Swaptions DI Index Options DI Futures Contracts DI Futures Options APPENDIX: NOTATION AND FORMULAE Swap Notation Gaussian Distributions Stochastic Calculus Linear Algebra Some Fourier Transform Technicalities The Chi-Squared Distribution Miscellaneous REFERENCES INDEX
