Brace Engineering BGM

Erscheinungsjahr 2007
ISBN: 978-1-58488-969-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 240 Seiten

Reihe: Chapman & Hall/CRC Financial Mathematics Series

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.

Zielgruppe

Practitioners, researchers, programmers, and students in quantitative finance and investment.

Autoren/Hrsg.

Brace, Alan

Fachgebiete

• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines

Inhaltsverzeichnis

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