Engineering BGM: 1st Edition (Hardback) book cover

Engineering BGM

1st Edition

By Alan Brace

Chapman and Hall/CRC

240 pages

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Hardback: 9781584889687
pub: 2007-11-01
$115.00
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pub: 2007-11-01
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Description

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.

Table of Contents

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

About the Series

Chapman and Hall/CRC Financial Mathematics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
BUS027000
BUSINESS & ECONOMICS / Finance
MAT000000
MATHEMATICS / General
MAT029000
MATHEMATICS / Probability & Statistics / General