Interest Rate Derivatives Valuation, Calibration and Sensitivity Analysis

Format:

Book

Author/Creator:

Beyna, Ingo

Series:

Lecture notes in economics and mathematical systems

Lecture Notes in Economics and Mathematical Systems v. 666

Language:

English

Subjects (All):

Interest rates--Mathematical models.

Interest rates.

Physical Description:

1 online resource

Place of Publication:

Dordrecht Springer 2012

Summary:

The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitiv

Contents:

Interest Rate Derivatives; Valuation, Calibrationand Sensitivity Analysis; Foreword; Preface; Acknowledgment; Contents; Chapter1 Literature Review; Chapter2 The Cheyette Model Class; 2.1 The Heath-Jarrow-Morton Framework; 2.2 Derivation of the Cheyette Model Class; 2.3 Particular Models in the Cheyette Model Class; 2.3.1 Ho-Lee Model; 2.3.2 Hull-White Model; 2.3.3 The Three Factor Exponential Model; 2.4 Remarks on the Cheyette Model Class; Chapter3 Analytical Pricing Formulas; 3.1 Bonds; 3.1.1 Multifactor Cheyette Model; 3.1.2 One-Factor Cheyette Model

3.1.3 The Three Factor Exponential Model3.2 Caplets/Floorlets; 3.2.1 The Three Factor Exponential Model; 3.3 Swaptions; Chapter4 Calibration; 4.1 Literature Review; 4.2 The Calibration Problem; 4.2.1 Formulation; 4.2.2 Constraints; 4.2.3 Characterization of the Optimization Space; 4.2.4 Quality Check; 4.3 Optimization Methods; 4.3.1 Newton Algorithm; 4.3.1.1 Description; 4.3.1.2 Results; 4.3.2 Powell Algorithm; 4.3.2.1 Description; 4.3.2.2 Results; 4.3.3 Downhill Simplex Algorithm; 4.3.3.1 Description; 4.3.3.2 Results; 4.3.4 Simulated Annealing; 4.3.4.1 Description; 4.3.4.2 Results

4.3.5 Genetic Optimization4.3.5.1 Description; 4.3.5.2 Results; 4.4 Numerical Results; Chapter5 Monte Carlo Methods; 5.1 Literature Review; 5.2 Simulations in the Cheyette Model Class; 5.3 Quasi-Monte Carlo Simulation; 5.4 Pricing Bonds and European Options; 5.4.1 Pricing Under the Forward Measure; 5.4.2 Distribution of the State Variables; 5.4.3 Covariance; 5.4.4 Numerical Results; 5.4.4.1 Bonds; 5.4.4.2 Caplets; 5.4.4.3 European Swaptions; 5.5 Pricing Bermudan Swaptions; 5.5.1 Problem Formulation; 5.5.2 Random Tree Methods; 5.5.2.1 The High Estimator; 5.5.2.2 The Low Estimator

5.5.3 Numerical Results5.6 Snowballs; 5.6.1 Numerical Results; Chapter6 Characteristic Function Method; 6.1 Literature Review; 6.2 Affine Diffusion Setup; 6.2.1 Fundamentals; 6.2.2 Classification of the Cheyette Model Class; 6.3 Characteristic Functions; 6.3.1 Fundamentals; 6.3.2 Characteristic Functions in the Affine Diffusion Setup; 6.3.3 Characteristic Functions in the Cheyette Model Class; 6.3.3.1 Ho-Lee Model; 6.3.3.2 Hull-White Model; 6.3.3.3 The Three Factor Exponential Model; 6.4 Pricing with Characteristic Functions; 6.4.1 Fundamentals; 6.4.2 Caplets; 6.4.3 Numerical Results

6.5 Numerical AnalysisChapter7 PDE Valuation; 7.1 Literature Review; 7.2 Derivation of the Valuation PDE; 7.2.1 Some Specific Examples; 7.2.1.1 Ho-Lee Model; 7.2.1.2 Three Factor Exponential Model; 7.3 Boundary Conditions; 7.3.1 Terminal Condition; 7.3.1.1 Bonds; 7.3.1.2 Caplets/Floorlets; 7.3.1.3 Swaptions; 7.3.2 Spatial Domain; 7.4 Remarks on the Valuation PDE; 7.5 Numerical Method for PDE Valuation; 7.5.1 Finite Difference with PSOR; 7.5.1.1 Discretization; 7.5.1.2 PSOR; 7.5.2 Sparse Grid Implementation; 7.5.2.1 The Sparse Grid Combination Technique; 7.5.2.2 Modified Sparse Grid

7.6 Numerical Results

Notes:

Print version record

Includes bibliographical references and index

Other Format:

Print version Beyna, Ingo. Interest Rate Derivatives : Valuation, Calibration and Sensitivity Analysis

ISBN:

9783642349256

3642349250

OCLC:

880908855

Access Restriction:

Restricted for use by site license