Kienitz / Caspers Interest Rate Derivatives Explained: Volume 2

Term Structure and Volatility Modelling
1. Auflage 2017
ISBN: 978-1-137-36019-9
Verlag: Palgrave Macmillan UK
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 261 Seiten

Reihe: Financial Engineering Explained

This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.
 


Jörg Kienitz is Partner at Quaternion Risk Management where he is responsible for business development, pricing models research and risk management consulting. Prior to this he was a Director at Deloitte and Co-lead of the quant team. Before joining Deloitte he was Head of Quantitative Analytics at Deutsche Postbank AG where he was involved in developing/implementing models for pricing, hedging and asset allocation. He lectures at university level on advanced financial modelling and implementation at the universities of Cape Town (UCT) and Wuppertal (BUW) where he is Adjunct Associate Professor, respectively Assistant Professor. Before that he lectured in the part time Masters programme at Oxford University on Financial Mathematics. He is a speaker at a number of major quant finance conferences including Global Derivatives and WBS Fixed Income. Jörg holds a PhD in Probability Theory from Bielefeld University.
Peter Caspers is senior quantitative analyst at Quaternion Risk Management. He has over 17 years of experience as a quant in different banks and is a co-author of QuantLib, an open-source library for quantitative finance. He holds a degree in mathematics and computer science.

Autoren/Hrsg.

Kienitz, Jörg

Caspers, Peter

Inhaltsverzeichnis

1;Contents;7
2;List of Figures;9
3;List of Tables;13
4;Goals of this Book and Global Overview;16
4.1;Introduction and Management Summary;16
4.2;Code;20
4.3;Further Reading;20
4.4;References;24
5;Products;27
6;1 Vanilla Bonds and Asset Swaps;28
6.1;1.1 Introduction and Objectives;28
6.2;1.2 The Z-Spread;28
6.3;1.3 Fixed Rate Bonds;29
6.4;1.4 Fixed Versus Float Vanilla Swaps;32
6.5;1.5 Hedging with Asset Swaps, the Credit Trap;36
6.6;1.6 Conclusion and Summary;37
6.7;References;38
7;2 Callability Features;39
7.1;2.1 Introduction and Objectives;39
7.2;2.2 Callability;39
7.3;2.3 Callable Fixed Bonds, Callable Swaps and Swaptions;42
7.4;2.4 Hedging and Model Calibration;46
7.5;2.5 Amortizing Structures;50
7.6;2.6 Callable Floater and Inverse Floater;53
7.7;2.7 Zero Bonds, Callable Zeros and Accreting Swaps;57
7.8;2.8 Conclusion and Summary;61
7.9;References;61
8;3 Structured Finance;62
8.1;3.1 Introduction and Objectives;62
8.2;3.2 Redemption Amount Variations;62
8.3;3.3 Draw Down Options;64
8.4;3.4 PIK Options and Capital Deferral Options;65
8.5;3.5 Tenor Options;66
8.6;3.6 Behavioural Models;67
8.7;3.7 Conclusion and Summary;67
9;4 More Exotic Features and Basis Risk Hedging;68
9.1;4.1 Introduction and Objectives;68
9.2;4.2 TaRNs and TaRN Swaps;68
9.3;4.3 Snowballs;71
9.4;4.4 Range Accruals;73
9.5;4.5 Volatility Notes;75
9.6;4.6 Structured Floating Rate Coupons;76
9.7;4.7 In-Currency Tenor Basis Swaps;77
9.8;4.8 Cross-Currency Basis Swaps;77
9.9;4.9 Conclusion and Summary;78
9.10;References;78
10;5 Exposures;79
10.1;5.1 Introduction and Objectives;79
10.2;5.2 Exposures---Summary and Illustrations;80
10.3;5.3 Examples;85
10.3.1;5.3.1 Interest Rate Swaps;86
10.3.2;5.3.2 Cross-Currency Swaps;87
10.3.3;5.3.3 Callable Swaps;90
10.4;5.4 Summary and Conclusions;92
10.5;Reference;92
11;Volatility;93
12;6 The Heston Model;94
12.1;6.1 Introduction and Objectives;94
12.2;6.2 Local Volatility Models;95
12.3;6.3 The Heston Model;98
12.4;6.4 Pricing;100
12.5;6.5 Applications and Calibration;103
12.5.1;6.5.1 Extensions of Heston;105
12.6;6.6 Conclusion and Summary;105
12.7;References;106
13;7 The SABR Model;107
13.1;7.1 Introduction and Objectives;107
13.2;7.2 Introduction;108
13.3;7.3 Approximation;113
13.4;7.4 Applications and Calibration;116
13.5;7.5 Numerical Technics for SABR;117
13.6;7.6 Extensions of SABR;126
13.6.1;7.6.1 Displaced/Normal SABR;126
13.6.2;7.6.2 ZABR;127
13.7;7.7 Recent Developments;133
13.7.1;7.7.1 Free SABR;133
13.7.2;7.7.2 Mixing SABR;137
13.8;7.8 Summary and Conclusions;139
13.9;References;140
14;Term Structure Models;142
15;8 Term Structure Models;143
15.1;8.1 Introduction and Objectives;143
15.2;8.2 Different Models for the Term Structure;143
15.2.1;8.2.1 Short Rate Models;145
15.2.2;8.2.2 Instantaneous Forward Rate Models;147
15.2.3;8.2.3 Market Models;147
15.3;8.3 Stochastic Volatility Enhancements;149
15.4;8.4 Stochastic Basis Spreads;149
15.4.1;8.4.1 Deterministic Basis;152
15.5;8.5 Pricing and Path Simulation;153
15.6;8.6 Summary and Conclusions;154
15.7;References;154
16;9 Short Rate Models;156
16.1;9.1 Introduction and Objectives;156
16.1.1;9.1.1 Gaussian Short Rate Model and the Hull--White Model;157
16.1.2;9.1.2 Affine Short Rate Models and the Cox--Ingersol--Ross Model (CIR);174
16.2;9.2 Multi-dimensional Models/N-Factor Models;178
16.2.1;9.2.1 Example: The Two-Factor Gaussian Short Rate/G2++ Model;179
16.2.2;9.2.2 Short Rate Models for Hybrids;183
16.2.3;9.2.3 Dynamics of Zero-Coupon Bonds in a Gaussian Short Rate Model;183
16.2.4;9.2.4 Dynamics of HW-GBM FX Model Under the Domestic Risk-Neutral Measure QD;184
16.2.5;9.2.5 Dynamics of HW-GBM FX Model Under the Domestic T-forward Measure QDT;185
16.3;9.3 Stochastic Volatility;185
16.4;9.4 Stochastic Basis;186
16.5;9.5 Conclusion and Summary;189
16.6;References;189
17;10 A Gaussian Rates-Credit Pricing Framework;191
17.1;10.1 Introduction and Objectives;191
17.2;10.2 The Option-Adjusted Spread (OAS);191
17.3;10.3 The 2F Rates-Credit LGM Model;192
17.4;10.4 Monte Carlo Paths in the 2F Rates-Credit LGM Model;195
17.5;10.5 Conclusion and Summary;197
17.6;References;197
18;11 Instantaneous Forward Rate Models and the Heath--Jarrow--Morton Framework;198
18.1;11.1 Introduction and Objectives;198
18.2;11.2 The Heath--Jarrow--Morton Framework;199
18.3;11.3 The Cheyette, Ritchken and Sankarasubramanian Model Class;200
18.3.1;11.3.1 The Hull--White Model;202
18.4;11.4 Cheyette Model Example;203
18.5;11.5 Summary and Conclusions;209
18.6;References;210
19;12 The Libor Market Model;211
19.1;12.1 Introduction and Objectives;211
19.2;12.2 Market Models;212
19.3;12.3 Libor Dynamics;212
19.3.1;12.3.1 Spot and Terminal Measure;214
19.3.2;12.3.2 Discretization;215
19.4;12.4 Modelling Volatility;217
19.5;12.5 Modelling Co-movement;218
19.5.1;12.5.1 Non-parametric;219
19.5.2;12.5.2 Parametric/Parsimonious;219
19.5.3;12.5.3 Factor Reduction;224
19.6;12.6 Interpolation;226
19.7;12.7 Libor Market and Swap Market Models;227
19.8;12.8 Extensions;229
19.9;12.9 Multi-tenor LMM and Stochastic Basis;231
19.10;12.10 Summary and Conclusions;232
19.11;References;233
20;A Numerical Techniques for Pricing and Exposure Modelling;234
21;A.1 Numerical Integration;234
22;A.1.1 Greeks;235
23;A.2 Fourier Transformation;235
24;A.2.1 Greeks;238
25;A.3 Finite Difference Techniques;238
26;A.3.1 Finite Differences;238
27;A.3.2 Finite Difference Schemes;239
28;A.3.2.1 Inner Scheme;239
29;A.3.2.2 Boundary Conditions;240
30;A.3.3 Consistency/Stability/Convergence;241
31;A.3.4 Solving for the Density;241
32;A.3.5 Solving for the Price;242
33;A.4 Monte Carlo Simulation;242
34;A.4.1 Random Numbers;244
35;A.4.1.1 Uniformly Distributed Randoms;244
36;A.4.1.2 Multiple Dimensions;244
37;A.4.1.3 Transforming to a Given Distribution;244
38;A.4.1.4 Multiple Dimensions;245
39;A.4.1.5 The Cholesky Decomposition;245
40;A.4.2 Path Simulation;246
41;A.4.2.1 The Exact Scheme;246
42;A.4.2.2 The Euler Scheme;247
43;A.4.2.3 The Predictor-Corrector Scheme;247
44;A.4.2.4 The Milstein Scheme;248
45;A.4.3 Averaging and Error Analysis;248
46;A.4.4 Special Purpose Schemes;251
47;A.5 The Longstaff-Schwartz Method;254
48;A.6 Further Considerations;256
49;References;256
50; Index;258