Robust libor modelling and pricing of derivative products:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2005
|
| Schriftenreihe: | Chapman & Hall/CRC financial mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVI, 202 S. graph. Darst. |
| ISBN: | 158488441X 9781584884415 |
Internformat
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| 100 | 1 | |a Schoenmakers, John |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Robust libor modelling and pricing of derivative products |c John Schoenmakers |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2005 | |
| 300 | |a XVI, 202 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
| 650 | 7 | |a Futures |2 gtt | |
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| 650 | 7 | |a Termijnhandel |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Interest rate futures |x Mathematical models | |
| 650 | 4 | |a Interest rates |x Mathematical models | |
| 650 | 4 | |a Derivative securities |x Prices |x Mathematical models | |
| 650 | 0 | 7 | |a Derivat |g Wertpapier |0 (DE-588)4381572-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804133295461498880 |
|---|---|
| adam_text | Contents
List of Tables
xiii
List of Figures
xv
1
Arbitrage-Free Modelling of Effective Interest Rates
1
1.1
Elements of Arbitrage Theory and Derivative Pricing
.... 1
1.1.1
Arbitrage-free Systems, Self-Financing Trading Strate¬
gies, Complete Markets
................. 1
1.1.2
Derivative Claim Pricing in Different Measures
.... 7
1.2
Modelling of Effective Forward Rates
............. 9
1.2.1
Libor
Rate Processes and Measures
........... 9
1.2.2
Swap Rate Processes and Measures
........... 15
1.3
Pricing of Caps and Swaptions in
Libor
and Swap Market Mod¬
els
................................. 18
1.3.1
Libor
Caps and Caplets
................. 18
1.3.2
Swaptions in a Swap Market Model
.......... 19
1.3.3
Approximating Swaptions in
a Libor
Market Model
. 20
1.3.4
Smile/Skew Extensions of the
Libor
Market Model
. . 23
2
Parametrisation of the
Libor
Market Model
25
2.1
General Volatility Structures
.................. 25
2.2
(Quasi) Time-Shift Homogeneous Models
........... 27
2.2.1
Correlation Structures from Correlation Functions
. . 27
2.2.2
Finitely Decomposable Correlation Functions
..... 27
2.2.3
Ratio Correlation Structures and Functions
...... 28
2.2.4
LMM with Piece-wise Constant Volatility Structure
. 30
2.2.5
Modified Hull-White Volatility Structure
....... 32
2.2.6
Parametric Scalar Volatility Function
......... 34
2.3
Parametrisation of Correlation Structures
........... 34
2.3.1
A Disadvantage of Low Factor Models
......... 34
2.3.2
Semi-parametric Framework for
Libor
Correlations
. . 36
2.3.3
Representation Theorems
................ 38
2.3.4
Generation of Low Parametric Structures
....... 42
2.3.5
Parametric Low Rank Structures
............ 45
2.4
Some Possible Applications of Parametric Structures
.... 47
2.4.1
Smoothing Historical
Libor
Correlations (sketch)
... 47
f
2.4.2
Calibration to Caps and Swaptions by Using Historical
Correlations (sketch)
................... 48
Implied Calibration of
a Libor
Market Model to Caps and
Swaptions
49
3.1
Orientation and General Aspects
................ 49
3.2
Assessment of the Calibration Problem
............ 51
3.2.1
Straightforward Least Squares, Stability Problems
. . 52
3.2.2
Stability Problems in the Laboratory
.......... 53
3.3
LSq Calibration and Stability Issues in Practice
....... 56
3.3.1
Transformation of Market Data and LSq Implementa¬
tion
............................ 57
3.3.2
LSq Calibration Studies, Stability Problems in Practice
59
3.4
Régularisation
via a Collateral Market Criterion
....... 64
3.4.1
Market Swaption Formula (MSF)
............ 64
3.4.2
Incorporation of the MSF in the Objective Function
. 67
3.4.3
MSF Calibration Tests,
Régularisation
of the Volatility
Function
.......................... 70
3.4.4
Calibration of Low Factor Models
........... 74
3.4.5
Implied Calibration to Swaptions Only
......... 74
3.5
Calibration of a Time-Shift Homogeneous LMM
....... 76
3.5.1
Volatility Structure of Hull-White
........... 76
3.5.2
Quasi Time-Shift Homogeneous Volatility Structure
. 81
Pricing of Exotic European Style Products
87
4.1
Exotic European Style Products
................ 87
4.1.1
Libor
Trigger Swap
.................... 87
4.1.2
Ratchet Cap
....................... 88
4.1.3
Sticky Cap
........................ 89
4.1.4
Auto-flex Cap
....................... 89
4.1.5
Callable Reverse Floater
................. 90
4.2
Factor Dependence of Exotic Products
............ 91
4.3
Case Studies
........................... 94
Pricing of
Bermudán
Style
Libor
Derivatives
103
5.1
Orientation
............................ 103
5.2
The
Bermudán
Pricing Problem
................ 104
5.3
Backward Construction of the Exercise Boundary
...... 106
5.4
Iterative Construction of the Optimal Stopping Time
.... 109
5.4.1
A One Step Improvement upon a Given Family of Stop¬
ping Times
........................ 109
5.4.2
Iterating to the Optimal Stopping Time and the Snell
Envelope
......................... 112
5.4.3
On the Implementation of the Iterative Procedure
. . 116
5.5
Duality; From Tight Lower Bounds to Tight Upper Bounds
. 118
5.5.1
Dual Approach
...................... 118
5.5.2
Converging Upper Bounds from Lower Bounds
.... 119
5.6
Monte Carlo Simulation of Upper Bounds
........... 122
5.7
Numerical Evaluation of
Bermudán
Swaptions by Different Meth¬
ods
................................ 124
5.8
Efficient Monte Carlo Construction of Upper Bounds
.... 126
5.8.1
Alternative Estimators for the Target Upper Bound
. 126
5.8.2
Two Canonical Approximative Processes
........ 130
5.8.3
Numerical Upper Bounds for
Bermudán
Swaptions
. . 131
5.9
Multiple Callable Structures
.................. 138
5.9.1
The Multiple Stopping Problem
............. 138
5.9.2
Iterative Algorithm for Multiple
Bermudán
Products
. 140
6
Pricing Long Dated Products via
Libor
Approximations
145
6.1
Introduction
........................... 145
6.2
Different
Lognormal
Approximations
............. 146
6.2.1
More
Lognormal
Approximations
............ 149
6.2.2
Simulation Analysis of Different
Libor
Approximations
152
6.3
Direct Simulation of
Lognormal
Approximations
....... 154
6.3.1
Random Field Simulation of the (^-approximation
. 154
6.3.2
Simulation of the
(gl ),
(gl), and ((^-approximation
162
6.3.3
Cost Analysis of
Euler SDE
Simulation and Direct Sim¬
ulation Methods
..................... 163
6.4
Efficiency Gain with Respect to SDE Simulation; an Optimal
Simulation Program
....................... 168
6.4.1
Simulation Alternatives
................. 168
6.4.2
An Optimal Simulation Program
............ 171
6.5
Practical Simulation Examples
................. 172
6.5.1
European Swaption
................... 172
6.5.2
Trigger Swap
....................... 173
6.5.3
Callable Reverse Floater
................. 174
6.6
Summarisation and Final Remarks
............... 175
A Appendix
177
A.I Glossary of Stochastic Calculus
................. 177
A.
1.1
Stochastic Processes in Continuous Time
....... 177
A.
1.2
Martingales and Stopping Times
............ 178
A.
1.3
Quadratic Variation and the
Ito
Stochastic Integral
. . 179
A.
1.4
Regular Conditional Probability
............ 183
A.
2
Minimum Search Procedures
.................. 184
A.
2.1
Halton
Quasi-random Numbers
............. 184
A.3 Additional Proofs
........................ 187
A.
3.1
Covariance of Two Black-Scholes Models
........ 187
A.3.2 Proof of Equality
(5.26)................. 188
A.
3.3
Proof of Proposition
5.2................. 189
A.3.4
Proof of Proposition
5.3...............<■ . 190
References
193
Index
199
The Libor
market mode! remains one of the most popular and advanced tools
for modelling interest rates and interest rate derivatives, but finding a useful
procedure for calibrating the model has been a perennial problem. Also the
respective pricing of exotic derivative products such as
Bermudán
callable
structures is considered highly non-trivial. In recent studies, author John
Schoenmakers
and his colleagues developed a fast and robust implied method
for calibrating the
Libor
model and a new generic procedure for the pricing of
callable derivative instruments in this model.
Within a compact, self-contained review of the requisite mathematical theory on
interest rate modelling, Robust
Libor
Modelling and Pricing of Derivative Products
introduces the author s new approaches and their impact on
Libor
modelling and
derivative pricing. Discussions include economically sensible parametrisations of
the
Libor
market model, stability issues connected to direct least-squares calibration
methods, European and
Bermudán
style exotics pricing, and
lognormal
approximations
suitable for the
Libor
market model.
A look at the available literature on
Libor
modelling shows that the issues
surrounding instabilty of calibration and its consequences have not been well
documented, and an effective general approach for treating
Bermudán
callable
Libor
products has been missing. This book fills these gaps and with clear
illustrations, examples, and explanations, offers new methods that surmount
some of the
Libor
model s thornier obstacles.
|
| any_adam_object | 1 |
| author | Schoenmakers, John |
| author_facet | Schoenmakers, John |
| author_role | aut |
| author_sort | Schoenmakers, John |
| author_variant | j s js |
| building | Verbundindex |
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.64/57/0151 |
| dewey-search | 332.64/57/0151 |
| dewey-sort | 3332.64 257 3151 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV019801760 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:27Z |
| institution | BVB |
| isbn | 158488441X 9781584884415 |
| language | English |
| lccn | 2004065976 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013127330 |
| oclc_num | 57344057 |
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| physical | XVI, 202 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Chapman & Hall/CRC financial mathematics series |
| spelling | Schoenmakers, John Verfasser aut Robust libor modelling and pricing of derivative products John Schoenmakers Boca Raton [u.a.] Chapman & Hall/CRC 2005 XVI, 202 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Futures gtt Instruments dérivés (Finances) - Prix - Modèles mathématiques Marchés à terme de taux d'intérêt - Modèles mathématiques Opties gtt Rente gtt Taux d'intérêt - Modèles mathématiques Termijnhandel gtt Wiskundige modellen gtt Mathematisches Modell Interest rate futures Mathematical models Interest rates Mathematical models Derivative securities Prices Mathematical models Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013127330&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013127330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Schoenmakers, John Robust libor modelling and pricing of derivative products Futures gtt Instruments dérivés (Finances) - Prix - Modèles mathématiques Marchés à terme de taux d'intérêt - Modèles mathématiques Opties gtt Rente gtt Taux d'intérêt - Modèles mathématiques Termijnhandel gtt Wiskundige modellen gtt Mathematisches Modell Interest rate futures Mathematical models Interest rates Mathematical models Derivative securities Prices Mathematical models Derivat Wertpapier (DE-588)4381572-8 gnd |
| subject_GND | (DE-588)4381572-8 |
| title | Robust libor modelling and pricing of derivative products |
| title_auth | Robust libor modelling and pricing of derivative products |
| title_exact_search | Robust libor modelling and pricing of derivative products |
| title_full | Robust libor modelling and pricing of derivative products John Schoenmakers |
| title_fullStr | Robust libor modelling and pricing of derivative products John Schoenmakers |
| title_full_unstemmed | Robust libor modelling and pricing of derivative products John Schoenmakers |
| title_short | Robust libor modelling and pricing of derivative products |
| title_sort | robust libor modelling and pricing of derivative products |
| topic | Futures gtt Instruments dérivés (Finances) - Prix - Modèles mathématiques Marchés à terme de taux d'intérêt - Modèles mathématiques Opties gtt Rente gtt Taux d'intérêt - Modèles mathématiques Termijnhandel gtt Wiskundige modellen gtt Mathematisches Modell Interest rate futures Mathematical models Interest rates Mathematical models Derivative securities Prices Mathematical models Derivat Wertpapier (DE-588)4381572-8 gnd |
| topic_facet | Futures Instruments dérivés (Finances) - Prix - Modèles mathématiques Marchés à terme de taux d'intérêt - Modèles mathématiques Opties Rente Taux d'intérêt - Modèles mathématiques Termijnhandel Wiskundige modellen Mathematisches Modell Interest rate futures Mathematical models Interest rates Mathematical models Derivative securities Prices Mathematical models Derivat Wertpapier |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013127330&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013127330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schoenmakersjohn robustlibormodellingandpricingofderivativeproducts |