Lévy processes in finance: pricing financial derivatives
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Chichester, West Sussex
Wiley
2003
|
Schriftenreihe: | Wiley series in probability and statistics
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Includes bibliographical references (p. [157]-164) and index |
Beschreibung: | XIII, 170 S. graph. Darst. |
ISBN: | 0470851562 |
Internformat
MARC
LEADER | 00000nam a2200000zc 4500 | ||
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100 | 1 | |a Schoutens, Wim |e Verfasser |4 aut | |
245 | 1 | 0 | |a Lévy processes in finance |b pricing financial derivatives |c Wim Schoutens |
264 | 1 | |a Chichester, West Sussex |b Wiley |c 2003 | |
300 | |a XIII, 170 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 0 | |a Wiley series in probability and statistics | |
500 | |a Includes bibliographical references (p. [157]-164) and index | ||
650 | 7 | |a Cours du marché |2 rasuqam | |
650 | 7 | |a Derivaten (financiën) |2 gtt | |
650 | 7 | |a Instrument dérivé (Finances) |2 rasuqam | |
650 | 4 | |a Instruments dérivés (Finances) - Prix - Modèles mathématiques | |
650 | 4 | |a Lévy, Processus de | |
650 | 7 | |a Mathématique financière |2 rasuqam | |
650 | 7 | |a Modèle mathématique |2 rasuqam | |
650 | 7 | |a Méthode de simulation |2 rasuqam | |
650 | 7 | |a Option exotique (Finances) |2 rasuqam | |
650 | 7 | |a Portfolio-theorie |2 gtt | |
650 | 7 | |a Prix de l'option |2 rasuqam | |
650 | 7 | |a Processus de Lévy |2 rasuqam | |
650 | 7 | |a Stochastische processen |2 gtt | |
650 | 7 | |a Taux d'intérêt |2 rasuqam | |
650 | 7 | |a Volatilité (Finances) |2 rasuqam | |
650 | 4 | |a Mathematisches Modell | |
650 | 4 | |a Derivative securities |x Prices |x Mathematical models | |
650 | 4 | |a Lévy processes | |
650 | 0 | 7 | |a Kreditmarkt |0 (DE-588)4073788-3 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Lévy-Prozess |0 (DE-588)4463623-4 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Preisbildung |0 (DE-588)4047103-2 |2 gnd |9 rswk-swf |
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943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010248057 |
Datensatz im Suchindex
_version_ | 1817704569144082432 |
---|---|
adam_text |
Contents
Preface
xi
Acknowledgements
xv
1
Introduction
і
1.1
Financial Assets
1
1.2
Derivative Securities
3
1.2.1
Options
3
1.2.2
Prices of Options on the S&P
500
Index
5
1.3
Modelling Assumptions
7
1.4
Arbitrage
9
2
Financial Mathematics in Continuous Time
11
2.1
Stochastic Processes and Filtrations
11
2.2
Classes of Processes
13
2.2.1
Markov Processes
13
2.2.2
Martingales
14
2.2.3
Finite- and Infinite-Variation Processes
14
2.3
Characteristic Functions
15
2.4
Stochastic Integrals and SDEs
16
2.5
Financial Mathematics in Continuous Time
17
2.5.1
Equivalent Martingale Measure
17
2.5.2
Pricing Formulas for European Options
19
2.6
Dividends
21
3
The Black-Scholes Model
23
3.1
The Normal Distribution
23
3.2
Brownian Motion
24
3.2.1
Definition
25
3.2.2
Properties
26
3.3
Geometric Brownian Motion
27
viii CONTENTS
3.4
The Black-Scholes Option Pricing Model
28
3.4.1
The Black-Scholes Market Model
29
3.4.2
Market Completeness
30
3.4.3
The Risk-Neutral Setting
30
3.4.4
The Pricing of Options under the Black-Scholes Model
30
4
Imperfections of the Black-Scholes Model
33
4.1
The Non-Gaussian Character
33
4.1.1
Asymmetry and Excess Kurtosis
33
4.1.2
Density Estimation
35
4.1.3
Statistical Testing
36
4.2
Stochastic Volatility
38
4.3
Inconsistency with Market Option Prices
39
5
Levy Processes and
OU
Processes
43
5.1
Levy Processes
44
5.1.1
Definition
44
5.1.2
Properties
45
5.2
OU
Processes
47
5.2.1
Self-Decomposability
47
5.2.2
OU
Processes
48
5.3
Examples of Levy Processes
50
50
51
52
53
54
56
57
59
60
62
65
67
67
68
69
70
Stock Price Models Driven by Levy Processes
73
6.1
Statistical Testing
73
6.1.1
Parameter Estimation
73
6.1.2
Statistical Testing
74
5.3.1
The
Poisson
Process
5.3.2
The Compound
Poisson
Process
5.3.3
The Gamma Process
5.3.4
The Inverse Gaussian Process
5.3.5
The Generalized Inverse Gaussian Process
5.3.6
The Tempered Stable Process
5.3.7
The Variance Gamma Process
5.3.8
The Normal Inverse Gaussian Process
5.3.9
The CGMY Process
5.3.10
The Meixner Process
5.3.11
The Generalized Hyperbolic Process
5.4
Adding
an Additional Drift Term
5.5
Examples of
OU
Processes
5.5.1
The Gamma-OU Process
5.5.2
The IG-OU Process
5.5.3
Other Examples
CONTENTS
ix
6.2
The Levy Market Model
76
6.2.1
Market Incompleteness
77
6.2.2
The Equivalent Martingale Measure
77
6.2.3
Pricing Formulas for European Options
80
6.3
Calibration of Market Option Prices
82
7
Levy Models with Stochastic Volatility
85
7.1
The BNS Model
85
7.1.1
The BNS Model with Gamma
S V
87
7.1.2
The BNS Model with
IG
S V
88
7.2
The Stochastic Time Change
88
7.2.1
The Integrated
CIR
Time Change
89
7.2.2
The IntOU Time Change
90
7.3
The Levy
S V
Market Model
91
7.4
Calibration of Market Option Prices
97
7.4.1
Calibration of the BNS Models
97
7.4.2
Calibration of the Levy
S V
Models
98
7.5
Conclusion
98
101
101
101
102
102
103
105
107
108
108
109
111
111
113
114
115
117
117
9
Exotic Option Pricing
119
9.1
Barrier and
Lookback
Options
119
9.1.1
Introduction
119
9.1.2
Black-Scholes Barrier and
Lookback
Option Prices
121
9.1.3
Lookback
and Barrier Options in a Levy Market
123
Simulation Techniques
8.1
Simulation of Basic Processes
8.1.1
Simulation of Standard Brownian Motion
8.1.2
Simulation of
a Poisson
Process
8.2
Simulation of a Levy Process
8.2.1
The Compound
Poisson
Approximation
8.2.2
On the Choice of the
Poisson
Processes
8.3
Simulation of an
OU
Process
8.4
Simulation of Particular Processes
8.4.1
The Gamma Process
8.4.2
The VG Process
8.4.3
The TS Process
8.4.4
The
IG
Process
8.4.5
The NIG Process
8.4.6
The Gamma-OU Process
8.4.7
The IG-OU Process
8.4.8
The
CIR
Process
8.4.9
BNS Model
x
CONTENTS
9.2
Other
Exotic
Options
125
9.2.1
The Perpetual American Call and Put Option
125
9.2.2
The Perpetual Russian Option
126
9.2.3
Touch-and-Out Options
126
9.3
Exotic Option Pricing by Monte Carlo Simulation
127
9.3.1
Introduction
127
9.3.2
Monte Carlo Pricing
127
9.3.3
Variance Reduction by Control
Variâtes
129
9.3.4
Numerical Results
132
9.3.5
Conclusion
134
10
Interest-Rate Models
135
10.1
General Interest-Rate Theory
135
10.2
The Gaussian HJM Model
138
10.3
The Levy HJM Model
141
10.4
Bond Option Pricing
142
10.5
Multi-Factor Models
144
Appendix A Special Functions
147
A.I Bessel Functions
147
A.2 Modified Bessel Functions
148
A.3 The Generalized Hypergeometric Series
149
A.4 Orthogonal Polynomials
149
A.4.1 Hermite polynomials with parameter
149
A.4.2 Meixner-Pollaczek Polynomials
150
Appendix
В
Levy Processes
151
B.I Characteristic Functions
151
B.
1.1
Distributions on the
Nonnegative
Integers
151
B.I
.2
Distributions on the Positive Half-Line
151
B.1.3 Distributions on the Real Line
152
B.2 Levy Triplets
153
B.2.1
γ
153
B.2.2 The Levy Measure
v(åx)
154
Appendixe S&P 500
Call Option Prices
155
References
157
Index
165 |
any_adam_object | 1 |
author | Schoutens, Wim |
author_facet | Schoutens, Wim |
author_role | aut |
author_sort | Schoutens, Wim |
author_variant | w s ws |
building | Verbundindex |
bvnumber | BV016969065 |
callnumber-first | H - Social Science |
callnumber-label | HG6024 |
callnumber-raw | HG6024.A3 |
callnumber-search | HG6024.A3 |
callnumber-sort | HG 46024 A3 |
callnumber-subject | HG - Finance |
classification_rvk | QP 890 SK 980 |
classification_tum | WIR 150f |
ctrlnum | (OCoLC)249359937 (DE-599)BVBBV016969065 |
dewey-full | 332.63/2 |
dewey-hundreds | 300 - Social sciences |
dewey-ones | 332 - Financial economics |
dewey-raw | 332.63/2 |
dewey-search | 332.63/2 |
dewey-sort | 3332.63 12 |
dewey-tens | 330 - Economics |
discipline | Mathematik Wirtschaftswissenschaften |
format | Book |
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id | DE-604.BV016969065 |
illustrated | Illustrated |
indexdate | 2024-12-06T15:16:01Z |
institution | BVB |
isbn | 0470851562 |
language | English |
lccn | 2003043297 |
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spelling | Schoutens, Wim Verfasser aut Lévy processes in finance pricing financial derivatives Wim Schoutens Chichester, West Sussex Wiley 2003 XIII, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references (p. [157]-164) and index Cours du marché rasuqam Derivaten (financiën) gtt Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Prix - Modèles mathématiques Lévy, Processus de Mathématique financière rasuqam Modèle mathématique rasuqam Méthode de simulation rasuqam Option exotique (Finances) rasuqam Portfolio-theorie gtt Prix de l'option rasuqam Processus de Lévy rasuqam Stochastische processen gtt Taux d'intérêt rasuqam Volatilité (Finances) rasuqam Mathematisches Modell Derivative securities Prices Mathematical models Lévy processes Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Preisbildung (DE-588)4047103-2 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 s Preisbildung (DE-588)4047103-2 s Lévy-Prozess (DE-588)4463623-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010248057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Schoutens, Wim Lévy processes in finance pricing financial derivatives Cours du marché rasuqam Derivaten (financiën) gtt Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Prix - Modèles mathématiques Lévy, Processus de Mathématique financière rasuqam Modèle mathématique rasuqam Méthode de simulation rasuqam Option exotique (Finances) rasuqam Portfolio-theorie gtt Prix de l'option rasuqam Processus de Lévy rasuqam Stochastische processen gtt Taux d'intérêt rasuqam Volatilité (Finances) rasuqam Mathematisches Modell Derivative securities Prices Mathematical models Lévy processes Kreditmarkt (DE-588)4073788-3 gnd Lévy-Prozess (DE-588)4463623-4 gnd Preisbildung (DE-588)4047103-2 gnd |
subject_GND | (DE-588)4073788-3 (DE-588)4463623-4 (DE-588)4047103-2 |
title | Lévy processes in finance pricing financial derivatives |
title_auth | Lévy processes in finance pricing financial derivatives |
title_exact_search | Lévy processes in finance pricing financial derivatives |
title_full | Lévy processes in finance pricing financial derivatives Wim Schoutens |
title_fullStr | Lévy processes in finance pricing financial derivatives Wim Schoutens |
title_full_unstemmed | Lévy processes in finance pricing financial derivatives Wim Schoutens |
title_short | Lévy processes in finance |
title_sort | levy processes in finance pricing financial derivatives |
title_sub | pricing financial derivatives |
topic | Cours du marché rasuqam Derivaten (financiën) gtt Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Prix - Modèles mathématiques Lévy, Processus de Mathématique financière rasuqam Modèle mathématique rasuqam Méthode de simulation rasuqam Option exotique (Finances) rasuqam Portfolio-theorie gtt Prix de l'option rasuqam Processus de Lévy rasuqam Stochastische processen gtt Taux d'intérêt rasuqam Volatilité (Finances) rasuqam Mathematisches Modell Derivative securities Prices Mathematical models Lévy processes Kreditmarkt (DE-588)4073788-3 gnd Lévy-Prozess (DE-588)4463623-4 gnd Preisbildung (DE-588)4047103-2 gnd |
topic_facet | Cours du marché Derivaten (financiën) Instrument dérivé (Finances) Instruments dérivés (Finances) - Prix - Modèles mathématiques Lévy, Processus de Mathématique financière Modèle mathématique Méthode de simulation Option exotique (Finances) Portfolio-theorie Prix de l'option Processus de Lévy Stochastische processen Taux d'intérêt Volatilité (Finances) Mathematisches Modell Derivative securities Prices Mathematical models Lévy processes Kreditmarkt Lévy-Prozess Preisbildung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010248057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT schoutenswim levyprocessesinfinancepricingfinancialderivatives |