Introduction to stochastic calculus applied to finance:
Suitable for students of mathematical finance, or a quick introduction to researchers and finance practitioners. This book covers the stochastic calculus theory required, as well as many key finance topics, including a chapter dedicated to credit risk modeling.
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Chapman & Hall /CRC financial mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Suitable for students of mathematical finance, or a quick introduction to researchers and finance practitioners. This book covers the stochastic calculus theory required, as well as many key finance topics, including a chapter dedicated to credit risk modeling. |
| Beschreibung: | 253 S. |
| ISBN: | 1584886269 9781584886266 |
Internformat
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| 240 | 1 | 0 | |a Introduction au calcul stochastique appliqué à la finance |
| 245 | 1 | 0 | |a Introduction to stochastic calculus applied to finance |c Damien Lamberton and Bernard Lapeyre |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a 253 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chapman & Hall /CRC financial mathematics series | |
| 520 | 3 | |a Suitable for students of mathematical finance, or a quick introduction to researchers and finance practitioners. This book covers the stochastic calculus theory required, as well as many key finance topics, including a chapter dedicated to credit risk modeling. | |
| 650 | 4 | |a Stochastischer Prozess / Optionspreistheorie / Portfolio-Management / Finanzmathematik / Theorie | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Investments |x Mathematics | |
| 650 | 4 | |a Options (Finance) |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804137190522880000 |
|---|---|
| adam_text | Contents
Introduction
9
1
Discrete-time models
15
1.1
Discrete-time formalism
...................... 15
1.2
Martingales and arbitrage opportunities
............. 18
1.3
Complete markets and option pricing
............... 22
1.4
Problem: Cox, Ross and Rubinstein model
............ 26
1.5
Exercises
.............................. 31
2
Optimal stopping problem and American options
37
2.1
Stopping time
............................ 37
2.2
The Snell envelope
......................... 38
2.3
Decomposition of supermartingales
................ 41
2.4
Snell envelope and Markov chains
................. 42
2.5
Application to American options
................. 43
2.6
Exercises
.............................. 46
3
Brownian motion and stochastic differential equations
51
3.1
General comments on continuous-time processes
........ 52
3.2
Brownian motion
.......................... 53
3.3
Continuous-time martingales
................... 55
3.4
Stochastic, integral and
Ito
calculus
................ 58
3.5
Stochastic differential equations
................... 72
3.6
Exercises
.............................. 80
4
The Black-Scholes model
87
4.1
Description of the model
...................... 87
4.2
Change of probability. Representation of martingales
...... 90
4.3
Pricing and hedging options in the Black-Scholes model
.... 91
4.4
American options
.......................... 96
4.5
Implied volatility and local volatility models
........... 101
4.6
The Black-Scholes model with dividends and call/put symmetry
103
4.7
Exercises
.............................. 104
4.8
Problems
.............................. 108
5 Option
pricing and partial differential equations
123
5.1
European option pricing and diffusions
..............123
5.2
Solving parabolic equations numerically
.............132
5.3
American options
..........................138
5.4
Exercises
..............................146
6
Interest rate models
149
6.1
Modelling principles
........................149
6.2
Some classical models
.......................158
6.3
Exercises
..............................169
7
Asset models with jumps
173
7.1
Poisson
process
...........................173
7.2
Dynamics of the risky asset
....................175
7.3
Martingales in a jump-diffusion model
..............177
7.4
Pricing options in a jump-diffusion model
............182
7.5
Exercises
..............................191
8
Credit risk models
195
8.1
Structural models
..........................195
8.2
Intensity-based models
.......................196
8.3
Copulas
...............................202
8.4
Exercises
..............................205
9
Simulation and algorithms for financial models
207
9.1
Simulation and financial models
..................207
9.2
Introduction to variance reduction methods
...........215
9.3
Exercises
..............................224
9.4
Computer experiments
.......................225
Appendix
235
A.I Normal random variables
.....................235
A.
2
Conditional expectation
......................237
A.3 Separation of convex sets
.....................241
Bibliography
243
Index
251
|
| adam_txt |
Contents
Introduction
9
1
Discrete-time models
15
1.1
Discrete-time formalism
. 15
1.2
Martingales and arbitrage opportunities
. 18
1.3
Complete markets and option pricing
. 22
1.4
Problem: Cox, Ross and Rubinstein model
. 26
1.5
Exercises
. 31
2
Optimal stopping problem and American options
37
2.1
Stopping time
. 37
2.2
The Snell envelope
. 38
2.3
Decomposition of supermartingales
. 41
2.4
Snell envelope and Markov chains
. 42
2.5
Application to American options
. 43
2.6
Exercises
. 46
3
Brownian motion and stochastic differential equations
51
3.1
General comments on continuous-time processes
. 52
3.2
Brownian motion
. 53
3.3
Continuous-time martingales
. 55
3.4
Stochastic, integral and
Ito
calculus
. 58
3.5
Stochastic differential equations
. 72
3.6
Exercises
. 80
4
The Black-Scholes model
87
4.1
Description of the model
. 87
4.2
Change of probability. Representation of martingales
. 90
4.3
Pricing and hedging options in the Black-Scholes model
. 91
4.4
American options
. 96
4.5
Implied volatility and local volatility models
. 101
4.6
The Black-Scholes model with dividends and call/put symmetry
103
4.7
Exercises
. 104
4.8
Problems
. 108
5 Option
pricing and partial differential equations
123
5.1
European option pricing and diffusions
.123
5.2
Solving parabolic equations numerically
.132
5.3
American options
.138
5.4
Exercises
.146
6
Interest rate models
149
6.1
Modelling principles
.149
6.2
Some classical models
.158
6.3
Exercises
.169
7
Asset models with jumps
173
7.1
Poisson
process
.173
7.2
Dynamics of the risky asset
.175
7.3
Martingales in a jump-diffusion model
.177
7.4
Pricing options in a jump-diffusion model
.182
7.5
Exercises
.191
8
Credit risk models
195
8.1
Structural models
.195
8.2
Intensity-based models
.196
8.3
Copulas
.202
8.4
Exercises
.205
9
Simulation and algorithms for financial models
207
9.1
Simulation and financial models
.207
9.2
Introduction to variance reduction methods
.215
9.3
Exercises
.224
9.4
Computer experiments
.225
Appendix
235
A.I Normal random variables
.235
A.
2
Conditional expectation
.237
A.3 Separation of convex sets
.241
Bibliography
243
Index
251 |
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| author | Lamberton, Damien Lapeyre, Bernard |
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| ctrlnum | (OCoLC)255797014 (DE-599)BVBBV022948509 |
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| dewey-ones | 332 - Financial economics |
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| dewey-search | 332.64530151922 |
| dewey-sort | 3332.64530151922 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| index_date | 2024-07-02T19:01:05Z |
| indexdate | 2024-07-09T21:08:21Z |
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| oclc_num | 255797014 |
| open_access_boolean | |
| owner | DE-739 DE-384 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-29T DE-703 |
| owner_facet | DE-739 DE-384 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-29T DE-703 |
| physical | 253 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Chapman & Hall /CRC financial mathematics series |
| spelling | Lamberton, Damien Verfasser aut Introduction au calcul stochastique appliqué à la finance Introduction to stochastic calculus applied to finance Damien Lamberton and Bernard Lapeyre 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2008 253 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall /CRC financial mathematics series Suitable for students of mathematical finance, or a quick introduction to researchers and finance practitioners. This book covers the stochastic calculus theory required, as well as many key finance topics, including a chapter dedicated to credit risk modeling. Stochastischer Prozess / Optionspreistheorie / Portfolio-Management / Finanzmathematik / Theorie Mathematik Mathematisches Modell Investments Mathematics Options (Finance) Mathematical models Stochastic analysis Stochastik (DE-588)4121729-9 gnd rswk-swf Finanzwirtschaft (DE-588)4017214-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Option (DE-588)4115452-6 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optionshandel (DE-588)4126185-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Finanzmathematik (DE-588)4017195-4 s Stochastik (DE-588)4121729-9 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Finanzwirtschaft (DE-588)4017214-4 s 1\p DE-604 Option (DE-588)4115452-6 s Stochastisches Modell (DE-588)4057633-4 s 2\p DE-604 Stochastische Analysis (DE-588)4132272-1 s Optionshandel (DE-588)4126185-9 s Lapeyre, Bernard Verfasser aut Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016153026&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lamberton, Damien Lapeyre, Bernard Introduction to stochastic calculus applied to finance Stochastischer Prozess / Optionspreistheorie / Portfolio-Management / Finanzmathematik / Theorie Mathematik Mathematisches Modell Investments Mathematics Options (Finance) Mathematical models Stochastic analysis Stochastik (DE-588)4121729-9 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Stochastisches Modell (DE-588)4057633-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Option (DE-588)4115452-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd Finanzmathematik (DE-588)4017195-4 gnd Optionshandel (DE-588)4126185-9 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4017214-4 (DE-588)4057633-4 (DE-588)4057630-9 (DE-588)4115452-6 (DE-588)4132272-1 (DE-588)4017195-4 (DE-588)4126185-9 (DE-588)4151278-9 |
| title | Introduction to stochastic calculus applied to finance |
| title_alt | Introduction au calcul stochastique appliqué à la finance |
| title_auth | Introduction to stochastic calculus applied to finance |
| title_exact_search | Introduction to stochastic calculus applied to finance |
| title_exact_search_txtP | Introduction to stochastic calculus applied to finance |
| title_full | Introduction to stochastic calculus applied to finance Damien Lamberton and Bernard Lapeyre |
| title_fullStr | Introduction to stochastic calculus applied to finance Damien Lamberton and Bernard Lapeyre |
| title_full_unstemmed | Introduction to stochastic calculus applied to finance Damien Lamberton and Bernard Lapeyre |
| title_short | Introduction to stochastic calculus applied to finance |
| title_sort | introduction to stochastic calculus applied to finance |
| topic | Stochastischer Prozess / Optionspreistheorie / Portfolio-Management / Finanzmathematik / Theorie Mathematik Mathematisches Modell Investments Mathematics Options (Finance) Mathematical models Stochastic analysis Stochastik (DE-588)4121729-9 gnd Finanzwirtschaft (DE-588)4017214-4 gnd Stochastisches Modell (DE-588)4057633-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Option (DE-588)4115452-6 gnd Stochastische Analysis (DE-588)4132272-1 gnd Finanzmathematik (DE-588)4017195-4 gnd Optionshandel (DE-588)4126185-9 gnd |
| topic_facet | Stochastischer Prozess / Optionspreistheorie / Portfolio-Management / Finanzmathematik / Theorie Mathematik Mathematisches Modell Investments Mathematics Options (Finance) Mathematical models Stochastic analysis Stochastik Finanzwirtschaft Stochastisches Modell Stochastischer Prozess Option Stochastische Analysis Finanzmathematik Optionshandel Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016153026&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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