Stochastic finance: an introduction with market examples
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| New Title: | Privault, Nicolas Introduction to Stochastic Finance with Market Examples |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2014
|
| Series: | Chapman & Hall/CRC financial mathematics series
|
| Subjects: | |
| Online Access: | Cover image Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVI, 426 S. graph. Darst. |
| ISBN: | 9781466594029 |
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MARC
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| 245 | 1 | 0 | |a Stochastic finance |b an introduction with market examples |c Nicolas Privault |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2014 | |
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| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Securities |x Prices |x Mathematical models | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Hedging (Finance) |x Mathematical models | |
| 650 | 4 | |a Stochastic analysis | |
| 650 | 4 | |a BUSINESS & ECONOMICS / Finance | |
| 650 | 4 | |a MATHEMATICS / General | |
| 650 | 4 | |a MATHEMATICS / Probability & Statistics / General | |
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Record in the Search Index
| _version_ | 1804152010454335488 |
|---|---|
| adam_text | Contents
List of Figures
xi
Preface
xv
Introduction
1
1
Assets, Portfolios and Arbitrage
7
1.1
Definitions and Formalism
................... 7
1.2
Portfolio Allocation and Short-Selling
............. 8
1.3
Arbitrage
............................. 9
1.4
Risk-Neutral Measures
..................... 12
1.5
Hedging of Contingent Claims
................. 13
1.6
Market Completeness
...................... 14
1.7
Example
............................. 15
Exercises
................................ 21
2
Discrete-Time Model
23
2.1
Stochastic Processes
....................... 23
2.2
Portfolio Strategies
....................... 24
2.3
Arbitrage
............................. 27
2.4
Contingent Claims
........................ 27
2.5
Martingales and Conditional Expectation
........... 29
2.6
Risk-Neutral Probability Measures
............... 33
2.7
Market Completeness
...................... 35
2.8
Cox-Ross-Rubinstein (CRR) Market Model
......... 35
Exercises
................................ 38
3
Pricing and Hedging in Discrete Time
39
3.1
Pricing of Contingent Claims
.................. 39
3.2
Hedging of Contingent Claims
-
Backward Induction
.... 43
3.3
Pricing of Vanilla Options in the CRR Model
......... 44
3.4
Hedging of Vanilla Options in the CRR model
........ 47
3.5
Hedging of Exotic Options in the CRR Model
........ 50
3.6
Convergence of the CRR Model
................ 56
Exercises
................................ 60
vu
viii Contents
4
Brownian
Motion
and Stochastic Calculus
63
4.1
Brownian Motion
........................ 63
4.2
Wiener Stochastic Integral
................... 67
4.3
Ito
Stochastic Integral
...................... 71
4.4
Deterministic Calculus
..................... 75
4.5
Stochastic Calculus
....................... 76
4.6
Geometric Brownian Motion
.................. 80
4.7
Stochastic Differential Equations
................ 83
Exercises
................................ 84
5
The Black-Scholes PDE
89
5.1
Continuous-Time Market Model
................ 89
5.2
Self-Financing Portfolio Strategies
............... 89
5.3
Arbitrage and Risk-Neutral Measures
............. 92
5.4
Market Completeness
...................... 94
5.5
Black-Scholes PDE
....................... 95
5.6
The Heat Equation
....................... 102
5.7
Solution of the Black-Scholes PDE
.............. 104
Exercises
................................ 107
6
Martingale Approach to Pricing and Hedging 111
6.1
Martingale Property of the
Ito
Integral
............
Ill
6.2
Risk-Neutral Measures
..................... 113
6.3
Girsanov Theorem and Change of Measure
.......... 115
6.4
Pricing by the Martingale Method
............... 117
6.5
Hedging Strategies
........................ 121
Exercises
................................ 126
7
Estimation of Volatility
135
7.1
Historical Volatility
....................... 135
7.2
Implied Volatility
........................ 136
7.3
Black-Scholes Formula vs. Market Data
............ 137
7.4
Local Volatility
......................... 141
8
Exotic Options
145
8.1
Generalities
............................ 145
8.2
Reflexion Principle
........................ 149
8.3
Barrier Options
......................... 157
8.4
Lookback
Options
........................ 174
8.5
Asian Options
.......................... 196
Exercises
................................ 209
Contents ix
9 American
Options
213
9.1 Filtrations
and Information Flow
................ 213
9.2
Martingales, Submartingales, and
Supermartingales
..... 214
9.3
Stopping Times
......................... 216
9.4
Perpetual American Options
.................. 225
9.5
Finite Expiration American Options
.............. 236
Exercises
................................ 243
10
Change of Numeraire and Forward Measures
253
10.1
Notion of
Numéraire
....................... 253
10.2
Change of
Numéraire
...................... 255
10.3
Foreign Exchange
........................ 262
10.4
Pricing of Exchange Options
.................. 267
10.5
Self-Financing Hedging by Change of
Numéraire
....... 269
Exercises
................................ 272
11
Forward Rate Modeling
277
11.1
Short-Term Models
....................... 277
11.2
Zero-Coupon Bonds
....................... 279
11.3
Forward Rates
.......................... 286
11.4
HJM Model
........................... 292
11.5
Forward Vasicek Rates
..................... 295
11.6
Modeling Issues
......................... 299
11.7
BGM Model
........................... 305
Exercises
................................ 308
12
Pricing of Interest Rate Derivatives
315
12.1
Forward Measures and Tenor Structure
............ 315
12.2
Bond Options
.......................... 317
12.3
Caplet Pricing
.......................... 318
12.4
Forward Swap Measures
..................... 321
12.5
Swaption Pricing on the
LIBOR
................. 322
Exercises
................................ 326
13
Default Risk in Bond Markets
335
13.1
Survival Probabilities and Failure Rate
............ 335
13.2
Stochastic Default
........................ 337
13.3
Defaultable Bonds
........................ 338
13.4
Credit Default Swaps
...................... 340
13.5
Exercises
............................. 341
14
Stochastic Calculus for Jump Processes
345
14.1
Poisson
Process
......................... 345
14.2
Compound
Poisson
Processes
.................. 351
14.3
Stochastic Integrals with Jumps
................ 353
14.4
Ito
Formula with Jumps
.................... 355
χ
Contents
14.5
Stochastic Differential Equations with Jumps
......... 357
14.6
Girsanov Theorem for Jump Processes
............ 361
Exercises
................................ 367
15
Pricing and Hedging in Jump Models
369
15.1
Risk-Neutral Measures
..................... 369
15.2
Pricing in Jump Models
..................... 370
15.3
Bbck-Scholes PDE with Jumps
................ 372
15.4
Exponential Models
....................... 373
15.5
Self-Financing Hedging with Jumps
.............. 376
Exercises
................................ 379
16
Basic Numerical Methods
381
16.1
The Heat Equation
....................... 381
16.2
Black-Scholes PDE
....................... 383
16.3
Euler
Discretization
....................... 386
16.4
Milshtein Discretization
..................... 387
Appendix: Background on Probability Theory
389
Probability Spaces and Events
. . .................. 389
Probability Measures
......................... 393
Conditional Probabilities and Independence
............ 394
Random Variables
........................... 395
Probability Distributions
....................... 397
Expectation of a Random Variable
.................. 402
Conditional Expectation
....................... 407
Moment Generating Functions
.................... 409
Exercises
................................ 411
Bibliography
415
Subject Index
421
Author Index
425
|
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| discipline | Wirtschaftswissenschaften |
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| spelling | Privault, Nicolas Verfasser (DE-588)1032387327 aut Stochastic finance an introduction with market examples Nicolas Privault Boca Raton [u.a.] Chapman & Hall/CRC 2014 XVI, 426 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Includes bibliographical references and index BUSINESS & ECONOMICS / Finance bisacsh MATHEMATICS / General bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Wirtschaft Securities Prices Mathematical models Finance Mathematical models Hedging (Finance) Mathematical models Stochastic analysis BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Stochastik (DE-588)4121729-9 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Stochastik (DE-588)4121729-9 s b DE-604 Fortgesetzt durch Privault, Nicolas Introduction to Stochastic Finance with Market Examples second edition 2023 http://images.tandf.co.uk/common/jackets/websmall/978146659/9781466594029.jpg Cover image Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027175264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Privault, Nicolas Stochastic finance an introduction with market examples BUSINESS & ECONOMICS / Finance bisacsh MATHEMATICS / General bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Wirtschaft Securities Prices Mathematical models Finance Mathematical models Hedging (Finance) Mathematical models Stochastic analysis BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Stochastik (DE-588)4121729-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4017195-4 |
| title | Stochastic finance an introduction with market examples |
| title_auth | Stochastic finance an introduction with market examples |
| title_exact_search | Stochastic finance an introduction with market examples |
| title_full | Stochastic finance an introduction with market examples Nicolas Privault |
| title_fullStr | Stochastic finance an introduction with market examples Nicolas Privault |
| title_full_unstemmed | Stochastic finance an introduction with market examples Nicolas Privault |
| title_new | Privault, Nicolas Introduction to Stochastic Finance with Market Examples |
| title_short | Stochastic finance |
| title_sort | stochastic finance an introduction with market examples |
| title_sub | an introduction with market examples |
| topic | BUSINESS & ECONOMICS / Finance bisacsh MATHEMATICS / General bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Wirtschaft Securities Prices Mathematical models Finance Mathematical models Hedging (Finance) Mathematical models Stochastic analysis BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Stochastik (DE-588)4121729-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Mathematisches Modell Wirtschaft Securities Prices Mathematical models Finance Mathematical models Hedging (Finance) Mathematical models Stochastic analysis Stochastik Finanzmathematik |
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