Pricing and hedging of derivative securities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
1999
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 444 S. graph. Darst. |
| ISBN: | 0198776195 |
Staff View
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| 100 | 1 | |a Nielsen, Lars Tyge |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Pricing and hedging of derivative securities |c Lars Tyge Nielsen |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 1999 | |
| 300 | |a XII, 444 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Derivative securities - Prices - Mathematics | |
| 650 | 7 | |a Futures |2 gtt | |
| 650 | 7 | |a Hedging |2 gtt | |
| 650 | 7 | |a Optiehandel |2 gtt | |
| 650 | 7 | |a Stochastische analyse |2 gtt | |
| 650 | 4 | |a Derivative securities -- Prices | |
| 650 | 4 | |a Hedging (Finance) | |
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Record in the Search Index
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| adam_text | CONTENTS
Introduction i
1 Stochastic Processes 2
1.1 Basic Notions 2
1.2 Brownian Motions 5
1.3 Generalized Brownian Motions 10
1.4 Information Structures 14
1.5 Wiener Processes 17
1.6 Generalized Wiener Processes 21
1.7 (*) Identification of Processes 26
1.8 Time Integrals 30
1.9 Stochastic Integrals 32
1.10 (*) Predictable Processes 44
1.11 Summary 46
1.12 (*) Notes 49
2 Ito Calculus 52
2.1 Ito Processes and Ito s Lemma 52
2.2 Integrals with Respect to Ito Processes 61
2.3 Further Manipulations of Ito s Formula 65
2.4 Stochastic Exponentials 73
2.5 Girsanov s Theorem 76
2.6 Summary 87
2.7 (*) Notes 89
3 Gaussian Processes 91
3.1 Basic Notions 91
3.2 Deterministic Integrands 93
3.3 (*) Brownian Bridge Processes 96
3.4 Conditionally Gaussian One factor Processes 103
3.5 Ornstein Uhlenbeck Processes 107
3.6 Summary 114
3.7 (*) Notes 116
4 Securities and Trading Strategies 117
4.1 Elements of the Model H8
4.2 (*) Almost Simple Trading Strategies 125
4.3 State Prices 130
4.4 The Interest Rate and the Prices of Risk 131
4.5 Existence and Uniqueness of Prices of Risk 133
xii CONTENTS
4.6 Arbitrage and Admissibility 145
4.7 (*) The Doubling Strategy 148
4.8 Changing the Unit of Account 152
4.9 Summary 156
4.10 (*) Notes 160
5 The Martingale Valuation Principle 165
5.1 Replication of Claims 165
5.2 Delta Hedging 168
5.3 Making a Trading Strategy Self financing 168
5.4 Dynamically Complete Markets 172
5.5 How to Replicate 175
5.6 Example: Cash or nothing Options 177
5.7 The State Price Process as a Primitive 182
5.8 Risk adjusted Probabilities 184
5.9 Summary 191
5.10 (*) Notes ¦ 194
6 The Black Scholes Model 197
6.1 Review of the Black Scholes Economy 197
6.2 The Value Function 201
6.3 Cash or nothing Options Revisited 208
6.4 Asset or nothing Options 211
6.5 Standard Call Options 214
6.6 Standard Put Options 225
6.7 (*) Black Scholes and the Heat Equation 228
6.8 (*) The Black Scholes PDE: Terminal Data 231
6.9 (*) The Black Scholes PDE: Integrability 237
6.10 (*) The Black Scholes PDE: Uniqueness 240
6.11 Summary 242
6.12 (*) Notes 247
7 Gaussian Term Structure Models 249
7.1 Zero coupon Bonds and Forward Rates 249
7.2 The Vasicek Model 253
7.3 The Risk adjusted Dynamics as Primitives 261
7.4 The Vasicek Model: Forward Rates 263
7.5 The Vasicek Model: Yields 272
7.6 The Merton Model 280
7.7 The Extended Vasicek Model 291
7.8 The Simplified Hull White Model 301
7.9 The Continuous time Ho Lee Model 305
7.10 Summary 309
7.11 (*) Notes 315
CONTENTS xiii
A Measure and Probability 317
A.I Sigma algebras 317
A.2 Measures and Measure Spaces 323
A.3 Borel Sigma algebras and Lebesgue Measures 328
A.4 Measurable Mappings 334
A.5 Convergence in Probability 340
A.6 Measures and Distribution Functions 341
A.7 Stochastic Independence 342
B Lebesgue Integrals and Expectations 346
B.I Lebesgue Integration 346
B.2 Tonelli s and Fubini s Theorems 354
B.3 Densities and Absolute Continuity 358
B.4 Locally Integrable Functions 362
B.5 Conditional Expectations and Probabilities 363
B.6 // spaces 367
C The Heat Equation 370
C.I The Martingale Solution 371
C.2 The Heat Equation: Initial Data 377
C.3 The Heat Equation: Integrability 382
C.4 The Heat Equation: Uniqueness 385
C.5 Notes 387
D Suggested Solutions to Exercises 389
D.I Solutions for Chapter 1 389
D.2 Solutions for Chapter 2 396
D.3 Solutions for Chapter 3 397
D.4 Solutions for Chapter 4 397
D.5 Solutions for Chapter 5 399
D.6 Solutions for Chapter 6 401
D.7 Solutions for Chapter 7 413
E Suggested Solutions to Exercises 421
E.I Solutions for Appendix A 421
E.2 Solutions for Appendix B 427
References 434
Index 439
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
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| spelling | Nielsen, Lars Tyge Verfasser aut Pricing and hedging of derivative securities Lars Tyge Nielsen 1. publ. Oxford [u.a.] Oxford Univ. Press 1999 XII, 444 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Derivative securities - Prices - Mathematics Futures gtt Hedging gtt Optiehandel gtt Stochastische analyse gtt Derivative securities -- Prices Hedging (Finance) Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Preisbildung (DE-588)4047103-2 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf Hedging (DE-588)4123357-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Preisbildung (DE-588)4047103-2 s Hedging (DE-588)4123357-8 s DE-188 Bewertung (DE-588)4006340-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008673690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nielsen, Lars Tyge Pricing and hedging of derivative securities Derivative securities - Prices - Mathematics Futures gtt Hedging gtt Optiehandel gtt Stochastische analyse gtt Derivative securities -- Prices Hedging (Finance) Derivat Wertpapier (DE-588)4381572-8 gnd Preisbildung (DE-588)4047103-2 gnd Bewertung (DE-588)4006340-9 gnd Hedging (DE-588)4123357-8 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4047103-2 (DE-588)4006340-9 (DE-588)4123357-8 |
| title | Pricing and hedging of derivative securities |
| title_auth | Pricing and hedging of derivative securities |
| title_exact_search | Pricing and hedging of derivative securities |
| title_full | Pricing and hedging of derivative securities Lars Tyge Nielsen |
| title_fullStr | Pricing and hedging of derivative securities Lars Tyge Nielsen |
| title_full_unstemmed | Pricing and hedging of derivative securities Lars Tyge Nielsen |
| title_short | Pricing and hedging of derivative securities |
| title_sort | pricing and hedging of derivative securities |
| topic | Derivative securities - Prices - Mathematics Futures gtt Hedging gtt Optiehandel gtt Stochastische analyse gtt Derivative securities -- Prices Hedging (Finance) Derivat Wertpapier (DE-588)4381572-8 gnd Preisbildung (DE-588)4047103-2 gnd Bewertung (DE-588)4006340-9 gnd Hedging (DE-588)4123357-8 gnd |
| topic_facet | Derivative securities - Prices - Mathematics Futures Hedging Optiehandel Stochastische analyse Derivative securities -- Prices Hedging (Finance) Derivat Wertpapier Preisbildung Bewertung |
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