Risk neutral valuation: pricing and hedging of financial derivatives
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2000
|
| Edition: | 3. printing, with corr. |
| Series: | Springer finance
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 296 S. graph. Darst. |
| ISBN: | 1852330015 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
1. Derivative Background 1
1.1 Financial Markets and Instruments 2
1.1.1 Derivative Instruments 2
1.1.2 Underlying securities 4
1.1.3 Markets 5
1.1.4 Types of Traders 6
1.1.5 Modelling Assumptions 7
1.2 Arbitrage 8
1.3 Arbitrage Relationships 11
1.3.1 Fundamental Determinants of Option Values 11
1.3.2 The Put Call Parity 13
1.3.3 Arbitrage Bounds 16
1.4 Single Period Market Models 20
Exercises 30
2. Probability Background 33
2.1 Measure 34
2.2 Integral 38
2.3 Probability 41
2.4 Equivalent Measures and Radon Nikodym Derivatives 47
2.5 Conditional Expectations 48
2.6 Properties of Conditional Expectation 51
2.7 Modes of Convergence 53
2.8 Convolution and Characteristic Functions 56
2.9 The Central Limit Theorem 60
Exercises 63
3. Stochastic Processes in Discrete Time 67
3.1 Information and Filtrations 67
3.2 Discrete Parameter Stochastic Processes 68
3.3 Discrete Parameter Martingales 70
3.3.1 Definition and Simple Properties 70
3.3.2 Martingale Convergence 72
3.3.3 Doob Decomposition 73
xii Contents
3.4 Martingale Transforms 73
3.5 Stopping Times and Optional Stopping 75
3.6 The Snell Envelope 78
Exercises 80
4. Mathematical Finance in Discrete Time 83
4.1 The Model 83
4.2 Existence of Equivalent Martingale Measures 87
4.2.1 The No Arbitrage Condition 87
4.2.2 Risk Neutral Pricing 93
4.3 Complete Markets 96
4.4 Risk Neutral Valuation 100
4.5 The Cox Ross Rubinstein Model 103
4.5.1 Model Structure 103
4.5.2 Risk Neutral Pricing 105
4.5.3 Hedging 107
4.5.4 Comparison With the General Arbitrage Bounds 110
4.6 Binomial Approximations Ill
4.6.1 Model Structure Ill
4.6.2 The Black Scholes Option Pricing Formula 113
4.6.3 Further Limiting Models 117
4.7 Multifactor Models 120
4.7.1 Extended Binomial Model 120
4.7.2 Multinomial Models 121
4.8 Further Contingent Claim Valuation in Discrete Time 123
4.8.1 American Options 123
4.8.2 Barrier Options 126
4.8.3 Lookback Options 127
4.8.4 A Three Period Example 127
Exercises 129
5. Stochastic Processes in Continuous Time 133
5.1 Filtrations; Finite Dimensional Distributions 133
5.2 Classes of Processes 134
5.3 Brownian Motion 138
5.4 Quadratic Variation of Brownian Motion 141
5.5 Stochastic Integrals; ltd Calculus 144
5.6 Ito s Lemma 149
5.6.1 Geometric Brownian Motion 152
5.7 Stochastic Differential Equations 154
5.8 Stochastic Calculus for Black Scholes Models 158
5.9 Weak Convergence of Stochastic Processes 162
5.9.1 The Spaces Cd and Dd 162
5.9.2 Definition and Motivation 163
5.9.3 Basic Theorems of Weak Convergence 164
Contents xiii
5.9.4 Weak Convergence Results for Stochastic Integrals.... 166
Exercises 167
6. Mathematical Finance in Continuous Time 171
6.1 Continuous time Financial Market Models 171
6.1.1 The Financial Market Model 171
6.1.2 Equivalent Martingale Measures 174
6.1.3 Risk neutral Pricing 177
6.1.4 Changes of Numeraire 180
6.2 The Generalised Black Scholes Model 184
6.2.1 The Model 184
6.2.2 Pricing and Hedging Contingent Claims 192
6.2.3 The Greeks 195
6.2.4 Volatility 197
6.3 Further contingent claim valuation 199
6.3.1 American Options 199
6.3.2 Asian Options 202
6.3.3 Barrier Options 204
6.3.4 Lookback Options 207
6.3.5 Binary Options 210
6.4 Discrete vs. Continuous Time Models 211
6.4.1 Convergence Reconsidered 211
6.4.2 Finite Market Approximations 212
6.4.3 Examples of Finite Market Approximations 214
6.5 Further Applications 221
6.5.1 Futures Markets 221
6.5.2 Currency Markets 224
Exercises 226
7. Incomplete Markets 229
7.1 Pricing in Incomplete Markets 229
7.1.1 A General Option Pricing Formula 229
7.1.2 The Esscher Measure 232
7.2 Hedging in Incomplete Markets 235
7.2.1 Variance Minimising Hedging 235
7.2.2 Risk Minimising Hedging 240
7.3 Stochastic Volatility Models 241
8. Interest Rate Theory 245
8.1 The Bond Market 246
8.1.1 The Term Structure of Interest Rates 246
8.1.2 Mathematical Modelling 248
8.1.3 Bond Pricing, 252
8.2 Short Rate Models 254
8.2.1 The Term Structure Equation 255
xiv Contents
8.2.2 Martingale Modelling 256
8.2.3 Parameter Estimation 260
8.3 Heath Jarrow Morton Methodology 262
8.3.1 The Heath Jarrow Morton Model Class 262
8.3.2 Forward Risk Neutral Martingale Measures 265
8.3.3 Completeness 267
8.4 Pricing and Hedging Contingent Claims 268
8.4.1 Short Rate Models 268
8.4.2 Gaussian HJM Framework 269
8.4.3 Swaps 271
8.4.4 Caps 272
Exercises 274
A. Hilbert Space 277
B. Projections and Conditional Expectations 279
C. The Separating Hyperplane Theorem 281
Bibliography 283
Index 293
|
| any_adam_object | 1 |
| author | Bingham, Nicholas H. 1945- Kiesel, Rüdiger 1962- |
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| author_sort | Bingham, Nicholas H. 1945- |
| author_variant | n h b nh nhb r k rk |
| building | Verbundindex |
| bvnumber | BV013139769 |
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| dewey-full | 332/.01/5118 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332/.01/5118 |
| dewey-search | 332/.01/5118 |
| dewey-sort | 3332 11 45118 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. printing, with corr. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:39:42Z |
| institution | BVB |
| isbn | 1852330015 |
| language | English |
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| physical | XIV, 296 S. graph. Darst. |
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| spelling | Bingham, Nicholas H. 1945- Verfasser (DE-588)118095315 aut Risk neutral valuation pricing and hedging of financial derivatives N. H. Bingham and Rüdiger Kiesel Risk-neutral valuation 3. printing, with corr. London [u.a.] Springer 2000 XIV, 296 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer finance Arbitrage (DE-588)4002820-3 gnd rswk-swf Zinsstruktur (DE-588)4067855-6 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 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 Bewertung (DE-588)4006340-9 s DE-604 Hedging (DE-588)4123357-8 s Zinsstruktur (DE-588)4067855-6 s Arbitrage (DE-588)4002820-3 s DE-188 Kiesel, Rüdiger 1962- Verfasser (DE-588)172185262 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008951590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bingham, Nicholas H. 1945- Kiesel, Rüdiger 1962- Risk neutral valuation pricing and hedging of financial derivatives Arbitrage (DE-588)4002820-3 gnd Zinsstruktur (DE-588)4067855-6 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Bewertung (DE-588)4006340-9 gnd Hedging (DE-588)4123357-8 gnd |
| subject_GND | (DE-588)4002820-3 (DE-588)4067855-6 (DE-588)4381572-8 (DE-588)4006340-9 (DE-588)4123357-8 |
| title | Risk neutral valuation pricing and hedging of financial derivatives |
| title_alt | Risk-neutral valuation |
| title_auth | Risk neutral valuation pricing and hedging of financial derivatives |
| title_exact_search | Risk neutral valuation pricing and hedging of financial derivatives |
| title_full | Risk neutral valuation pricing and hedging of financial derivatives N. H. Bingham and Rüdiger Kiesel |
| title_fullStr | Risk neutral valuation pricing and hedging of financial derivatives N. H. Bingham and Rüdiger Kiesel |
| title_full_unstemmed | Risk neutral valuation pricing and hedging of financial derivatives N. H. Bingham and Rüdiger Kiesel |
| title_short | Risk neutral valuation |
| title_sort | risk neutral valuation pricing and hedging of financial derivatives |
| title_sub | pricing and hedging of financial derivatives |
| topic | Arbitrage (DE-588)4002820-3 gnd Zinsstruktur (DE-588)4067855-6 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Bewertung (DE-588)4006340-9 gnd Hedging (DE-588)4123357-8 gnd |
| topic_facet | Arbitrage Zinsstruktur Derivat Wertpapier Bewertung Hedging |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008951590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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