Quantitative modeling of derivative securities: from theory to practice
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; Lodnon ; New York ; Washington, D.C.
Chapman & Hall/CRC
[2000]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 322 Seiten Diagramme |
| ISBN: | 1584880317 |
Internformat
MARC
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| 100 | 1 | |a Avellaneda, Marco |d 1955-2022 |0 (DE-588)171583396 |4 aut | |
| 245 | 1 | 0 | |a Quantitative modeling of derivative securities |b from theory to practice |c Marco Avellaneda ; in collaboration with Peter Laurence |
| 264 | 1 | |a Boca Raton ; Lodnon ; New York ; Washington, D.C. |b Chapman & Hall/CRC |c [2000] | |
| 264 | 4 | |c © 2000 | |
| 300 | |a xii, 322 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Bourse |2 ram | |
| 650 | 7 | |a Futures |2 gtt | |
| 650 | 7 | |a Marchés à terme d'instruments financiers |2 ram | |
| 650 | 7 | |a Opties |2 gtt | |
| 650 | 7 | |a Options (finances) |2 ram | |
| 650 | 7 | |a Termijnhandel |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Derivative securities | |
| 650 | 4 | |a Exotic options (Finance) | |
| 650 | 4 | |a Options (Finance) | |
| 650 | 0 | 7 | |a Derivat |g Wertpapier |0 (DE-588)4381572-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
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| 775 | 0 | 8 | |i Äquivalent |a Avellaneda, Marco |t Quantitative modeling of derivative securities |b 2020 |z 978-0-367-57914-2 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008778010 | ||
Datensatz im Suchindex
| _version_ | 1804127582180868096 |
|---|---|
| adam_text | Contents
Introduction ix
1 Arbitrage Pricing Theory: The One Period Model 1
1.1 The Arrow Debreu Model 2
1.2 Security Space Diagram: A Geometric Interpretation of Theorem 1.1 8
1.3 Replication 11
1.4 The Binomial Model 13
1.5 Complete and Incomplete Markets 14
1.6 The One Period Trinomial Model 16
1.7 Exercises 18
References and Further Reading 19
2 The Binomial Option Pricing Model 21
2.1 Recursion Relation for Pricing Contingent Claims 22
2.2 Delta Hedging and the Replicating Portfolio 24
2.3 Pricing European Puts and Calls 26
Portfolio Delta 27
Money Market Account 27
Puts 28
2.4 Relation Between the Parameters of the Tree and the Stock
Price Fluctuations 28
Calibration of the Volatility Parameter 31
Expected Growth Rate 32
Implementation of Binomial Trees 33
2.5 The Limit for dt —*¦ 0: Log Normal Approximation 34
2.6 The Black Scholes Formula 35
References and Further Reading 39
3 Analysis of the Black Scholes Formula 41
3.1 Delta 42
Option Deltas 44
3.2 Practical Delta Hedging 45
3.3 Gamma: The Convexity Factor 48
3.4 Theta: The Time Decay Factor 51
3.5 The Binomial Model as a Finite Difference Scheme for the
Black Scholes Equation 54
References and Further Reading 55
iv CONTENTS
4 Refinements of the Binomial Model 57
4.1 Term Structure of Interest Rates 57
4.2 Constructing a Risk Neutral Measure with Time Dependent Volatility 63
4.3 Deriving a Volatility Term Structure from Option Market Data 66
4.4 Underlying Assets That Pay Dividends 70
4.5 Futures Contracts as the Underlying Security 73
4.6 Valuation of a Stream of Uncertain Cash Flows 75
References and Further Reading 76
5 American Style Options, Early Exercise, and Time Optionality 77
5.1 American Style Options 77
5.2 Early Exercise Premium 78
5.3 Pricing American Options Using the Binomial Model: The Dynamic
Programming Equation 80
5.4 Hedging 82
5.5 Characterization of the Solution for dt 3C 1: Free Boundary Problem for the
Black Scholes Equation 82
References and Further Reading 88
A A PDE Approach to the Free Boundary Condition 89
A.I A Proof of the Free Boundary Condition 90
6 Trinomial Model and Finite Difference Schemes 93
6.1 Trinomial Model 93
6.2 Stability Analysis 95
6.3 Calibration of the Model 96
6.4 Tree Trimming and Far Field Boundary Conditions 100
6.5 Implicit Schemes 103
References and Further Reading 106
7 Brownian Motion and Ito Calculus 107
7.1 Brownian Motion 107
7.2 Elementary Properties of Brownian Paths 109
7.3 Stochastic Integrals Ill
7.4 Ito s Lemma 117
7.5 Ito Processes and Ito Calculus 120
References and Further Reading 122
A Properties of the Ito Integral 123
8 Introduction to Exotic Options: Digital and Barrier Options 127
8.1 Digital Options 128
European Digitals 128
American Digitals 135
8.2 Barrier Options 139
Pricing Barrier Options Using Trees or Lattices 141
Closed Form Solutions 142
Hedging Barrier Options 145
8.3 Double Barrier Options 146
Range Discount Note 147
Range Accruals 148
Double Knock out Options 150
References and Further Reading 150
CONTENTS v
A Proofs of Lemmas 8.1 and 8.2 151
A. 1 A Consequence of the Invariance of Brownian Motion Under Reflections . . .151
A.2 The Case [i ^ 0 153
B Closed Form Solutions for Double Barrier Options 155
B.I Exit Probabilities of a Brownian Trajectory from a Strip — B Z A . . . .155
B.2 Applications to Pricing Barrier Options 158
9 Ito Processes, Continuous Time Martingales, and
Girsanov s Theorem 161
9.1 Martingales and Doob Meyer Decomposition 161
9.2 Exponential Martingales 163
9.3 Girsanov s Theorem 165
References and Further Reading 168
A Proof of Equation (9.11) 169
10 Continuous Time Finance: An Introduction 171
10.1 The Basic Model 171
10.2 Trading Strategies 173
10.3 Arbitrage Pricing Theory 176
References and Further Reading 181
11 Valuation of Derivative Securities 183
11.1 The General Principle 183
11.2 Black Scholes Model 185
11.3 Dynamic Hedging and Dynamic Completeness 189
11.4 Fokker Planck Theory: Computing Expectations Using PDEs 193
References and Further Reading 196
A Proof of Proposition 11.5 197
12 Fixed Income Securities and the Term Structure of Interest Rates 199
12.1 Bonds 199
12.2 Duration 206
12.3 Term Rates, Forward Rates, and Futures Implied Rates 209
12.4 Interest Rate Swaps 212
12.5 Caps and Floors 217
12.6 Swaptions and Bond Options 218
12.7 Instantaneous Forward Rates: Definition 221
12.8 Building an Instantaneous Forward Rate Curve 224
References and Further Reading 227
13 The Heath Jarrow Morton Theorem and Multidimensional
Term Structure Models 229
13.1 The Heath Jarrow Morton Theorem 230
13.2 The Ho Lee Model 234
13.3 Mean Reversion: The Modified Vasicek or Hull White Model 237
13.4 Factor Analysis of the Term Structure 239
13.5 Example: Construction of a Two Factor Model with
Parametric Components 245
13.6 More General Volatility Specifications in the HJM Equation 248
References and Further Reading 251
vi CONTENTS
14 Exponential Affine Models 253
14.1 A Characterization of EA Models 255
14.2 Gaussian State Variables: General Formulas 258
14.3 Gaussian Models: Explicit Formulas 261
14.4 Square Root Processes and the Non Central Chi Squared Distribution .... 264
14.5 One Factor Square Root Model: Discount Factors and Forward Rates 268
References and Further Reading 272
A Behavior of Square Root Processes for Large Times 273
B Characterization of the Probability Density Function of
Square Root Processes 275
C The Square Root Diffusion with v = 1 277
15 Interest Rate Options 279
15.1 Forward Measures 279
Definition and Examples 279
15.2 Commodity Options with Stochastic Interest Rate 282
15.3 Options on Zero Coupon Bonds 283
15.4 Money Market Deposits with Yield Protection 285
Forward Rates and Forward Measures 286
15.5 Pricing Caps 289
General Considerations 289
Cap Pricing with Gaussian Models 292
Cap Pricing with Square Root Models 293
Cap Pricing and Implied Volatilities 297
15.6 Bond Options and Swaptions 299
General Pricing Relations 299
Jamshidian s Theorem 301
Volatility Analysis 303
15.7 Epilogue: The Brace Gatarek Musiela model 308
References and Further Reading 312
Index 313
|
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| id | DE-604.BV012896494 |
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| indexdate | 2024-07-09T18:35:38Z |
| institution | BVB |
| isbn | 1584880317 |
| language | English |
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| spelling | Avellaneda, Marco 1955-2022 (DE-588)171583396 aut Quantitative modeling of derivative securities from theory to practice Marco Avellaneda ; in collaboration with Peter Laurence Boca Raton ; Lodnon ; New York ; Washington, D.C. Chapman & Hall/CRC [2000] © 2000 xii, 322 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Bourse ram Futures gtt Marchés à terme d'instruments financiers ram Opties gtt Options (finances) ram Termijnhandel gtt Wiskundige modellen gtt Derivative securities Exotic options (Finance) Options (Finance) Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Laurence, Peter aut Äquivalent Avellaneda, Marco Quantitative modeling of derivative securities 2020 978-0-367-57914-2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008778010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Avellaneda, Marco 1955-2022 Laurence, Peter Quantitative modeling of derivative securities from theory to practice Bourse ram Futures gtt Marchés à terme d'instruments financiers ram Opties gtt Options (finances) ram Termijnhandel gtt Wiskundige modellen gtt Derivative securities Exotic options (Finance) Options (Finance) Derivat Wertpapier (DE-588)4381572-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4114528-8 |
| title | Quantitative modeling of derivative securities from theory to practice |
| title_auth | Quantitative modeling of derivative securities from theory to practice |
| title_exact_search | Quantitative modeling of derivative securities from theory to practice |
| title_full | Quantitative modeling of derivative securities from theory to practice Marco Avellaneda ; in collaboration with Peter Laurence |
| title_fullStr | Quantitative modeling of derivative securities from theory to practice Marco Avellaneda ; in collaboration with Peter Laurence |
| title_full_unstemmed | Quantitative modeling of derivative securities from theory to practice Marco Avellaneda ; in collaboration with Peter Laurence |
| title_short | Quantitative modeling of derivative securities |
| title_sort | quantitative modeling of derivative securities from theory to practice |
| title_sub | from theory to practice |
| topic | Bourse ram Futures gtt Marchés à terme d'instruments financiers ram Opties gtt Options (finances) ram Termijnhandel gtt Wiskundige modellen gtt Derivative securities Exotic options (Finance) Options (Finance) Derivat Wertpapier (DE-588)4381572-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Bourse Futures Marchés à terme d'instruments financiers Opties Options (finances) Termijnhandel Wiskundige modellen Derivative securities Exotic options (Finance) Options (Finance) Derivat Wertpapier Mathematisches Modell |
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