An introduction to the mathematics of financial derivatives:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Diego, Calif. [u.a.]
Academic Press
2000
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXVII, 527 S. graph.Darst. |
| ISBN: | 0125153929 9780125153928 |
Staff View
MARC
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| 100 | 1 | |a Neftci, Salih N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to the mathematics of financial derivatives |c Salih N. Neftci |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a San Diego, Calif. [u.a.] |b Academic Press |c 2000 | |
| 300 | |a XXVII, 527 S. |b graph.Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Effectenhandel |2 gtt | |
| 650 | 7 | |a Instrument dérivé (Finances) |2 rasuqam | |
| 650 | 4 | |a Instruments dérivés (Finances) - Mathématiques | |
| 650 | 7 | |a Marché financier |2 rasuqam | |
| 650 | 7 | |a Mathématique financière |2 rasuqam | |
| 650 | 7 | |a Portfolio-theorie |2 gtt | |
| 650 | 7 | |a Taux d'intérêt |2 rasuqam | |
| 650 | 7 | |a Termijnhandel |2 gtt | |
| 650 | 7 | |a Théorie des probabilités |2 rasuqam | |
| 650 | 7 | |a Wiskundige economie |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Derivative securities -- Mathematics | |
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PREFACE TO THE SECOND EDITION xxi
INTRODUCTION xxiii
CHAPTER • 1 Financial Derivatives
A Brief Introduction
1 Introduction 1
2 Definitions 2
3 Types of Derivatives 2
3.1 Cash and Carry Markets 3
3.2 Price Discovery Markets 4
3.3 Expiration Date 4
4 Forwards and Futures 5
4.1 Futures 6
5 Options 7
5.1 Some Notation 7
6 Swaps 9
6.1 A Simple Interest Rate Swap 10
7 Conclusions 11
8 References 11
9 Exercises 11
vii
viii Contents
CHAPTER • 2 A Primer on the Arbitrage Theorem
1 Introduction 13
2 Notation 14
2.1 Asset Prices 15
2.2 States of the World 15
2.3 Returns and Payoffs 16
2.4 Portfolio 17
3 A Basic Example of Asset Pricing 17
3.1 A First Glance at the Arbitrage Theorem 19
3.2 Relevance of the Arbitrage Theorem 20
3.3 The Use of Synthetic Probabilities 21
3.4 Martingales and Submartingales 24
3.5 Normalization 24
3.6 Equalization of Rates of Return 25
3.7 The No Arbitrage Condition 26
4 A Numerical Example 27
4.1 Case 1: Arbitrage Possibilities 27
4.2 Case 2: Arbitrage Free Prices 28
4.3 An Indeterminacy 29
5 An Application: Lattice Models 29
6 Payouts and Foreign Currencies 32
6.1 The Case with Dividends 32
6.2 The Case with Foreign Currencies 34
7 Some Generalizations 36
7.1 Time Index 36
7.2 States of the World 36
7.3 Discounting 37
8 Conclusions: A Methodology for Pricing
Assets 37
9 References 38
10 Appendix: Generalization of the Arbitrage
Theorem 38
11 Exercises 40
Contents jx
CHAPTER ? 3 Calculus in Deterministic and
Stochastic Environments
1 Introduction 45
1.1 Information Flows 46
1.2 Modeling Random Behavior 46
2 Some Tools of Standard Calculus 47
3 Functions 47
3.1 Random Functions 48
3.2 Examples of Functions 49
4 Convergence and Limit 52
4.1 The Derivative 53
4.2 The Chain Rule 57
4.3 The Integral 59
4.4 Integration by Parts 65
5 Partial Derivatives 66
5.1 Example 67
5.2 Total Differentials 67
5.3 Taylor Series Expansion 68
5.4 Ordinary Differential Equations 72
6 Conclusions 73
7 References 74
8 Exercises 74
CHAPTER ? 4 Pricing Derivatives
Models and Notation
1 Introduction 77
2 Pricing Functions 78
2.1 Forwards 78
2.2 Options 80
3 Application: Another Pricing Method 84
3.1 Example 85
4 The Problem 86
4.1 A First Look at Ito's Lemma 86
4.2 Conclusions 88
5 References 88
6 Exercises 89
x Contents
CHAPTER ? 5 Tools in Probability Theory
1 Introduction 91
2 Probability 91
2.1 Example 92
2.2 Random Variable 93
3 Moments 94
3.1 First Two Moments 94
3.2 Higher Order Moments 95
4 Conditional Expectations 97
4.1 Conditional Probability 97
4.2 Properties of Conditional Expectations 99
5 Some Important Models 100
5.1 Binomial Distribution in Financial Markets 100
5.2 Limiting Properties 101
5.3 Moments 102
5.4 The Normal Distribution 103
5.5 The Poisson Distribution 106
6 Markov Processes and Their Relevance 108
6.1 The Relevance 109
6.2 The Vector Case 110
7 Convergence of Random Variables 112
7.1 Types of Convergence and Their Uses 112
7.2 Weak Convergence 113
8 Conclusions 116
9 References 116
10 Exercises 117
CHAPTER • 6 Martingales and Martingale
Representations
1 Introduction 119
2 Definitions 120
2.1 Notation 120
2.2 Continuous Time Martingales 121
3 The Use of Martingales in Asset Pricing 122
Contents xi
4 Relevance of Martingales in Stochastic
Modeling 124
4.1 An Example 126
5 Properties of Martingale Trajectories 127
6 Examples of Martingales 130
6.1 Example 1: Brownian Motion 130
6.2 Example 2: A Squared Process 132
6.3 Example 3: An Exponential Process 133
6.4 Example 4: Right Continuous Martingales 134
7 The Simplest Martingale 134
7.1 An Application 135
7.2 An Example 136
8 Martingale Representations 137
8.1 An Example 137
8.2 Doob Meyer Decomposition 140
9 The First Stochastic Integral 143
9.1 Application to Finance: Trading Gains 144
10 Martingale Methods and Pricing 145
11 A Pricing Methodology 146
11.1 A Hedge 147
11.2 Time Dynamics 147
11.3 Normalization and Risk Neutral Probability 150
11.4 A Summary 152
12 Conclusions 152
13 References 153
14 Exercises 154
CHAPTER ? 7 Differentiation in Stochastic
Environments
1 Introduction 156
2 Motivation 157
3 A Framework for Discussing
Differentiation 161
4 The "Size" of Incremental Errors 164
5 One Implication 167
xii Contents
6 Putting the Results Together 169
6.1 Stochastic Differentials 170
7 Conclusions 171
8 References 171
9 Exercises 171
CHAPTER * 8 The Wiener Process and Rare
Events in Financial Markets
1 Introduction 173
1.1 Relevance of the Discussion 174
2 Two Generic Models 175
2.1 The Wiener Process 176
2.2 The Poisson Process 178
2.3 Examples 180
2.4 Back to Rare Events 182
3 SDE in Discrete Intervals, Again 183
4 Characterizing Rare and Normal Events 184
4.1 Normal Events 187
4.2 Rare Events 189
5 A Model for Rare Events 190
6 Moments That Matter 193
7 Conclusions 195
8 Rare and Normal Events in Practice 196
8.1 The Binomial Model 196
8.2 Normal Events 197
8.3 Rare Events 198
8.4 The Behavior of Accumulated Changes 199
9 References 202
10 Exercises 203
CHAPTER • 9 Integration in Stochastic
Environments
The ho Integral
1 Introduction 204
Contents x^j
1.1 The Ito Integral and SDEs 206
1.2 The Practical Relevance of the Ito Integral 207
2 The Ito Integral 208
2.1 The Riemann Stieltjes Integral 209
2.2 Stochastic Integration and Riemann Sums 211
2.3 Definition: The Ito Integral 213
2.4 An Expository Example 214
3 Properties of the Ito Integral 220
3.1 The Ito Integral Is a Martingale 220
3.2 Pathwise Integrals 224
4 Other Properties of the Ito Integral 226
4.1 Existence 226
4.2 Correlation Properties 226
4.3 Addition 227
5 Integrals with Respect to Jump Processes 227
6 Conclusions 228
7 References 228
8 Exercises 228
CHAPTER • 10 Ito's Lemma
1 Introduction 230
2 Types of Derivatives 231
2.1 Example 232
3 Ito's Lemma 232
3.1 The Notion of "Size" in Stochastic Calculus 235
3.2 First Order Terms 237
3.3 Second Order Terms 238
3.4 Terms Involving Cross Products 239
3.5 Terms in the Remainder 240
4 The Ito Formula 240
5 Uses of Ito's Lemma 241
5.1 Ito's Formula as a Chain Rule 241
5.2 Ito's Formula as an Integration Tool 242
6 Integral Form of Ito's Lemma 244
7 Ito's Formula in More Complex Settings 245
xiv Contents
7.1 Multivariate Case 245
7.2 Ito's Formula and Jumps 248
8 Conclusions 250
9 References 251
10 Exercises 251
CHAPTER ? 11 The Dynamics of Derivative Prices
Stochastic Differential Equations
1 Introduction 252
1.1 Conditions on a, and rt 253
2 A Geometric Description of Paths Implied by
SDEs 254
3 Solution of SDEs 255
3.1 What Does a Solution Mean? 255
3.2 Types of Solutions 256
3.3 Which Solution Is to Be Preferred? 258
3.4 A Discussion of Strong Solutions 258
3.5 Verification of Solutions to SDEs 261
3.6 An Important Example 262
4 Major Models of SDEs 265
4.1 Linear Constant Coefficient SDEs 266
4.2 Geometric SDEs 267
4.3 Square Root Process 269
4 4 Mean Reverting Process 270
4.5 Ornstein Uhlenbeck Process 271
5 Stochastic Volatility 271
6 Conclusions 272
7 References 272
8 Exercises 273
CHAPTER • 12 Pricing Derivative Products
Partial Differential Equations
1 Introduction 275
2 Forming Risk Free Portfolios 276
3 Accuracy of the Method 280
Contents xv
3.1 An Interpretation 282
4 Partial Differential Equations 282
4.1 Why Is the PDE an "Equation"? 283
4.2 What Is the Boundary Condition? 283
5 Classification of PDEs 284
5.1 Example 1: Linear, First Order PDE 284
5.2 Example 2: Linear, Second Order PDE 286
6 A Reminder: Bivariate, Second Degree
Equations 289
6.1 Circle 290
6.2 Ellipse 290
6.3 Parabola 292
6.4 Hyperbola 292
7 Types of PDEs 292
7.1 Example: Parabolic PDE 293
8 Conclusions 293
9 References 294
10 Exercises 294
CHAPTER • 13 The Black Scholes PDE
An Application
1 Introduction 296
2 The Black Scholes PDE 296
2.1 A Geometric Look at the Black Scholes Formula 298
3 PDEs in Asset Pricing 299
3.1 Constant Dividends 300
4 Exotic Options 301
4.1 Lookback Options 301
4.2 Ladder Options 301
4.3 Trigger or Knock in Options 302
4.4 Knock out Options 302
4.5 Other Exotics 302
4.6 The Relevant PDEs 303
5 Solving PDEs in Practice 304
5.1 Closed Form Solutions 304
xvi Contents
5.2 Numerical Solutions 306
6 Conclusions 309
7 References 310
8 Exercises 310
CHAPTER ? 14 Pricing Derivative Products
Equivalent Martingale Measures
1 Translations of Probabilities 312
1.1 Probability as "Measure" 312
2 Changing Means 316
2.1 Method 1: Operating on Possible Values 317
2.2 Method 2: Operating on Probabilities 321
3 The Girsanov Theorem 322
3.1 A Normally Distributed Random Variable 323
3.2 A Normally Distributed Vector 325
3.3 The Radon Nikodym Derivative 327
3.4 Equivalent Measures 328
4 Statement of the Girsanov Theorem 329
5 A Discussion of the Girsanov Theorem 331
5.1 Application to SDEs 332
6 Which Probabilities? 334
7 A Method for Generating Equivalent
Probabilities 337
7.1 An Example 340
8 Conclusions 342
9 References 342
10 Exercises 343
CHAPTER * 15 Equivalent Martingale Measures
Applications
1 Introduction 345
2 A Martingale Measure 346
2.1 The Moment Generating Function 346
2.2 Conditional Expectation of Geometric Processes 348
3 Converting Asset Prices into Martingales 349
Contents xvii
3.1 Determining P 350
3.2 The Implied SDEs 352
4 Application: The Black Scholes Formula 353
4.1 Calculation 356
5 Comparing Martingale and PDE
Approaches 358
5.1 Equivalence of the Two Approaches 359
5.2 Critical Steps of the Derivation 363
5.3 Integral Form of the Ito Formula 364
6 Conclusions 365
7 References 366
8 Exercises 366
CHAPTER * 16 New Results and Tools for
Interest Sensitive Securities
1 Introduction 368
2 A Summary 369
3 Interest Rate Derivatives 371
4 Complications 375
4.1 Drift Adjustment 376
4.2 Term Structure 377
5 Conclusions 377
6 References 378
7 Exercises 378
CHAPTER • 17 Arbitrage Theorem in a New
Setting
Normalization and Random Interest Rates
1 Introduction 379
2 A Model for New Instruments 381
2.1 The New Environment 383
2.2 Normalization 389
2.3 Some Undesirable Properties 392
2.4 A New Normalization 395
2.5 Some Implications 399
xviii Contents
3 Conclusions 404
4 References 404
5 Exercises 404
CHAPTER ? 18 Modeling Term Structure and
Related Concepts
1 Introduction 407
2 Main Concepts 408
2.1 Three Curves 409
2.2 Movements on the Yield Curve 412
3 A Bond Pricing Equation 414
3.1 Constant Spot Rate 414
3.2 Stochastic Spot Rates 416
3.3 Moving to Continuous Time 417
3.4 Yields and Spot Rates 418
4 Forward Rates and Bond Prices 419
4.1 Discrete Time 419
4.2 Moving to Continuous Time 420
5 Conclusions: Relevance of the
Relationships 423
6 References 424
7 Exercises 424
CHAPTER ? 19 Classical and HJM Approaches to
Fixed Income
1 Introduction 426
2 The Classical Approach 427
2.1 Example 1 428
2.2 Example 2 429
2.3 The General Case 429
2.4 Using the Spot Rate Model 432
2.5 Comparison with the Black Scholes World 434
3 The HJM Approach to Term Structure 435
3.1 Which Forward Rate? 436
3.2 Arbitrage Free Dynamics in HJM 437
Contents xjx
3.3 Interpretation 440
3.4 The r, in the HJM Approach 441
3.5 Another Advantage of the HJM Approach 443
3.6 Market Practice 444
4 How to Fit rt to Initial Term Structure 444
4.1 Monte Carlo 445
4.2 Tree Models 446
4.3 Closed Form Solutions 447
5 Conclusions 447
6 References 447
7 Exercises 448
CHAPTER ? 20 Classical PDE Analysis for Interest
Rate Derivatives
1 Introduction 451
2 The Framework 454
3 Market Price of Interest Rate Risk 455
4 Derivation of the PDE 457
4.1 A Comparison 459
5 Closed Form Solutions of the PDE 460
5.1 Case 1: A Deterministic rt 460
5.2 Case 2: A Mean Reverting r, 461
5.3 Case 3: More Complex Forms 464
6 Conclusions 465
7 References 465
8 Exercises 465
CHAPTER ? 21 Relating Conditional Expectations
to PDEs
1 Introduction 467
2 From Conditional Expectations to PDEs 469
2.1 Case 1: Constant Discount Factors 469
2.2 Case 2: Bond Pricing 472
2.3 Case 3: A Generalization 475
2.4 Some Clarifications 475
xx Contents
2.5 Which Drift? 476
2.6 Another Bond Price Formula 477
2.7 Which Formula? 479
3 From PDEs to Conditional Expectations 479
4 Generators, Feynman Kac Formula, and Other
Tools 482
4.1 Ito Diffusions 482
4.2 Markov Property 483
4.3 Generator of an Ito Diffusion 483
4.4 A Representation for A 484
4.5 Kolmogorov's Backward Equation 485
5 Feynman Kac Formula 487
6 Conclusions 487
7 References 487
8 Exercises 487
CHAPTER * 22 Stopping Times and American Type
Securities
1 Introduction 489
2 Why Study Stopping Times? 491
2.1 American Style Securities 492
3 Stopping Times 492
4 Uses of Stopping Times 493
5 A Simplified Setting 494
5.1 The Model 494
6 A Simple Example 499
7 Stopping Times and Martingales 504
7.1 Martingales 504
7.2 Dynkin's Formula 504
8 Conclusions 505
9 References 505
10 Exercises 505
BIBLIOGRAPHY 509
INDEX 513 |
| any_adam_object | 1 |
| author | Neftci, Salih N. |
| author_facet | Neftci, Salih N. |
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| author_sort | Neftci, Salih N. |
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| dewey-full | 332.63/2 332.63/221 |
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| dewey-ones | 332 - Financial economics |
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| dewey-sort | 3332.63 12 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013236384 |
| illustrated | Illustrated |
| indexdate | 2025-03-20T19:10:42Z |
| institution | BVB |
| isbn | 0125153929 9780125153928 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009019419 |
| oclc_num | 247405368 |
| open_access_boolean | |
| owner | DE-898 DE-BY-UBR DE-824 DE-573 DE-M347 DE-92 DE-91 DE-BY-TUM DE-N2 DE-1102 DE-858 DE-355 DE-BY-UBR DE-1049 DE-19 DE-BY-UBM DE-Aug4 DE-521 DE-739 DE-634 DE-188 |
| owner_facet | DE-898 DE-BY-UBR DE-824 DE-573 DE-M347 DE-92 DE-91 DE-BY-TUM DE-N2 DE-1102 DE-858 DE-355 DE-BY-UBR DE-1049 DE-19 DE-BY-UBM DE-Aug4 DE-521 DE-739 DE-634 DE-188 |
| physical | XXVII, 527 S. graph.Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Academic Press |
| record_format | marc |
| spelling | Neftci, Salih N. Verfasser aut An introduction to the mathematics of financial derivatives Salih N. Neftci 2. ed. San Diego, Calif. [u.a.] Academic Press 2000 XXVII, 527 S. graph.Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Effectenhandel gtt Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Mathématiques Marché financier rasuqam Mathématique financière rasuqam Portfolio-theorie gtt Taux d'intérêt rasuqam Termijnhandel gtt Théorie des probabilités rasuqam Wiskundige economie gtt Wiskundige modellen gtt Mathematik Derivative securities -- Mathematics Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s Derivat Wertpapier (DE-588)4381572-8 s DE-604 http://www.loc.gov/catdir/toc/els033/99069121.html Table of contents http://www.loc.gov/catdir/description/els033/99069121.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009019419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neftci, Salih N. An introduction to the mathematics of financial derivatives Effectenhandel gtt Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Mathématiques Marché financier rasuqam Mathématique financière rasuqam Portfolio-theorie gtt Taux d'intérêt rasuqam Termijnhandel gtt Théorie des probabilités rasuqam Wiskundige economie gtt Wiskundige modellen gtt Mathematik Derivative securities -- Mathematics Derivat Wertpapier (DE-588)4381572-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4017195-4 |
| title | An introduction to the mathematics of financial derivatives |
| title_auth | An introduction to the mathematics of financial derivatives |
| title_exact_search | An introduction to the mathematics of financial derivatives |
| title_full | An introduction to the mathematics of financial derivatives Salih N. Neftci |
| title_fullStr | An introduction to the mathematics of financial derivatives Salih N. Neftci |
| title_full_unstemmed | An introduction to the mathematics of financial derivatives Salih N. Neftci |
| title_short | An introduction to the mathematics of financial derivatives |
| title_sort | an introduction to the mathematics of financial derivatives |
| topic | Effectenhandel gtt Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Mathématiques Marché financier rasuqam Mathématique financière rasuqam Portfolio-theorie gtt Taux d'intérêt rasuqam Termijnhandel gtt Théorie des probabilités rasuqam Wiskundige economie gtt Wiskundige modellen gtt Mathematik Derivative securities -- Mathematics Derivat Wertpapier (DE-588)4381572-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Effectenhandel Instrument dérivé (Finances) Instruments dérivés (Finances) - Mathématiques Marché financier Mathématique financière Portfolio-theorie Taux d'intérêt Termijnhandel Théorie des probabilités Wiskundige economie Wiskundige modellen Mathematik Derivative securities -- Mathematics Derivat Wertpapier Finanzmathematik |
| url | http://www.loc.gov/catdir/toc/els033/99069121.html http://www.loc.gov/catdir/description/els033/99069121.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009019419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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