Introduction to the mathematics of finance: arbitrage and option pricing
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2012
|
| Edition: | 2. ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 287 S. graph. Darst. |
| ISBN: | 9781461435815 9781461435822 1461435811 |
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MARC
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| 100 | 1 | |a Roman, Steven |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to the mathematics of finance |b arbitrage and option pricing |c Steven Roman |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2012 | |
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Record in the Search Index
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| adam_text | Titel: Introduction to the mathematics of finance
Autor: Roman, Steven
Jahr: 2012
Contents
Preface, vii
Notation Key and Greek Alphabet, xv
0 Introduction
Motivation, 1
The Derivative Pricing Problem, 3
Miscellaneous Mathematical Facts, 8
Part 1—Options and Arbitrage
1 Background on Options
Stock Options, 13
The Purpose of Options, 17
Profit and Payoff Curves, 18
The Time Value of an Option, 22
Selling Short, 24
Exercises, 26
2 An Aperitif on Arbitrage
Forward Contracts, 29
Futures Contracts, 31
The Put-Call Option Parity Formula, 33
Comparing Option Prices, 35
Exercises, 36
Part 2—Discrete-Time Pricing Models
3 Discrete Probability
Partitions, 41
Overview of Probability, 46
Probability Spaces, 48
Independence, 52
The Binomial Distribution, 53
Conditional Probability, 56
Random Variables, 58
Expectation, 65
Variance and Standard Deviation, 69
Conditional Expectation, 72
Exercises, 78
4 Stochastic Processes, Filtrations
and Martingales
State Trees, 85
Information Structures, 87
Information Structures, Probabilities and Path numbers,:
Information Structures and Stochastic Processes, 92
Martingales, 94
An Example, 98
Exercises, 101
5 Discrete-Time Pricing Models
Assumptions, 103
The Basic Model, 104
Portfolios and Trading Strategies, 107
Preserving Gains in a Trading Strategy, 114
Arbitrage Trading Strategies, 117
Martingale Measures, 119
Characterizing Arbitrage, 123
Computing Martingale Measures, 126
The Pricing Problem: Alternatives and Replication, 128
Uniqueness of Martingale Measures, 133
Exercises, 135
6 The Binomial Model
The General Binomial Model, 141
Standard Binomial Models, 145
Exercises, 154
7 Pricing Nonattainable Alternatives
in an Incomplete Market
Incompleteness in a Discrete-Time Model, 157
Mathematical Background, 158
Pricing Nonattainable Alternatives, 164
Exercises, 167
8 Optimal Stopping and American Options
An Example, 169
The Model, 170
The Payoff Process, 170
Stopping Times, 171
Payoff under a Stopping Time, 174
Existence of Optimal Stopping Times, 176
Computing the Snell Envelope, 177
The Smallest Dominating Supermartingale, 180
Additional Facts about Martingales, 181
Characterizing Optimal Stopping Times, 184
Optimal Stopping Times and the Doob Decomposition, 185
The Smallest Optimal Stopping Time, 186
The Largest Optimal Stopping Time, 187
Exercises, 188
Part 3—The Black-Scholes Option Pricing Formula
9 Continuous Probability
General Probability Spaces, 193
Probability Measures on R, 196
Distribution Functions, 197
Density Functions, 201
Random Variables, 203
The Normal Distribution, 206
Convergence in Distribution, 207
The Central Limit Theorem, 209
Exercises, 212
10 The Black-Scholes Option Pricing Formula
Stock Prices and Brownian Motion, 215
The Binomial Model in the Limit: Brownian Motion, 221
Taking the Limit as At -^ 0, 222
The Natural Binomial Model, 226
The Martingale Measure Binomial Model, 229
Are the Assumptions Realistic?, 232
The Black-Scholes Option Pricing Formula, 233
How Black-Scholes Is Used in Practice: Volatility Smiles, 236
How Dividends Affect the Use of Black-Scholes, 238
The Binomial Model from a Different Perspective: Ito s Lemma, 239
Exercises, 242
Appendix A: Convexity and the Separation Theorem
Convex, Closed and Compact Sets, 246
Convex Hulls, 248
Linear and Affine Hyperplanes, 249
Separation, 250
Appendix B: Closed, Convex Cones
Closed, Convex Cones, 256
The Main Result, 263
Selected Solutions, 271
References, 281
Index, 283
|
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332/.01/513 |
| dewey-search | 332/.01/513 |
| dewey-sort | 3332 11 3513 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-10T00:17:36Z |
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| isbn | 9781461435815 9781461435822 1461435811 |
| language | English |
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| spelling | Roman, Steven Verfasser aut Introduction to the mathematics of finance arbitrage and option pricing Steven Roman 2. ed. New York [u.a.] Springer 2012 XVI, 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 Erscheint auch als Online-Ausgabe 10.1007/978-1-4614-3582-2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024988932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roman, Steven Introduction to the mathematics of finance arbitrage and option pricing Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 |
| title | Introduction to the mathematics of finance arbitrage and option pricing |
| title_auth | Introduction to the mathematics of finance arbitrage and option pricing |
| title_exact_search | Introduction to the mathematics of finance arbitrage and option pricing |
| title_full | Introduction to the mathematics of finance arbitrage and option pricing Steven Roman |
| title_fullStr | Introduction to the mathematics of finance arbitrage and option pricing Steven Roman |
| title_full_unstemmed | Introduction to the mathematics of finance arbitrage and option pricing Steven Roman |
| title_short | Introduction to the mathematics of finance |
| title_sort | introduction to the mathematics of finance arbitrage and option pricing |
| title_sub | arbitrage and option pricing |
| topic | Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik |
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