Introduction to the mathematics of finance: from risk management to options pricing
"This book is specifically written for upper-division undergraduate or beginning graduate students in mathematics, finance, or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a c...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2004
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "This book is specifically written for upper-division undergraduate or beginning graduate students in mathematics, finance, or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formula as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options."--BOOK JACKET. |
| Physical Description: | XIV, 354 S. graph. Darst. |
| ISBN: | 0387213643 0387213759 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
Notation Key
and Greek Alphabet
xv
Introduction
1
Portfolio Risk Management
1
Option Pricing Models
2
Assumptions
4
Arbitrage
4
1
Probability I: An Introduction to Discrete Probability
7
1.1
Overview
7
1.2
Probability Spaces
11
1.3
Independence
15
1.4
Binomial Probabilities
16
1.5
Random Variables
21
1.6
Expectation
25
1.7
Variance and Standard Deviation
29
1.8
Covariance and Correlation; Best Linear Predictor
31
Exercises
36
2
Portfolio Management and the Capital Asset Pricing Model
41
2.1
Portfolios, Returns and Risk
41
2.2
Two-Asset Portfolios
46
2.3
Multi-Asset Portfolios
52
Exercises
75
3
Background on Options
79
3.1
Stock Options
79
3.2
The Purpose of Options
79
3.3
Profit and Payoff Curves
80
3.4
Selling Short
85
Exercises
85
4
An Aperitif on Arbitrage
89
4.1
Background on Forward Contracts
89
4.2
The Pricing of Forward Contracts
90
4.3
The Put-Call Option Parity Formula
92
4.4
Option Prices
96
Exercises
99
xii Contents
Probability II: More Discrete Probability
103
5.1
Conditional Probability
103
5.2
Partitions and Measurability
104
5.3
Algebras
109
5.4
Conditional Expectation
115
5.5
Stochastic Processes
126
5.6
Filtrations and Martingales
126
Exercises
134
Discrete-Time Pricing Models
139
6.1
Assumptions
139
6.2
Positive Random Variables
141
6.3
The Basic Model by Example
141
6.4
The Basic Model
144
6.5
Portfolios and Trading Strategies
148
6.6
The Pricing Problem: Alternatives and Replication
158
6.7
Arbitrage Trading Strategies
163
6.8
Admissible Arbitrage Trading Strategies
165
6.9
Characterizing Arbitrage
167
6.10
Computing Martingale Measures
177
Exercises
182
The Cox-Ross-Rubinstein Model
187
7.1
The Model
187
7.2
Martingale Measures in the CRR model
190
7.3
Pricing in the CRR Model
193
7.4
Another Look at the CRR Model via Random Walks
195
Exercises
200
Probability III: Continuous Probability
203
8.1
General Probability Spaces
203
8.2
Probability Measures on
Ж
207
8.3
Distribution Functions
210
8.4
Density Functions
214
8.5
Types of Probability Measures on
Ж
217
8.6
Random Variables
219
8.7
The Normal Distribution
222
8.8
Convergence in Distribution
224
8.9
The Central Limit Theorem
228
Exercises
233
Contents xiii
9 The Black-Scholes Option
Pricing Formula
237
9.1 Stock
Prices and Brownian Motion
237
9.2
The CRR Model in the Limit: Brownian Motion
245
9.3
Taking the Limit as
Δί
-> 0 248
9.4
The Natural CRR Model
253
9.5
The Martingale Measure CRR Model
258
9.6
More on the Model From a Different Perspective:
Itô s
Lemma
263
9.7
Are the Assumptions Realistic?
265
9.8
The Black-Scholes Option Pricing Formula
266
9.9
How Black-Scholes is Used in Practice:
Volatility Smiles and Surfaces
270
9.10
How Dividends Affect the Use of Black-Scholes
273
Exercises
274
10
Optimal Stopping and American Options
277
10.1
An Example
277
10.2
The Model
278
10.3
The Payoffs
278
10.4
Stopping Times
279
10.5
Stopping the Payoff Process
280
10.6
The Stopped Value of an American Option
281
10.7
The Initial Value of an American Option, or
What to Do At Time i0
282
10.8
What to Do At Time tk
286
10.9
Optimal Stopping Times and the Snell Envelop
288
10.10
Existence of Optimal Stopping Times
288
10.11
Characterizing the Snell Envelop
290
10.12
Additional Facts About Martingales
295
10.13
Characterizing Optimal Stopping Times
298
10.14
Optimal Stopping Times and the Doob Decomposition
299
10.15
The Smallest Optimal Stopping Time
300
10.16
The Largest Optimal Stopping Time
302
Exercises
303
Appendix A: Pricing Nonattainable Alternatives in an
Incomplete Market
305
A.
1
Fair Value in an Incomplete Market
305
A.2 Mathematical Background
306
A.3 Pricing Nonattainable Alternatives
315
Exercises
318
xiv Contents
Appendix
В:
Convexity and the Separation Theorem
321
B.I Convex, Closed and Compact Sets
321
B.2 Convex Hulls
322
B.3 Linear and
Affine Hyperplanes 323
В.
4
Separation
325
Selected Solutions
331
References
349
Index
351
|
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| dewey-sort | 3332 11 3513 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| series2 | Undergraduate texts in mathematics |
| spelling | Roman, Steven Verfasser aut Introduction to the mathematics of finance from risk management to options pricing Steven Roman New York [u.a.] Springer 2004 XIV, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics "This book is specifically written for upper-division undergraduate or beginning graduate students in mathematics, finance, or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formula as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options."--BOOK JACKET. Financiering gtt Finanças larpcal Gestion de portefeuille - Modèles mathématiques Investissements - Mathématiques Matemática aplicada larpcal Modèle de fixation du prix des actifs Opties gtt Options (Finances) - Prix Portfolio-theorie gtt Wiskunde gtt Mathematik Mathematisches Modell Investments Mathematics Capital assets pricing model Portfolio management Mathematical models Options (Finance) Prices Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s DE-188 Capital-Asset-Pricing-Modell (DE-588)4121078-5 s Optionspreistheorie (DE-588)4135346-8 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roman, Steven Introduction to the mathematics of finance from risk management to options pricing Financiering gtt Finanças larpcal Gestion de portefeuille - Modèles mathématiques Investissements - Mathématiques Matemática aplicada larpcal Modèle de fixation du prix des actifs Opties gtt Options (Finances) - Prix Portfolio-theorie gtt Wiskunde gtt Mathematik Mathematisches Modell Investments Mathematics Capital assets pricing model Portfolio management Mathematical models Options (Finance) Prices Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd Optionspreistheorie (DE-588)4135346-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4121078-5 (DE-588)4135346-8 (DE-588)4017195-4 (DE-588)4123623-3 |
| title | Introduction to the mathematics of finance from risk management to options pricing |
| title_auth | Introduction to the mathematics of finance from risk management to options pricing |
| title_exact_search | Introduction to the mathematics of finance from risk management to options pricing |
| title_full | Introduction to the mathematics of finance from risk management to options pricing Steven Roman |
| title_fullStr | Introduction to the mathematics of finance from risk management to options pricing Steven Roman |
| title_full_unstemmed | Introduction to the mathematics of finance from risk management to options pricing Steven Roman |
| title_short | Introduction to the mathematics of finance |
| title_sort | introduction to the mathematics of finance from risk management to options pricing |
| title_sub | from risk management to options pricing |
| topic | Financiering gtt Finanças larpcal Gestion de portefeuille - Modèles mathématiques Investissements - Mathématiques Matemática aplicada larpcal Modèle de fixation du prix des actifs Opties gtt Options (Finances) - Prix Portfolio-theorie gtt Wiskunde gtt Mathematik Mathematisches Modell Investments Mathematics Capital assets pricing model Portfolio management Mathematical models Options (Finance) Prices Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd Optionspreistheorie (DE-588)4135346-8 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Financiering Finanças Gestion de portefeuille - Modèles mathématiques Investissements - Mathématiques Matemática aplicada Modèle de fixation du prix des actifs Opties Options (Finances) - Prix Portfolio-theorie Wiskunde Mathematik Mathematisches Modell Investments Mathematics Capital assets pricing model Portfolio management Mathematical models Options (Finance) Prices Capital-Asset-Pricing-Modell Optionspreistheorie Finanzmathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798732&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT romansteven introductiontothemathematicsoffinancefromriskmanagementtooptionspricing |