Option valuation: a first course in financial mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2012
|
| Schriftenreihe: | Chapman & Hall/CRC financial mathematics series
A Chapman & Hall book |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIII, 252 S. graph. Darst. |
| ISBN: | 9781439889114 |
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| 100 | 1 | |a Junghenn, Hugo D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Option valuation |b a first course in financial mathematics |c Hugo D. Junghenn |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2012 | |
| 300 | |a XIII, 252 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
| 490 | 0 | |a A Chapman & Hall book | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Options (Finance) |x Mathematics | |
| 650 | 4 | |a Derivative securities |x Mathematics | |
| 650 | 4 | |a Business mathematics | |
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Datensatz im Suchindex
| _version_ | 1804148911895478272 |
|---|---|
| adam_text | Contents
Preface
xi
1
Interest and Present Value
1
1.1
Compound Interest
....................... 1
1.2
Annuities
............................. 3
1.3
Bonds
............................... 6
1.4
Rate of Return
.......................... 7
1.5
Exercises
............................. 9
2
Probability Spaces
13
2.1
Sample Spaces and Events
................... 13
2.2
Discrete Probability Spaces
................... 14
2.3
General Probability Spaces
................... 16
2.4
Conditional Probability
..................... 20
2.5
Independence
........................... 22
2.6
Exercises
............................. 24
3
Random Variables
27
3.1
Definition and General Properties
............... 27
3.2
Discrete Random Variables
................... 29
3.3
Continuous Random Variables
................. 32
3.4
Joint Distributions
........................ 34
3.5
Independent Random Variables
................ 35
3.6
Sums of Independent Random Variables
............ 38
3.7
Exercises
............................. 41
4
Options and Arbitrage
43
4.1
Arbitrage
.............................
44
4.2
Classification of Derivatives
................... 46
4.3
Forwards
............................. 46
4.4
Currency Forwards
....................... 48
4.5
Futures
.............................. 49
4.6
Options
..............................
50
4.7
Properties of Options
...................... 53
4.8
Dividend-Paying Stocks
.....................
55
4.9
Exercises
............................. ^7
vii
Vlil
5
Discrete-Time Portfolio Processes
59
5.1
Discrete-Time Stochastic Processes
............... 59
5.2
Self-Financing Portfolios
.................... 61
5.3
Option Valuation by Portfolios
................. 64
5.4
Exercises
............................. 66
6
Expectation of a Random Variable
67
6.1
Discrete Case: Definition and Examples
............ 67
6.2
Continuous Case: Definition and Examples
.......... 68
6.3
Properties of Expectation
.................... 69
6.4
Variance of a Random Variable
................. 71
6.5
The Central Limit Theorem
.................. 73
6.6
Exercises
............................. 75
7
The Binomial Model
77
7.1
Construction of the Binomial Model
.............. 77
7.2
Pricing a Claim in the Binomial Model
............ 80
7.3
The Cox-Ross-Rubinstein Formula
............... 83
7.4
Exercises
............................. 86
8
Conditional Expectation and Discrete-Time Martingales
89
8.1
Definition of Conditional Expectation
............. 89
8.2
Examples of Conditional Expectation
............. 92
8.3
Properties of Conditional Expectation
............. 94
8.4
Discrete-Time Martingales
................... 96
8.5
Exercises
............................. 98
9
The Binomial Model Revisited
101
9.1
Martingales in the Binomial Model
.............. 101
9.2
Change of Probability
...................... 103
9.3
American Claims in the Binomial Model
........... 105
9.4
Stopping Times
......................... 108
9.5
Optimal Exercise of an American Claim
............
Ill
9.6
Dividends in the Binomial Model
............... 114
9.7
The General Finite Market Model
............... 115
9.8
Exercises
............................. 117
10
Stochastic Calculus
119
10.1
Differential Equations
...................... 119
10.2
Continuous-Time Stochastic Processes
............. 120
10.3
Brownian Motion
........................ 122
10.4
Variation of Brownian Paths
.................. 123
10.5
Riemann-Stieltjes Integrals
................... 126
10.6
Stochastic Integrals
....................... 126
10.7
The Ito-Doeblin Formula
.................... 131
10.8
Stochastic Differential Equations
................ 136
їх
10.9
Exercises
............................. 139
11
The Black-Scholes-Merton Model
141
11.1
The Stock Price SDE
...................... 141
11.2
Continuous-Time Portfolios
................... 142
11.3
The Black-Scholes-Merton PDE
................ 143
11.4
Properties of the BSM Call Function
............. 146
11.5
Exercises
............................. 149
12
Continuous-Time Martingales
151
12.1
Conditional Expectation
.................... 151
12.2
Martingales: Definition and Examples
............. 152
12.3
Martingale Representation Theorem
.............. 154
12.4
Moment Generating Functions
................. 156
12.5
Change of Probability and Girsanov s Theorem
........ 158
12.6
Exercises
............................. 161
13
The BSM Model Revisited
163
13.1
Risk-Neutral Valuation of a Derivative
............ 163
13.2
Proofs of the Valuation Formulas
............... 165
13.3
Valuation under
Ρ
........................ 167
13.4
The Feynman-Kac Representation Theorem
......... 168
13.5
Exercises
............................. 171
14
Other Options
173
14.1
Currency Options
........................ 173
14.2
Forward Start Options
..................... 175
14.3
Chooser Options
......................... 176
14.4
Compound Options
....................... 177
14.5
Path-Dependent Derivatives
.................. 178
14.5.1
Barrier Options
...................... 179
14.5.2
Lookback
Options
.................... 185
14.5.3
Asian Options
...................... 191
14.6
Quantos
.............................. 195
14.7
Options on Dividend-Paying Stocks
.............. 197
14.7.1
Continuous Dividend Stream
.............. 197
14.7.2
Discrete Dividend Stream
................ 198
14.8
American Claims in the BSM Model
.............. 200
14.9
Exercises
............................. 203
A Sets and Counting
209
В
Solution of the BSM PDE
215
С
Analytical Properties of the BSM Call Function
219
D
Hints and Solutions to Odd-Numbered Problems
225
Bibliography
247
Index
249
Finance/Mathematics
irst Course in Financial Mathematics
Option Valuation: A First Course in Financial Mathematics
provides a straightforward introduction to the mathematics and
models used in the valuation of financial derivatives. It examines
the principles of option pricing in detail via standard binomial and
stochastic calculus models. Developing the requisite mathematical
background as needed, the text introduces probability theory and
stochastic calculus at an undergraduate level.
The first nine chapters of the book describe option valuation
techniques in discrete time, focusing on the binomial model. The
author shows how the binomial model offers a practical method
for pricing options using relatively elementary mathematical tools.
The binomial model also enables a clear, concrete exposition of
fundamental principles of finance, such as arbitrage and hedging,
without the distraction of complex mathematical constructs. The
remaining chapters illustrate the theory in continuous time, with
an emphasis on the more mathematically sophisticated Black-
Scholes-Merton model.
Largely self-contained, this classroom-tested text offers a sound
introduction to applied probability through a mathematical finance
perspective. Numerous examples and exercises help readers
gain expertise with financial calculus methods and increase their
general mathematical sophistication. The exercises range from
routine applications to spreadsheet projects to the pricing of a
variety of complex financial instruments. Hints and solutions to
odd-numbered problems are given in an appendix.
CRC
Press
Taylor Si Francis Group
an
informa
business
www.
с
rep ress.com
6000
Broken Sound Parkway, NW
Suite
300,
Boca Raton. FL
33487
711
Third Avenue
New York, NY
1001 7
2
Park Square, Milton Park
Abingdon, Oxon
0X1 4
4RN, UK
K14G40
9
781439 889114
|
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| dewey-ones | 332 - Financial economics |
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| dewey-sort | 3332.64 6530151 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV039943516 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:14:40Z |
| institution | BVB |
| isbn | 9781439889114 |
| language | English |
| lccn | 2011044664 |
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| spelling | Junghenn, Hugo D. Verfasser aut Option valuation a first course in financial mathematics Hugo D. Junghenn Boca Raton [u.a.] CRC Press 2012 XIII, 252 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series A Chapman & Hall book Mathematik Options (Finance) Mathematics Derivative securities Mathematics Business mathematics Option (DE-588)4115452-6 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Option (DE-588)4115452-6 s Finanzmathematik (DE-588)4017195-4 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024801559&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024801559&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Junghenn, Hugo D. Option valuation a first course in financial mathematics Mathematik Options (Finance) Mathematics Derivative securities Mathematics Business mathematics Option (DE-588)4115452-6 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4115452-6 (DE-588)4017195-4 |
| title | Option valuation a first course in financial mathematics |
| title_auth | Option valuation a first course in financial mathematics |
| title_exact_search | Option valuation a first course in financial mathematics |
| title_full | Option valuation a first course in financial mathematics Hugo D. Junghenn |
| title_fullStr | Option valuation a first course in financial mathematics Hugo D. Junghenn |
| title_full_unstemmed | Option valuation a first course in financial mathematics Hugo D. Junghenn |
| title_short | Option valuation |
| title_sort | option valuation a first course in financial mathematics |
| title_sub | a first course in financial mathematics |
| topic | Mathematik Options (Finance) Mathematics Derivative securities Mathematics Business mathematics Option (DE-588)4115452-6 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Mathematik Options (Finance) Mathematics Derivative securities Mathematics Business mathematics Option Finanzmathematik |
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