Quantitative finance: its development, mathematical foundations, and current scope
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 401 S. graph. Darst. |
| ISBN: | 9780470431993 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quantitative finance |b its development, mathematical foundations, and current scope |c T. W. Epps |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XVIII, 401 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Investments |x Mathematical models | |
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface
xv
Acronyms and Abbreviations
xviii
PART I PERSPECTIVE AND PREPARATION
1
Introduction and Overview
3
1.1
An Elemental View of Assets and Markets
3
1.1.1
Assets as Bundles of Claims
4
1.1.2
Financial Markets as Transportation Agents
5
1.1.3
Why Is Transportation Desirable?
5
1.1.4
What Vehicles Are Available?
6
1.1.5
What Is There to Learn about Assets and Markets?
7
1.1.6
Why the Need for Quantitative Finance?
8
1.2
Where We Go from Here
8
2
Tools from Calculus and Analysis
11
2.1
Some Basics from Calculus
12
2.2
Elements of Measure Theory
15
vii
VIU
CONTENTS
2.2.1
Sets and Collections of Sets
15
2.2.2
Set Functions and Measures
16
2.3
Integration
18
2.3.1
Riemann-Stieltjes
19
2.3.2
Lebesgue/Lebesgue-Stieltjes
20
2.3.3
Properties of the Integral
21
2.4
Changes of Measure
23
Probability
25
3.1
Probability Spaces
25
3.2
Random Variables and Their Distributions
28
3.3
Independence of Random Variables
33
3.4
Expectation
34
3.4.1
Moments
36
3.4.2
Conditional Expectations and Moments
38
3.4.3
Generating Functions
40
3.5
Changes of Probability Measure
41
3.6
Convergence Concepts
42
3.7
Laws of Large Numbers and Central-Limit Theorems
45
3.8
Important Models for Distributions
46
3.8.1
Continuous Models
46
3.8.2
Discrete Models
51
PART II PORTFOLIOS AND PRICES
Interest and Bond Prices
55
4.1
Interest Rates and Compounding
55
4.2
Bond Prices, Yields, and Spot Rates
57
4.3
Forward Bond Prices and Rates
63
Exercises
66
Empirical Project
1 67
Models of Portfolio Choice
71
5.1
Models That Ignore Risk
72
5.2
Mean-Variance Portfolio Theory
75
5.2.1
Mean-Variance Efficient Portfolios
75
5.2.2
The Single-Index Model
79
Exercises
81
Empirical Project
2 82
CONTENTS
IX
Prices in a Mean-Variance World
87
6.1
The Assumptions
87
6.2
The Derivation
88
6.3
Interpretation
91
6.4
Empirical Evidence
91
6.5
Some Reflections
94
Exercises
95
Rational Decisions under Risk
97
7.1
The Setting and the Axioms
98
7.2
The
Expected-Utility (EU)
Theorem
100
7.3
Applying
EU
Theory
103
7.3.1
Implementing
EU
Theory in Financial Modeling
104
7.3.2
Inferring Utilities and Beliefs
105
7.3.3
Qualitative Properties of Utility Functions
106
7.3.4
Measures of Risk Aversion
107
7.3.5
Examples of Utility Functions
108
7.3.6
Some Qualitative Implications of the
EU
Model
109
7.3.7
Stochastic Dominance
114
7.4
Is the
Markowitz
Investor Rational?
117
Exercises
121
Empirical Project
3 123
Observed Decisions under Risk
127
8.1
Evidence about Choices under Risk
128
8.1.1
Allais
Paradox
128
8.1.2
Prospect Theory
129
8.1.3
Preference Reversals
131
8.1.4
Risk Aversion and Diminishing Marginal Utility
133
8.2
Toward Behavioral Finance
134
Exercises
136
Distributions of Returns
139
9.1
Some Background
140
9.2
The Normal/Lognormal Model
143
9.3
The Stable Model
147
9.4
Mixture Models
150
9.5
Comparison and Evaluation
152
Exercises
153
X
CONTENTS
10 Dynamics
of Prices and
Returns
155
ЮЛ
Evidence for First-Moment Independence
155
10.2
Random Walks and Martingales
160
10.3
Modeling Prices in Continuous Time
164
10.3.1
Poisson
and Compound-Poisson Processes
165
10.3.2
Brownian Motions
167
10.3.3
Martingales in Continuous Time
171
Exercises
171
Empirical Project
4 173
11
Stochastic Calculus
177
11.1
Stochastic Integrals
178
11.1.1
Ito
Integrals with Respect to a Brownian Motion (BM)
178
11.1.2
From
Ito
Integrals to
Ito
Processes
180
11.1.3
Quadratic Variations of
Ito
Processes
182
11.1.4
Integrals with Respect to
Ito
Processes
183
11.2
Stochastic Differentials
183
11.3
Itô s
Formula for Differentials
185
11.3.1
Functions of a BM Alone
185
11.3.2
Functions of Time and a BM
186
11.3.3
Functions of Time and General
Ito
Processes
187
Exercises
189
12
Portfolio Decisions over Time
191
12.1
The Consumption-Investment Choice
192
12.2
Dynamic Portfolio Decisions
193
12.2.1
Optimizing via Dynamic Programming
194
12.2.2
A Formulation with Additively Separable Utility
198
Exercises
200
13
Optimal Growth
201
13.1
Optimal Growth in Discrete Time
203
13.2
Optimal Growth in Continuous Time
206
13.3
Some Qualifications
209
Exercises
211
Empirical Project
5 213
CONTENTS
XI
14 Dynamic Models
for Prices
217
14.1
Dynamic Optimization (Again)
218
14.2
Static Implications: The Capital Asset Pricing Model
219
14.3
Dynamic Implications: The Lucas Model
220
14.4
Assessment
223
14.4.1
The Puzzles
224
14.4.2
The Patches
225
14.4.3
Some Reflections
226
Exercises
227
15
Efficient Markets
229
15.1
Event Studies
230
15.1.1
Methods
231
15.1.2
A Sample Study
232
15.2
Dynamic Tests
234
15.2.1
Early History
234
15.2.2
Implications of the Dynamic Models
236
15.2.3
Excess Volatility
237
Exercises
241
PART III PARADIGMS FOR PRICING
16
Static Arbitrage Pricing
245
16.1
Pricing Paradigms: Optimization versus Arbitrage
246
16.2
The Arbitrage Pricing Theory (APT)
248
16.3
Arbitraging Bonds
252
16.4
Pricing a Simple Derivative Asset
254
Exercises
257
17
Dynamic Arbitrage Pricing
261
17.1
Dynamic Replication
262
17.2
Modeling Prices of the Assets
263
17.3
The Fundamental Partial Differential Equation (PDE)
264
17.3.1
The Feynman-Kac Solution to the PDE
266
17.3.2
Working out the Expectation
269
17.4
Allowing Dividends and Time-Varying Rates
271
Exercises
272
18
Properties of Option Prices
275
18.1
Bounds on Prices of European Options
275
XII CONTENTS
18.2
Properties of Black-Scholes Prices
277
18.3
Delta Hedging
280
18.4
Does Black-Scholes Still Work?
282
18.5
American-Style Options
283
Exercises
285
Empirical Project
6 285
19
Martingale Pricing
289
19.1
Some Preparation
290
19.2
Fundamental Theorem of Asset Pricing
291
19.3
Implications for Pricing Derivatives
294
19.4
Applications
296
19.5
Martingale versus Equilibrium Pricing
298
19.6
Numeraires, Short Rates, and Equivalent Martingale Measures
300
19.7
Replication and Uniqueness of the EMM
302
Exercises
304
20
Modeling Volatility
307
20.1
Models with Price-Dependent Volatility
308
20.1.1
The Constant-Elasticity-of-Variance Model
308
20.1.2
The Hobson-Rogers Model
309
20.2
Autoregressive
Conditional Heteroskedasticity Models
310
20.3
Stochastic Volatility
312
20.4
Is Replication Possible?
313
Exercises
314
21
Discontinuous Price Processes
317
21.1
Merton s Jump-Diffusion Model
318
21.2
The Variance-Gamma Model
322
21.3
Stock Prices as Branching Processes
324
21.4
Is Replication Possible?
326
Exercises
327
22
Options on Jump Processes
329
22.1
Options under Jump-Diffusions
330
22.2
A Primer on Characteristic Functions
336
22.3
Using Fourier Methods to Price Options
339
22.4
Applications to Jump Models
341
Exercises
344
CONTENTS
ХІІІ
23
Options on Stochastic Volatility Processes
347
23.1
Independent Price/Volatility Shocks
348
23.2
Dependent Price/Volatility Shocks
350
23.3
Stochastic Volatility with Jumps in Price
354
23.4
Further Advances
356
Exercises
357
Empirical Project
7 358
Solutions to Exercises
363
References
391
Index
397
|
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| indexdate | 2024-07-09T21:31:30Z |
| institution | BVB |
| isbn | 9780470431993 |
| language | English |
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| spelling | Epps, T. W. 1943- Verfasser (DE-588)139388362 aut Quantitative finance its development, mathematical foundations, and current scope T. W. Epps Hoboken, NJ Wiley 2009 XVIII, 401 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell Finance Mathematical models Investments Mathematical models Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content 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=017137978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Epps, T. W. 1943- Quantitative finance its development, mathematical foundations, and current scope Mathematisches Modell Finance Mathematical models Investments Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4123623-3 |
| title | Quantitative finance its development, mathematical foundations, and current scope |
| title_auth | Quantitative finance its development, mathematical foundations, and current scope |
| title_exact_search | Quantitative finance its development, mathematical foundations, and current scope |
| title_full | Quantitative finance its development, mathematical foundations, and current scope T. W. Epps |
| title_fullStr | Quantitative finance its development, mathematical foundations, and current scope T. W. Epps |
| title_full_unstemmed | Quantitative finance its development, mathematical foundations, and current scope T. W. Epps |
| title_short | Quantitative finance |
| title_sort | quantitative finance its development mathematical foundations and current scope |
| title_sub | its development, mathematical foundations, and current scope |
| topic | Mathematisches Modell Finance Mathematical models Investments Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Mathematisches Modell Finance Mathematical models Investments Mathematical models Finanzmathematik Lehrbuch |
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