Financial derivatives: pricing, applications, and mathematics
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. paperback ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 338 S. graph. Darst. |
| ISBN: | 9780521066792 9780521815109 |
Staff View
MARC
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| 100 | 1 | |a Baz, Jamil |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Financial derivatives |b pricing, applications, and mathematics |c Jamil Baz ; George Chacko |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XI, 338 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Derivative securities | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018765483 | ||
Record in the Search Index
| _version_ | 1804140891157299200 |
|---|---|
| adam_text | Contents
Acknowledgments page
xi
Introduction
1
1
Preliminary Mathematics
5
1.1
Random Walk
5
1.2
Another Take on Volatility and Time
8
1.3
A First Glance at
Itô s
Lemma
9
1.4
Continuous Time: Brownian Motion; More
on
Itô s
Lemma
11
1.5
Two-Dimensional Brownian Motion
14
1.6
Bivariate
Itô s
Lemma
15
1.7
Three Paradoxes of Finance
16
1.7.1
Paradox
1:
Siegel s Paradox
16
1.7.2
Paradox
2:
The Stock, Free-Lunch Paradox
18
1.7.3
Paradox
3:
The Skill Versus Luck Paradox
19
2
Principles of Financial Valuation
22
2.1
Uncertainty, Utility Theory, and Risk
22
2.2
Risk and the Equilibrium Pricing of Securities
28
2.3
The Binomial Option-Pricing Model
41
2.4
Limiting Option-Pricing Formula
46
2.5
Continuous-Time Models
47
2.5.1
The Black-Scholes/Merton Model
-
Pricing
Kernel Approach
48
2.5.2
The Black-Scholes/Merton Model
-
Probabilistic Approach
57
2.5.3
The Black-Scholes/Merton Model
-
Hedging
Approach
61
VH
viii Contents
2.6
Exotic
Options
63
2.6.1
Digital Options
64
2.6.2
Power Options
65
2.6.3
Asian
Options
67
2.6.4
Barrier
Options
71
3
Interest
Rate Models
78
3.1
Interest Rate Derivatives: Not So
Simple
78
3.2
Bonds
and Yields
80
3.2.1
Prices and Yields to Maturity
80
3.2.2
Discount Factors, Zero-Coupon Rates, and
Coupon Bias
82
3.2.3
Forward Rates
85
3.3
Naive Models of Interest Rate Risk
88
3.3.1
Duration
88
3.3.2
Convexity
99
3.3.3
The Free Lunch in the Duration Model
104
3.4
An Overview of Interest Rate Derivatives
108
3.4.1
Bonds with Embedded Options
109
3.4.2
Forward Rate Agreements
110
3.4.3 Eurostrip
Futures
112
3.4.4
The Convexity Adjustment
113
3.4.5
Swaps
118
3.4.6
Caps and Floors
120
3.4.7
Swaptions
121
3.5
Yield Curve Swaps
122
3.5.1
The CMS Swap
122
3.5.2
The
Quanto
Swap
127
3.6
Factor Models
131
3.6.1
A General Single-Factor Model
131
3.6.2
The Merton Model
135
3.6.3
The Vasicek Model
139
3.6.4
The Cox-Ingersoll-Ross Model
142
3.6.5
Risk-Neutral Valuation
144
3.7
Term-Structure-Consistent Models
147
3.7.1
Equilibrium Versus Fitting
147
3.7.2
The
Но
-Lee
Model
153
3.7.3
The
Но
-Lee
Model with Time-Varying
Volatility
157
3.7.4
The Black-Derman-Toy Model
162
3.8
Risky Bonds and Their Derivatives
166
3.8.1
The Merton Model
167
3.8.2
The Jarrow-Turnbull Model
168
Contents ix
3.9
The Heath, Jarrow, and Morton Approach
172
3.10
Interest Rates as Options
180
4
Mathematics of Asset Pricing
184
4.1
Random Walks
184
4.1.1
Description
184
4.1.2
Gambling Recreations
186
4.2
Arithmetic Brownian Motion
192
4.2.1
Arithmetic Brownian Motion as a Limit of a
Simple Random Walk
192
4.2.2
Moments of an Arithmetic Brownian Motion
196
4.2.3
Why Sample Paths Are Not Differentiable
198
4.2.4
Why Sample Paths Are Continuous
198
4.2.5
Extreme Values and Hitting Times
199
4.2.6
The Arcsine Law Revisited
203
4.3
Geometric Brownian Motion
204
4.3.1
Description
204
4.3.2
Moments of a Geometric Brownian
Motion
207
4.4
Ito
Calculus
209
4.4.1
Riemann-Stieljes, Stratonovitch, and
Ito
Integrals
209
4.4.2
Itô s
Lemma
214
4.4.3
Multidimensional
Itô s
Lemma
222
4.5
Mean-Reverting Processes
225
4.5.1
Introduction
225
4.5.2
The Ornstein-Uhlenbeck Process
225
4.5.3
Calculations of Moments with the Dynkin
Operator
226
4.5.4
The Square-Root Process
228
4.6
Jump Process
229
4.6.1
Pure Jumps
229
4.6.2
Time Between Two Jumps
231
4.6.3
Jump Diffusions
232
4.6.4
Itô s
Lemma for Jump Diffusions
233
4.7
Kolmogorov Equations
234
4.7.1
The Kolmogorov Forward Equation
234
4.7.2
The Dirac Delta Function
236
4.7.3
The Kolmogorov Backward Equation
236
4.8
Martingales
239
4.8.1
Definitions and Examples
239
4.8.2
Some Useful Facts About Martingales
241
4.8.3
Martingales and Brownian Motion
242
χ
Contents
4.9 Dynamic Programming 245
4.9.1
The Traveling Salesman
245
4.9.2 Optimal
Control of
Ito
Processes:
Finite
Horizon
247
4.9.3
Optimal Control of
Ito
Processes:
Infinite Horizon
248
4.10
Partial Differential Equations
253
4.10.1
The Kolmogorov Forward Equation Revisited
253
4.10.2
Risk-Neutral Pricing Equation
256
4.10.3
The Laplace Transform
257
4.10.4
Resolution of the Kolmogorov Forward
Equation
262
4.10.5
Resolution of the Risk-Neutral Pricing
Equation
265
Bibliography
269
Index
327
|
| any_adam_object | 1 |
| author | Baz, Jamil |
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| author_facet | Baz, Jamil |
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| bvnumber | BV035908166 |
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.632 |
| dewey-search | 332.632 |
| dewey-sort | 3332.632 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV035908166 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:07:11Z |
| institution | BVB |
| isbn | 9780521066792 9780521815109 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018765483 |
| oclc_num | 502257603 |
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| owner_facet | DE-355 DE-BY-UBR |
| physical | XI, 338 S. graph. Darst. |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Baz, Jamil Verfasser aut Financial derivatives pricing, applications, and mathematics Jamil Baz ; George Chacko 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2009 XI, 338 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Derivative securities Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s b DE-604 Chacko, George 1967- Sonstige (DE-588)124785514 oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018765483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baz, Jamil Financial derivatives pricing, applications, and mathematics Derivative securities Derivat Wertpapier (DE-588)4381572-8 gnd |
| subject_GND | (DE-588)4381572-8 |
| title | Financial derivatives pricing, applications, and mathematics |
| title_auth | Financial derivatives pricing, applications, and mathematics |
| title_exact_search | Financial derivatives pricing, applications, and mathematics |
| title_full | Financial derivatives pricing, applications, and mathematics Jamil Baz ; George Chacko |
| title_fullStr | Financial derivatives pricing, applications, and mathematics Jamil Baz ; George Chacko |
| title_full_unstemmed | Financial derivatives pricing, applications, and mathematics Jamil Baz ; George Chacko |
| title_short | Financial derivatives |
| title_sort | financial derivatives pricing applications and mathematics |
| title_sub | pricing, applications, and mathematics |
| topic | Derivative securities Derivat Wertpapier (DE-588)4381572-8 gnd |
| topic_facet | Derivative securities Derivat Wertpapier |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018765483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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