Stochastic finance: a numeraire approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2011
|
| Series: | Chapman & Hall/CRC financial mathematics series
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 313 - 322; Index |
| Physical Description: | XV, 326 S. graph. Darst. |
| ISBN: | 9781439812501 1439812500 |
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MARC
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| 245 | 1 | 0 | |a Stochastic finance |b a numeraire approach |c Jan Vecer |
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Record in the Search Index
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| adam_text | Contents
Introduction
ix
1 Elements
of Finance
1
1.1
Price
............................... 3
1.2
Arbitrage
............................. 11
1.3
Time Value of Assets, Arbitrage and No-Arbitrage Assets
. . 14
1.4
Money Market, Bonds, and Discounting
............ 17
1.5
Dividends
............................. 20
1.6
Portfolio
............................. 21
1.7
Evolution of a Self-Financing Portfolio
............ 23
1.8
Fundamental Theorems of Asset Pricing
............ 28
1.9
Change of Measure via
Radon-Nikodým
Derivative
..... 44
1.10
Leverage: Forwards and Futures
................ 48
2
Binomial Models
59
2.1
Binomial Model for No-Arbitrage Assets
........... 60
2.1.1
One-Step Model
..................... 61
2.1.2
Hedging in the Binomial Model
............. 65
2.1.3
Multiperiod Binomial Model
.............. 66
2.1.4
Numerical Example
................... 67
2.1.5
Probability Measures for Exotic No-Arbitrage Assets
. 73
2.2
Binomial Model with an Arbitrage Asset
........... 75
2.2.1
American Option Pricing in the Binomial Model
... 78
2.2.2
Hedging
.......................... 79
2.2.3
Numerical Example
................... 81
3
Diffusion Models
91
3.1
Geometric Brownian Motion
.................. 93
3.2
General European Contracts
.................. 99
3.3
Price as an Expectation
..................... 109
3.4
Connections with Partial Differential Equations
.......
Ill
3.5
Money as a Reference Asset
.................. 114
3.6
Hedging
.............................. 117
3.7
Properties of European Call and Put Options
........ 122
3.8
Stochastic Volatility Models
.................. 127
3.9
Foreign Exchange Market
.................... 130
3.9.1
Forwards
......................... 131
vi
Stochastic Finance: A Numeraire Approach
3.9.2
Options
.......................... 133
4
Interest Rate Contracts
137
4.1
Forward
LIBOR
......................... 138
4.1.1
Backset
LIBOR
...................... 139
4.1.2
Caplet
........................... 140
4.2
Swaps and Swaptions
...................... 141
4.3
Term Structure Models
..................... 143
5
Barrier Options
149
5.1
Types of Barrier Options
.................... 150
5.2
Barrier Option Pricing via Power Options
........... 152
5.2.1
Constant Barrier
..................... 152
5.2.2
Exponential Barrier
................... 157
5.3
Price of a Down-and-In Call Option
.............. 160
5.4
Connections with the Partial Differential Equations
..... 165
6
Lookback
Options
171
6.1
Connections of
Lookbacks
with Barrier Options
....... 171
6.1.1
Case
α
= 1........................ 173
6.1.2
Case a
< 1........................ 174
6.1.3
Hedging
.......................... 178
6.2
Partial Differential Equation Approach for
Lookbacks
.... 180
6.3
Maximum Drawdown
...................... 187
7
American Options
191
7.1
American Options on No-Arbitrage Assets
.......... 192
7.2
American Call and Puts on Arbitrage Assets
......... 194
7.3
Perpetual American Put
.................... 195
7.4
Partial Differential Equation Approach
............ 199
8
Contracts on Three or More Assets:
Quantos,
Rainbows
and Friends
207
8.1
Pricing in the Geometric Brownian Motion Model
...... 209
8.2
Hedging
.............................. 213
9
Asian Options
219
9.1
Pricing in the Geometric Brownian Motion Model
...... 226
9.2
Hedging of Asian Options
.................... 230
9.3
Reduction of the Pricing Equations
.............. 233
10
Jump Models
239
10.1
Poisson
Process
......................... 240
10.2
Geometric
Poisson
Process
................... 243
10.3
Pricing Equations
........................ 248
10.4
European Call Option in Geometric
Poisson
Model
..... 251
Contents
vii
10.5
Levy Models with Multiple Jump Sizes
............ 256
A Elements of Probability Theory
267
A.I Probability, Random Variables
................. 267
A.
2
Conditional Expectation
.................... 271
A.
2.1
Some Properties of Conditional Expectation
...... 274
A.3 Martingales
............................ 274
A.4 Brownian Motion
........................ 279
A.
5
Stochastic Integration
...................... 283
A.6 Stochastic Calculus
....................... 285
A.
7
Connections with Partial Differential Equations
....... 287
Solutions to Selected Exercises
293
References
313
Index
323
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV036569392 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:43:05Z |
| institution | BVB |
| isbn | 9781439812501 1439812500 |
| language | English |
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| physical | XV, 326 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
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| series2 | Chapman & Hall/CRC financial mathematics series A Chapman & Hall book |
| spelling | Večeř, Jan Verfasser (DE-588)170065774 aut Stochastic finance a numeraire approach Jan Vecer Boca Raton, Fla. [u.a.] CRC Press 2011 XV, 326 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series A Chapman & Hall book Literaturverz. S. 313 - 322; Index Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Geldmarkt (DE-588)4019899-6 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 s Geldmarkt (DE-588)4019899-6 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=020490551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Večeř, Jan Stochastic finance a numeraire approach Finanzmathematik (DE-588)4017195-4 gnd Geldmarkt (DE-588)4019899-6 gnd Kreditmarkt (DE-588)4073788-3 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4019899-6 (DE-588)4073788-3 |
| title | Stochastic finance a numeraire approach |
| title_auth | Stochastic finance a numeraire approach |
| title_exact_search | Stochastic finance a numeraire approach |
| title_full | Stochastic finance a numeraire approach Jan Vecer |
| title_fullStr | Stochastic finance a numeraire approach Jan Vecer |
| title_full_unstemmed | Stochastic finance a numeraire approach Jan Vecer |
| title_short | Stochastic finance |
| title_sort | stochastic finance a numeraire approach |
| title_sub | a numeraire approach |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Geldmarkt (DE-588)4019899-6 gnd Kreditmarkt (DE-588)4073788-3 gnd |
| topic_facet | Finanzmathematik Geldmarkt Kreditmarkt |
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