An introduction to financial option valuation: mathematics, stochastics and computation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ., reprint. with corr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 267 - 270 |
| Beschreibung: | XXI, 273 S. graph. Darst. |
| ISBN: | 0521838843 9780521838849 0521547571 9780521547574 |
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| 100 | 1 | |a Higham, Desmond J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to financial option valuation |b mathematics, stochastics and computation |c Desmond J. Higham |
| 250 | |a 1. publ., reprint. with corr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XXI, 273 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804138919088881664 |
|---|---|
| adam_text | Contents
List of illustrations poge
xiii
Preface
xvii
1
Options
1
1.1
What are options?
1
1.2
Why do we study options?
2
1.3
How are options traded?
4
1.4
Typical option prices
6
1.5
Other financial derivatives
7
1.6
Notes and references
7
1.7
Program of Chapter
1
and walkthrough
8
2
Option valuation preliminaries
11
2.1
Motivation
11
2.2
Interest rates
11
2.3
Short selling
12
2.4
Arbitrage
13
2.5
Put-call parity
13
2.6
Upper and lower bounds on option values
14
2.7
Notes and references
16
2.8
Program of Chapter
2
and walkthrough
17
3
Random variables
21
3.1
Motivation
21
3.2
Random variables, probability and mean
21
3.3
Independence
23
3.4
Variance
24
3.5
Normal distribution
25
3.6
Central Limit Theorem
27
3.7
Notes and references
28
3.8
Program of Chapter
3
and walkthrough
29
vu
viii Contents
4
Computer
Simulation 33
4.1 Motivation 33
4.2
Pseudo-random numbers
33
4.3
Statistical tests
34
4.4
Notes and references
40
4.5
Program of Chapter
4
and walkthrough
41
5
Asset price movement
45
5.1
Motivation
45
5.2
Efficient market hypothesis
45
5.3
Asset price data
46
5.4
Assumptions
48
5.5
Notes and references
49
5.6
Program of Chapter
5
and walkthrough
50
6
Asset price model: Part I
53
6.1
Motivation
53
6.2
Discrete asset model
53
6.3
Continuous asset model
55
6.4 Lognormal
distribution
56
6.5
Features of the asset model
57
6.6
Notes and references
59
6.7
Program of Chapter
6
and walkthrough
60
7
Asset price model: Part II
63
7.1
Computing asset paths
63
7.2
Timescale
invariance
66
7.3
Sum-of-square returns
68
7.4
Notes and references
69
7.5
Program of Chapter
7
and walkthrough
71
8
Black-Scholes PDE and formulas
73
8.1
Motivation
73
8.2
Sum-of-square increments for asset price
74
8.3
Hedging
76
8.4
Black-Scholes PDE
78
8.5
Black-Scholes formulas
80
8.6
Notes and references
82
8.7
Program of Chapter
8
and walkthrough
83
9
More
:
on hedging
9.1
Motivation
9.2
Discrete hedging
9.3
Delta at expiry
9.4
Large-scale test
9.5
Long-Term Capital Management
9.6
Notes
9.7
Program of Chapter
9
and walkthrough
10
The Greeks
10.1
Motivation
10.2
The Greeks
10.3
Interpreting the Greeks
10.4
Black-Scholes PDE solution
10.5
Notes and references
10.6
Program of Chapter
10
and walkthrough
Contents
ix
87
87
87
89
92
93
94
96
99
99
99
101
101
102
104
11
More on the Black-Scholes formulas
105
11.1
Motivation
105
105
106
106
108
111
111
115
115
115
116
118
120
123
123
123
123
124
127
11.2
Where is
μ?
11.3
Time dependency
11.4
The big picture
11.5
Change of variables
11.6
Notes and references
11.7
Program of Chapter
11
and walkthrough
12
Risk
neutrality
12.1
Motivation
12.2
Expected payoff
12.3
Risk neutrality
12.4
Notes and references
12.5
Program of Chapter
12
and walkthrough
13
Solving a nonlinear equation
13.1
Motivation
13.2
General problem
13.3
Bisection
13.4
Newton
13.5
Further practical issues
x
Contents
13.6
Notes and references
127
13.7
Program of Chapter
13
and walkthrough
128
14
Implied volatility
131
14.1
Motivation
131
14.2
Implied volatility
131
14.3
Option value as a function of volatility
131
14.4
Bisection and Newton
133
14.5
Implied volatility with real data
135
14.6
Notes and references
137
14.7
Program of Chapter
14
and walkthrough
137
15
Monte Carlo method
141
15.1
Motivation
141
15.2
Montecarlo
141
15.3
Monte Carlo for option valuation
144
15.4
Monte Carlo for Greeks
145
15.5
Notes and references
148
15.6
Program of Chapter
15
and walkthrough
149
16
Binomial method
151
16.1
Motivation
151
16.2
Method
151
16.3
Deriving the parameters
153
16.4
Binomial method in practice
154
16.5
Notes and references
156
16.6
Program of Chapter
16
and walkthrough
159
17
Cash-or-nothing options
163
17.1
Motivation
163
17.2
Cash-or-nothing options
163
17.3
Black-Scholes for cash-or-nothing options
164
17.4
Delta behaviour
166
17.5
Risk neutrality for cash-or-nothing options
167
17.6
Notes and references
168
17.7
Program of Chapter
17
and walkthrough
170
18
American options
173
18.1
Motivation
173
18.2
American call and put
173
Contents xi
18.3 Black-Scholes
for
American
options
174
18.4
Binomial method for an
American
put
176
18.5
Optimal exercise boundary
177
18.6
Monte Carlo for an American put
180
18.7
Notes and references
182
18.8
Program of Chapter
18
and walkthrough
183
19
Exotic options
187
19.1
Motivation
187
19.2
Barrier options
187
19.3
Lookback
options
191
19.4
Asian options
192
19.5
Bermudán
and shout options
193
19.6
Monte Carlo and binomial for exotics
194
19.7
Notes and references
196
19.8
Program of Chapter
19
and walkthrough
199
20
Historical volatility
203
20.1
Motivation
203
20.2
Monte Carlo-type estimates
203
20.3
Accuracy of the sample variance estimate
204
20.4
Maximum likelihood estimate
206
20.5
Other volatility estimates
207
20.6
Example with real data
208
20.7
Notes and references
209
20.8
Program of Chapter
20
and walkthrough
210
21
Monte Carlo Part II: variance reduction by
antithetic
variâtes
215
21.1
Motivation
215
21.2
The big picture
215
21.3
Dependence
216
21.4
Antithetic
variâtes:
uniform example
217
21.5
Analysis of the uniform case
219
21.6
Normal case
221
21.7
Multivariate case
222
21.8
Antithetic
variâtes
in option valuation
222
21.9
Notes and references
225
21.10
Program of Chapter
21
and walkthrough
225
xii Contents
22 Monte Carlo
Part III: variance reduction by control
variâtes
229
22.1
Motivation
229
22.2
Control
variâtes
229
22.3
Control
variâtes
in option valuation
231
22.4
Notes and references
232
22.5
Program of Chapter
22
and walkthrough
234
23
Finite difference methods
237
23.1
Motivation
237
23.2
Finite difference operators
237
23.3
Heat equation
238
23.4
Discretization
239
23.5
FTCS and BTCS
240
23.6
Local accuracy
246
23.7 Von
Neumann stability and convergence
247
23.8
Crank-Nicolson
249
23.9
Notes and references
251
23.10
Program of Chapter
23
and walkthrough
252
24
Finite difference methods for the Black-Scholes PDE
257
24.1
Motivation
257
24.2
FTCS, BTCS and Crank-Nicolson for Black-Scholes
257
24.3
Down-and-out call example
260
24.4
Binomial method as finite differences
261
24.5
Notes and references
262
24.6
Program of Chapter
24
and walkthrough
265
References
267
Index
271
|
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| indexdate | 2024-07-09T21:35:50Z |
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| spelling | Higham, Desmond J. Verfasser aut An introduction to financial option valuation mathematics, stochastics and computation Desmond J. Higham 1. publ., reprint. with corr. Cambridge [u.a.] Cambridge Univ. Press 2008 XXI, 273 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 267 - 270 Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Optionsgeschäft (DE-588)4043670-6 gnd rswk-swf Optionsgeschäft (DE-588)4043670-6 s Bewertung (DE-588)4006340-9 s Mathematische Methode (DE-588)4155620-3 s DE-604 Optionspreistheorie (DE-588)4135346-8 s Capital-Asset-Pricing-Modell (DE-588)4121078-5 s Black-Scholes-Modell (DE-588)4206283-4 s Monte-Carlo-Simulation (DE-588)4240945-7 s MATLAB (DE-588)4329066-8 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017383062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Higham, Desmond J. An introduction to financial option valuation mathematics, stochastics and computation Monte-Carlo-Simulation (DE-588)4240945-7 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd Mathematische Methode (DE-588)4155620-3 gnd Bewertung (DE-588)4006340-9 gnd Optionspreistheorie (DE-588)4135346-8 gnd MATLAB (DE-588)4329066-8 gnd Optionsgeschäft (DE-588)4043670-6 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4206283-4 (DE-588)4121078-5 (DE-588)4155620-3 (DE-588)4006340-9 (DE-588)4135346-8 (DE-588)4329066-8 (DE-588)4043670-6 |
| title | An introduction to financial option valuation mathematics, stochastics and computation |
| title_auth | An introduction to financial option valuation mathematics, stochastics and computation |
| title_exact_search | An introduction to financial option valuation mathematics, stochastics and computation |
| title_full | An introduction to financial option valuation mathematics, stochastics and computation Desmond J. Higham |
| title_fullStr | An introduction to financial option valuation mathematics, stochastics and computation Desmond J. Higham |
| title_full_unstemmed | An introduction to financial option valuation mathematics, stochastics and computation Desmond J. Higham |
| title_short | An introduction to financial option valuation |
| title_sort | an introduction to financial option valuation mathematics stochastics and computation |
| title_sub | mathematics, stochastics and computation |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Capital-Asset-Pricing-Modell (DE-588)4121078-5 gnd Mathematische Methode (DE-588)4155620-3 gnd Bewertung (DE-588)4006340-9 gnd Optionspreistheorie (DE-588)4135346-8 gnd MATLAB (DE-588)4329066-8 gnd Optionsgeschäft (DE-588)4043670-6 gnd |
| topic_facet | Monte-Carlo-Simulation Black-Scholes-Modell Capital-Asset-Pricing-Modell Mathematische Methode Bewertung Optionspreistheorie MATLAB Optionsgeschäft |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017383062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT highamdesmondj anintroductiontofinancialoptionvaluationmathematicsstochasticsandcomputation |