Option valuation under stochastic volatility: with Mathematica code
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Newport Beach, Calif.
Finance Press
2000
|
| Series: | Finance, mathematics, business and economics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 350 S. graph. Darst. |
| ISBN: | 0967637201 |
Staff View
MARC
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| 245 | 1 | 0 | |a Option valuation under stochastic volatility |b with Mathematica code |c Alan L. Lewis |
| 264 | 1 | |a Newport Beach, Calif. |b Finance Press |c 2000 | |
| 300 | |a VII, 350 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Finance, mathematics, business and economics | |
| 650 | 4 | |a Options (Finances) - Prix - Modèles mathématiques | |
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| 650 | 4 | |a Mathematisches Modell | |
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Record in the Search Index
| _version_ | 1817681127489404928 |
|---|---|
| adam_text |
Contents
Preface
.
vi
Historical Volatility of the S&P
500
Index
. viii
1.
Introduction and Summary of Results
. 1
Summary of Results
. 3
The Hedging Argument of Black and Scholes
. 11
The Drift Cancellation and Option Sensitivities
. 14
The Hedging Argument under Stochastic Volatility
. 15
The Martingale Approach
. 21
App. 1.1
Parameter Estimators for the GARCH Diffusion Model
. 28
App. 1.2
Solutions to PDEs
. 31
2.
The Fundamental Transform
. 34
Assumptions
. 34
The Transform-based Solution
. 36
Some Models with Closed-form Solutions
. 52
Analytic Characteristic Functions
. 55
A Bond Price Analogy and Option Price Bound
. 59
App. 2.1
Recovery of the Black and Scholes Solution
. 64
App. 2.2
Mathematica Code
for Chapter
2. 67
App. 2.3
General Properties of Option Prices
. 71
3.
The Volatility of Volatility Series Expansion
. 76
Assumptions
. 76
General Steps in the
ξ
—
expansion
. 77
The Two Series for a Parameterized Model
. 83
App. 3.1
Details of the Volatility of Volatility Expansion
. 87
4.
Mixing Solutions and Applications
. 96
The Basic Mixing Solution
. 97
Connection between Mixing Densities and the Fundamental Transform
101
A Monte Carlo Application
. 104
Arbitrary Payoff Functions
. 109
A More General Model without Correlation
. 110
IV
5.
The Smile
. 120
Introduction and Summary of Results
. 121
The Symmetric Case
. 128
The Correlated Case
. 137
Deducing the Risk-adjusted Volatility Process from Option Prices
. 145
App. 5.1
Calculating Volatility Moments
. 149
App. 5.2
Working with Differential Operators in
Mathematica
. 158
App. 5.3
Additional
Mathematica
Code for Chapter
5. 160
App. 5.4
Calculating with the Mixing Theorem
. 169
6.
The Term Structure of Implied Volatility
. 176
Deterministic Volatility
. 177
Deterministic Volatility II: a Transform Perspective
. 180
Stochastic Volatility
—
The Eigenvalue Connection
. 182
Example I: The Square Root Model
. 187
Example II: The
3/2
Model
. 190
Example III: The GARCH Diffusion Model
. 191
A Variational Principle Method
. 197
A Differential Equation (Dsolve) Method
. 206
App. 6.1
Mathematica
Code for Chapter
6. 213
7.
Utility-based Equilibrium Models
. 220
A Representative Agent Economy
. 221
Examples
. 232
The Pure Investment Problem with a Distant Planning Horizon
. 237
Preference Adjustments to the Volatility of Volatility Series Expansion
240
The Effect of Risk Attitudes on Option Prices
. 245
8.
Duality and Changes of Numeraire
. 248
Put-Call Duality
. 249
Introduction to the Change of Numeraire
. 253
Mathematics of the Change of Numeraire
. 255
Implications for the Term Structure
. 258
9.
Volatility Explosions and the
Failure of the Martingale Pricing Formula
. 260
Introduction
. 261
The Feller Boundary Classifications
. 262
Volatility Explosions I
. 270
Volatility Explosions II. Failure of the Martingale Pricing Formula
. 279
When Martingale Pricing Fails: Generalized Pricing Formulas
. 284
Generalized Pricing Formulas and the Transform-based Solutions
. 288
Generalized Pricing Formulas. Example I: the
3/2
Model
. 297
Generalized Pricing Formulas. Example II: the CEV Model
. 305
10.
Option Prices at Large Volatility
. 314
Introduction
. 314
Asymptotica for the Fundamental Transform
. 316
11.
Solutions to Models
. 330
The Square Root Model
. 330
The
3/2
Model
. 331
Geometric Brownian Motion
. 334
References
. 339
Index
. 345
Frequent Notations and Abbreviations
. 348
About the Author
. 350 |
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| id | DE-604.BV014336605 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:25Z |
| institution | BVB |
| isbn | 0967637201 |
| language | English |
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| physical | VII, 350 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Finance Press |
| record_format | marc |
| series2 | Finance, mathematics, business and economics |
| spelling | Lewis, Alan L. Verfasser aut Option valuation under stochastic volatility with Mathematica code Alan L. Lewis Newport Beach, Calif. Finance Press 2000 VII, 350 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finance, mathematics, business and economics Options (Finances) - Prix - Modèles mathématiques Opções financeiras (modelos matemáticos) larpcal Mathematisches Modell Options (Finance) Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 s Statistisches Modell (DE-588)4121722-6 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009834989&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lewis, Alan L. Option valuation under stochastic volatility with Mathematica code Options (Finances) - Prix - Modèles mathématiques Opções financeiras (modelos matemáticos) larpcal Mathematisches Modell Options (Finance) Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| subject_GND | (DE-588)4135346-8 (DE-588)4121722-6 |
| title | Option valuation under stochastic volatility with Mathematica code |
| title_auth | Option valuation under stochastic volatility with Mathematica code |
| title_exact_search | Option valuation under stochastic volatility with Mathematica code |
| title_full | Option valuation under stochastic volatility with Mathematica code Alan L. Lewis |
| title_fullStr | Option valuation under stochastic volatility with Mathematica code Alan L. Lewis |
| title_full_unstemmed | Option valuation under stochastic volatility with Mathematica code Alan L. Lewis |
| title_short | Option valuation under stochastic volatility |
| title_sort | option valuation under stochastic volatility with mathematica code |
| title_sub | with Mathematica code |
| topic | Options (Finances) - Prix - Modèles mathématiques Opções financeiras (modelos matemáticos) larpcal Mathematisches Modell Options (Finance) Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| topic_facet | Options (Finances) - Prix - Modèles mathématiques Opções financeiras (modelos matemáticos) Mathematisches Modell Options (Finance) Prices Mathematical models Optionspreistheorie Statistisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009834989&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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