Stochastic implied volatility: a factor-based model
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
2004
|
| Series: | Lecture notes in economics and mathematical systems
545 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 229 S. graph. Darst. |
| ISBN: | 3540221832 |
Staff View
MARC
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| 100 | 1 | |a Hafner, Reinhold |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic implied volatility |b a factor-based model |c Reinhold Hafner |
| 264 | 1 | |a Berlin u.a. |b Springer |c 2004 | |
| 300 | |a XI, 229 S. |b graph. Darst. | ||
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| 490 | 1 | |a Lecture notes in economics and mathematical systems |v 545 | |
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| 650 | 7 | |a Econometrische analyse |2 gtt | |
| 650 | 7 | |a Martingalen |2 gtt | |
| 650 | 7 | |a Portfolio-theorie |2 gtt | |
| 650 | 7 | |a Stochastische modellen |2 gtt | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 Motivation and Objectives 1
1.2 Structure of the Work 5
2 Continuous time Financial Markets 9
2.1 The Financial Market 10
2.1.1 Assets and Trading Strategies 10
2.1.2 Absence of Arbitrage and Martingale Measures 13
2.2 Risk Neutral Pricing of Contingent Claims 15
2.2.1 Contingent Claims 15
2.2.2 Risk Neutral Valuation Formula 18
2.2.3 Attainability and Market Completeness 20
3 Implied Volatility 23
3.1 The Black Scholes Model 24
3.1.1 The Financial Market Model 24
3.1.2 Pricing and Hedging of Contingent Claims 25
3.1.3 The Black Scholes Option Pricing Formula 27
3.1.4 The Greeks 29
3.2 The Concept of Implied Volatility 32
3.2.1 Definition 32
3.2.2 Calculation 34
3.2.3 Interpretation 35
3.3 Features of Implied Volatility 38
3.3.1 Volatility Smiles 38
3.3.2 Volatility Term Structures 39
3.3.3 Volatility Surfaces 41
3.4 Modelling Implied Volatility 43
3.4.1 Overview 43
3.4.2 Implied Volatility as an Endogenous Variable 45
3.4.3 Implied Volatility as an Exogenous Variable 51
X Contents
3.4.4 Comparison of Approaches 56
4 The General Stochastic Implied Volatility Model 59
4.1 The Financial Market Model 60
4.1.1 Model Specification 60
4.1.2 Movements of the Volatility Surface 61
4.2 Risk Neutral Implied Volatility Dynamics 63
4.2.1 Change of Measure and Drift Restriction 63
4.2.2 Interpretation of Terms in the Risk Neutral Drift 68
4.2.3 Existence and Uniqueness of the Risk Neutral Measure. 68
4.3 Pricing and Hedging of Contingent Claims 70
5 Properties of DAX Implied Volatilities 73
5.1 The DAX Option 73
5.1.1 Contract Specifications 73
5.1.2 Previous Studies 75
5.2 Data 76
5.2.1 Raw Data and Data Preparation 76
5.2.2 Correcting for Taxes and Dividends 78
5.2.3 Liquidity Aspects 82
5.3 Structure of DAX Implied Volatilities 83
5.3.1 Estimation of the DAX Volatility Surface 83
5.3.2 Empirical Results 92
5.3.3 Identification and Selection of Volatility Risk Factors .. 99
5.4 Dynamics of DAX Implied Volatilities 102
5.4.1 Time Series Properties of DAX Volatility Risk Factors . 102
5.4.2 Relating Volatility Risk Factors to Index Returns and
other Market Variables 109
5.5 Summary of Empirical Observations 113
6 A Four Eactor Model for DAX Implied Volatilities 115
6.1 The Model under the Objective Measure 115
6.1.1 Model Specification 115
6.1.2 Model Estimation 118
6.1.3 Model Testing 124
6.2 The Model under the Risk Neutral Measure 131
6.2.1 Risk Neutral Stock Price and Volatility Dynamics 131
6.2.2 The Market Price of Risk Process 133
6.2.3 Pricing and Hedging of Contingent Claims 137
6.2.4 Model Calibration 140
6.3 Model Review and Conclusion 144
Contents XI
7 Model Applications 145
7.1 Pricing and Hedging of Exotic Derivatives 145
7.1.1 Product Overview 145
7.1.2 Exotic Equity Index Derivatives 147
7.1.3 Volatility Derivatives 153
7.2 Value at Risk for Option Portfolios 158
7.2.1 The Value at Risk Concept 158
7.2.2 Computing VaR for Option Portfolios 160
7.2.3 A Case Study 162
7.2.4 Beyond VaR: Expected Shortfall 167
7.3 Volatility Trading 170
7.3.1 Definition and Motivation 170
7.3.2 Volatility Trade Design 171
7.3.3 Profitability of DAX Volatility Trading Strategies 178
8 Summary and Conclusion 187
A Some Mathematical Preliminaries 193
A.I Probability Theory 193
A.2 Continuous time Stochastic Processes 194
B Pricing of a Variance Swap via Static Replication 201
List of Abbreviations 205
List of Symbols 207
References 215
Index 225
|
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| spelling | Hafner, Reinhold Verfasser aut Stochastic implied volatility a factor-based model Reinhold Hafner Berlin u.a. Springer 2004 XI, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 545 Zugl.: Augsburg, Univ., Diss., 2004 u.d.T.: Hafner, Reinhold: A factor-based stochastic implied volatility model Beweeglijkheid gtt Econometrische analyse gtt Martingalen gtt Portfolio-theorie gtt Stochastische modellen gtt Stochastic processes Optionspreis (DE-588)4115453-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf DAX-Futures (DE-588)4266833-5 gnd rswk-swf Volatilität (DE-588)4268390-7 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Derivat Wertpapier (DE-588)4381572-8 s Optionspreis (DE-588)4115453-8 s Volatilität (DE-588)4268390-7 s DAX-Futures (DE-588)4266833-5 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Lecture notes in economics and mathematical systems 545 (DE-604)BV000000036 545 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012819518&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hafner, Reinhold Stochastic implied volatility a factor-based model Lecture notes in economics and mathematical systems Beweeglijkheid gtt Econometrische analyse gtt Martingalen gtt Portfolio-theorie gtt Stochastische modellen gtt Stochastic processes Optionspreis (DE-588)4115453-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd DAX-Futures (DE-588)4266833-5 gnd Volatilität (DE-588)4268390-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4115453-8 (DE-588)4381572-8 (DE-588)4266833-5 (DE-588)4268390-7 (DE-588)4057633-4 (DE-588)4113937-9 |
| title | Stochastic implied volatility a factor-based model |
| title_auth | Stochastic implied volatility a factor-based model |
| title_exact_search | Stochastic implied volatility a factor-based model |
| title_full | Stochastic implied volatility a factor-based model Reinhold Hafner |
| title_fullStr | Stochastic implied volatility a factor-based model Reinhold Hafner |
| title_full_unstemmed | Stochastic implied volatility a factor-based model Reinhold Hafner |
| title_short | Stochastic implied volatility |
| title_sort | stochastic implied volatility a factor based model |
| title_sub | a factor-based model |
| topic | Beweeglijkheid gtt Econometrische analyse gtt Martingalen gtt Portfolio-theorie gtt Stochastische modellen gtt Stochastic processes Optionspreis (DE-588)4115453-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd DAX-Futures (DE-588)4266833-5 gnd Volatilität (DE-588)4268390-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Beweeglijkheid Econometrische analyse Martingalen Portfolio-theorie Stochastische modellen Stochastic processes Optionspreis Derivat Wertpapier DAX-Futures Volatilität Stochastisches Modell Hochschulschrift |
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