Stochastic Implied Volatility
A Factor-Based Model
(Sprache: Englisch)
PThis book presents a factor-based model of the stochastic evolution of the implied volatility surface. The model allows for the integrated and consistent pricing and hedging, risk management, and trading of equity index derivatives as well as volatility...
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PThis book presents a factor-based model of the stochastic evolution of the implied volatility surface. The model allows for the integrated and consistent pricing and hedging, risk management, and trading of equity index derivatives as well as volatility derivatives. In the first part, the book develops a unifying theory for the analysis of contingent claims under both the real-world measure and the risk-neutral measure in an environment of stochastic implied volatility. On the basis of transaction data, the second part of the book provides extensive statistical analyses on the dynamics of the implied volatility surface of German DAX options and proposes a four-factor model to describe its evolution. The model is validated and tested on market data. The final part deals with potential applications of the model in the fields of exotic option pricing, value at risk, and volatility trading. /P
Klappentext zu „Stochastic Implied Volatility “
This book presents a factor-based model of the stochastic evolution of the implied volatility surface. The model allows for the integrated and consistent pricing and hedging, risk management, and trading of equity index derivatives as well as volatility derivatives. In the first part, the book develops a unifying theory for the analysis of contingent claims under both the real-world measure and the risk-neutral measure in an environment of stochastic implied volatility. On the basis of transaction data, the second part of the book provides extensive statistical analyses on the dynamics of the implied volatility surface of German DAX options and proposes a four-factor model to describe its evolution. The model is validated and tested on market data. The final part deals with potential applications of the model in the fields of exotic option pricing, value at risk, and volatility trading.
Inhaltsverzeichnis zu „Stochastic Implied Volatility “
1 Introduction.- 1.1 Motivation and Objectives.- 1.2 Structure of the Work.- 2 Continuous-time Financial Markets.- 2.1 The Financial Market.- 2.1.1 Assets and Trading Strategies.- 2.1.2 Absence of Arbitrage and Martingale Measures.- 2.2 Risk-Neutral Pricing of Contingent Claims.- 2.2.1 Contingent Claims.- 2.2.2 Risk-Neutral Valuation Formula.- 2.2.3 Attainability and Market Completeness.- 3 Implied Volatility.- 3.1 The Black-Scholes Model.- 3.1.1 The Financial Market Model.- 3.1.2 Pricing and Hedging of Contingent Claims.- 3.1.3 The Black-Scholes Option Pricing Formula.- 3.1.4 The Greeks.- 3.2 The Concept ofImplied Volatility.- 3.2.1 Definition.- 3.2.2 Calculation.- 3.2.3 Interpretation.- 3.3 Features of Implied Volatility.- 3.3.1 Volatility Smiles.- 3.3.2 Volatility Term Structures.- 3.3.3 Volatility Surfaces.- 3.4 Modelling Implied Volatility.- 3.4.1 Overview.- 3.4.2 Implied Volatility as an Endogenous Variable.- 3.4.3 Implied Volatility as an Exogenou s Var iabl e.- 3.4.4 Comparison of Approaches.- 4 The General Stochastic Implied Volatility Model.- 4.1 The Financial Market Model.- 4.1.1 Model Specification.- 4.1.2 Movements of the Volatility Surface.- 4.2 Risk-Neutral Implied Volatility Dynamics.- 4.2.1 Change of Measure and Drift Restriction.- 4.2.2 Interpretation of Terms in the Risk-Neutral Drift.- 4.2.3 Existence and Uniqueness of the Risk-Neutral Measure.- 4.1 4.3 Pricing and Hedging of Cont ingent Claims.- 5 Properties of DAX Implied Volatilities.- 5.1 The DAX Option.- 5.1.1 Contract Specifications.- 5.1.2 Previous Studies.- 5.2 Data.- 5.2.1 Raw Data and Data Preparation.- 5.2.2 Correcting for Taxes and Dividends.- 5.2.3 Liquidity Aspects.- 5.3 Structure of DAX Implied Volatilities.- 5.3.1 Estimation of the DAX Volatility Surface.- 5.3.2 Empirical Results.- 5.3.3 Identification and Selection of Volatility Risk Factors.- 5.4 Dynamics of DAX Implied Volatilities.- 5.4.1 Time-Series Properties of DAX Volatility Risk Factors.- 5.4.2 Relating Volatility Risk
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Factors to Index Returns and other Market Variables.- 5.5 Summary of Empirical Observations.- 6 A Four-Factor Model for DAX Implied Volatilities.- 6.1 The Model under the Objective Measure.- 6.1.1 Model Specification.- 6.1.2 Model Estimation.- 6.1.3 Model Testing.- 6.2 The Model under the Risk-Neutral Measure.- 6.2.1 Risk-Neutral Stock Price and Volatility Dynamics.- 6.2.2 The Market Price of Risk Process.- 6.2.3 Pricing and Hedging of Contingent Claims.- 6.2.4 Model Calibration.- 6.3 Model Review and Conclusion.- 7 Model Applications.- 7.1 Pricing and Hedging of Exotic Derivatives.- 7.1.1 Product Overview.- 7.1.2 Exotic Equity Index Derivatives.- 7.1.3 Volatility Derivatives.- 7.2 Value at Risk for Option Portfolios.- 7.2.1 The Value at Risk Concept.- 7.2.2 Computing VaR for Option Portfolios.- 7.2.3 A Case Study.- 7.2.4 Beyond VaR: Expected Shortfall.- 7.3 Volatility Trading.- 7.3.1 Definition and Motivation.- 7.3.2 Volatility Trade Design.- 7.3.3 Profitability of DAX Volatility Trading Strategies.- 8 Summary and Conclusion.- A Some Mathematical Preliminaries;A.l Probability Theory;A.2 Continuous-time Stochastic Processes.- B Pricing of a Variance Swap via Static Replication.- List of Abbreviations.- List of Symbols.- References.
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Bibliographische Angaben
- Autoren: Reinhold Hafner , R. Hafner
- 252 Seiten, 13 Schwarz-Weiß-Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540221832
- ISBN-13: 9783540221838
- Erscheinungsdatum: 05.08.2004
Sprache:
Englisch
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