A Time Series Approach to Option Pricing
Models, Methods and Empirical Performances
E-Book
A Time Series Approach to Option Pricing
Models, Methods and Empirical Performances
The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.
1;Notation;6 2;Contents;10 3;List of Figures;12 4;List of Tables;16 5;1 Introduction;18 5.1;References;25 6;2 The Time Series Toolbox for Financial Returns;27 6.1;2.1 Stylized Facts;27 6.1.1;2.1.1 Stationarity, Ergodicity and Autocorrelation;28 6.1.2;2.1.2 Time-Varying Volatility and Leverage Effects;31 6.1.3;2.1.3 Semi Fat-Tailed Distributions;32 6.2;2.2 Symmetric GARCH Models;34 6.2.1;2.2.1 From Linear to Non-linear Models;34 6.2.2;2.2.2 Definitions;37 6.2.3;2.2.3 Stationarity Properties;39 6.2.4;2.2.4 Covariance Structure of the Squares;43 6.2.5;2.2.5 Why We Need More: Kurtosis and Asymmetry in a GARCH(1,1) Model;47 6.3;2.3 Asymmetric Extensions;49 6.3.1;2.3.1 GJR Model;51 6.3.2;2.3.2 EGARCH Model;53 6.3.3;2.3.3 APARCH Model;55 6.3.4;2.3.4 Concluding Remarks;57 6.4;2.4 Conditional Distribution of Returns;58 6.4.1;2.4.1 Generalized Hyperbolic Distributions;58 6.4.2;2.4.2 Mixture of Two Gaussian Distributions;61 6.4.3;2.4.3 Some Practical Remarks;63 6.5;2.5 GARCH in Mean;64 6.6;2.6 Dealing with the Estimation Challenge;65 6.6.1;2.6.1 Maximum Likelihood;66 6.6.2;2.6.2 Quasi Maximum Likelihood;67 6.6.3;2.6.3 Recursive Estimation;68 6.6.4;2.6.4 Empirical Finite Sample Properties of the Three Estimation Methodologies;69 6.7;2.7 From GARCH Processes to Continuous Diffusions;74 6.7.1;2.7.1 Convergence Toward Hull1987 Diffusions;75 6.7.2;2.7.2 Convergence Toward Diffusions with Deterministic Volatilities;77 6.7.3;2.7.3 Convergence Toward the ch2:Heston1993 Model;77 6.8;References;78 7;3 From Time Series of Returns to Option Prices: The Stochastic Discount Factor Approach;83 7.1;3.1 Description of the Economy Under the Historical Probability;84 7.2;3.2 Option Pricing in Discrete Time;86 7.2.1;3.2.1 Arbitrage-Free Price of a European Contingent Claim;86 7.2.2;3.2.2 The Stochastic Discount Factor;89 7.2.3;3.2.3 Economic Interpretation: The CCAPM Model;91 7.3;3.3 The Extended Girsanov Principle;96 7.3.1;3.3.1 Definition and Properties;96 7.3.2;3.3.2 Risk-Neutral Dynamics for Classical Distributions;99 7.4;3.4 The Conditional Esscher Transform;100 7.4.1;3.4.1 Definition and Properties;100 7.4.2;3.4.2 Risk-Neutral Dynamics for Classical Distributions;105 7.4.2.1;The Generalized Hyperbolic Distribution;106 7.4.2.2;Mixture of Gaussian Distributions;109 7.4.2.3;Gaussian Jumps;110 7.5;3.5 Second Order Esscher Transform;111 7.6;3.6 The Empirical Martingale Simulation Method;115 7.7;3.7 Remarks on Closed-Form Option Pricing Formulas;117 7.8;3.8 Proofs of Chapter 3;119 7.9;References;127 8;4 Empirical Performances of Discrete Time Series Models;130 8.1;4.1 Historical Dynamics of Option Prices;131 8.2;4.2 The Heston and Nandi Case: Calibration vs. Estimation;144 8.3;4.3 Empirical Performances of Heavy Tailed Models;164 8.3.1;4.3.1 Estimation Strategies;164 8.3.2;4.3.2 Pricing Performances;177 8.4;4.4 Conclusion;187 8.5;References;188 9;Mathematical Appendix;190 9.1;Gaussian Random Variables;190 9.2;Conditional Expectation;191 9.3;Monte Carlo Methods;195 9.4;Convergence of Discrete Time Markov Processes to Diffusions;198 9.5;From Moment Generating Functions to Option Prices;199 9.6;References;200 10;Index;201
Chorro, Christophe
Guégan, Dominique
Ielpo, Florian
| ISBN | 9783662450376 |
|---|---|
| Artikelnummer | 9783662450376 |
| Medientyp | E-Book - PDF |
| Auflage | 2. Aufl. |
| Copyrightjahr | 2014 |
| Verlag | Springer-Verlag |
| Umfang | 202 Seiten |
| Sprache | Englisch |
| Kopierschutz | Digitales Wasserzeichen |
