Financial Models with Levy Processes and Volatility Clustering.
Svetlozar T. Rachev
Bok Engelsk 2011 · Electronic books.
| Omfang | 1 online resource (416 pages)
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| Utgave | 1st ed.
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| Opplysninger | Intro -- Financial Models with Levy Processes and Volatility Clustering -- Contents -- Preface -- About the Authors -- CHAPTER 1 Introduction -- 1.1 The Need for Better Financial Modeling of Asset Prices -- 1.2 The Family of Stable Distribution and Its Properties -- 1.2.1 Parameterization of the Stable Distribution -- 1.2.2 Desirable Properties of the Stable Distributions -- 1.2.3 Considerations in the Use of the Stable Distribution -- 1.3 Option Pricing with Volatility Clustering -- 1.3.1 Non-Gaussian GARCH Models -- 1.4 Model Dependencies -- 1.5 Monte Carlo -- 1.6 Organization of the Book -- References -- CHAPTER 2 Probability Distributions -- 2.1 Basic Concepts -- 2.2 Discrete Probability Distributions -- 2.2.1 Bernoulli Distribution -- 2.2.2 Binomial Distribution -- 2.2.3 Poisson Distribution -- 2.3 Continuous Probability Distributions -- 2.3.1 Probability Distribution Function, Probability Density Function, and Cumulative Distribution Function -- 2.3.2 Normal Distribution -- 2.3.3 Exponential Distribution -- 2.3.4 Gamma Distribution -- 2.3.5 Variance Gamma Distribution -- 2.3.6 Inverse Gaussian Distribution -- 2.4 Statistic Moments and Quantiles -- 2.4.1 Location -- 2.4.2 Dispersion -- 2.4.3 Asymmetry -- 2.4.4 Concentration in Tails -- 2.4.5 Statistical Moments -- 2.4.6 Quantiles -- 2.4.7 Sample Moments -- 2.5 Characteristic Function -- 2.6 Joint Probability Distributions -- 2.6.1 Conditional Probability -- 2.6.2 Joint Probability Distribution Defined -- 2.6.3 Marginal Distribution -- 2.6.4 Dependence of Random Variables -- 2.6.5 Covariance and Correlation -- 2.6.6 Multivariate Normal Distribution -- 2.6.7 Elliptical Distributions -- 2.6.8 Copula Functions -- 2.7 Summary -- References -- CHAPTER 3 Stable and Tempered Stable Distributions -- 3.1 α-Stable Distribution -- 3.1.1 Definition of an α-Stable Random Variable.. - 3.1.2 Useful Properties of an α-Stable Random Variable -- 3.1.3 Smoothly Truncated Stable Distribution -- 3.2 Tempered Stable Distributions -- 3.2.1 Classical Tempered Stable Distribution -- 3.2.2 Generalized Classical Tempered Stable Distribution -- 3.2.3 Modified Tempered Stable Distribution -- 3.2.4 Normal Tempered Stable Distribution -- 3.2.5 Kim-Rachev Tempered Stable Distribution -- 3.2.6 Rapidly Decreasing Tempered Stable Distribution -- 3.3 Infinitely Divisible Distributions -- 3.3.1 Exponential Moments -- 3.4 Summary -- 3.5 Appendix -- 3.5.1 The Hypergeometric Function -- 3.5.2 The Confluent Hypergeometric Function -- References -- CHAPTER 4 Stochastic Processes in Continuous Time -- 4.1 Some Preliminaries -- 4.2 Poisson Process -- 4.2.1 Compounded Poisson Process -- 4.3 Pure Jump Process -- 4.3.1 Gamma Process -- 4.3.2 Inverse Gaussian Process -- 4.3.3 Variance Gamma Process -- 4.3.4 α-Stable Process -- 4.3.5 Tempered Stable Process -- 4.4 Brownian Motion -- 4.4.1 Arithmetic Brownian Motion -- 4.4.2 Geometric Brownian Motion -- 4.5 Time-Changed Brownian Motion -- 4.5.1 Variance Gamma Process -- 4.5.2 Normal Inverse Gaussian Process -- 4.5.3 Normal Tempered Stable Process -- 4.6 L´evy Process -- 4.7 Summary -- References -- CHAPTER 5 Conditional Expectation and Change of Measure -- 5.1 Events, σ-Fields, and Filtration -- 5.2 Conditional Expectation -- 5.3 Change of Measures -- 5.3.1 Equivalent Probability Measure -- 5.3.2 Change of Measure for Continuous-Time Processes -- 5.3.3 Change of Measure in Tempered Stable Processes -- 5.4 Summary -- References -- CHAPTER 6 Exponential L ´ evy Models -- 6.1 Exponential L´evy Models -- 6.2 Fitting α-Stable and Tempered Stable Distributions -- 6.2.1 Fitting the Characteristic Function -- 6.2.2 Maximum Likelihood Estimation with Numerical Approximation of the Density Function.. - 6.2.3 Assessing the Goodness of Fit -- 6.3 Illustration: Parameter Estimation for Tempered Stable Distributions -- 6.4 Summary -- 6.5 Appendix: Numerical Approximation of Probability Density and Cumulative Distribution Functions -- 6.5.1 Numerical Method for the Fourier Transform -- References -- CHAPTER 7 Option Pricing in Exponential L ´ evy Models -- 7.1 Option Contract -- 7.2 Boundary Conditions for the Price of an Option -- 7.3 No-Arbitrage Pricing and Equivalent Martingale Measure -- 7.4 Option Pricing under the Black-Scholes Model -- 7.5 European Option Pricing under Exponential Tempered Stable Models -- 7.5.1 Illustration: Implied Volatility -- 7.5.2 Illustration: Calibrating Risk-Neutral Parameters -- 7.5.3 Illustration: Calibrating Market Parameters and Risk-Neutral Parameters Together -- 7.6 Subordinated Stock Price Model -- 7.6.1 Stochastic Volatility L´evy Process Model -- 7.7 Summary -- References -- CHAPTER 8 Simulation -- 8.1 Random Number Generators -- 8.1.1 Uniform Distributions -- 8.1.2 Discrete Distributions -- 8.1.3 Continuous Nonuniform Distributions -- 8.1.4 Simulation of Particular Distributions -- 8.2 Simulation Techniques for L´evy Processes -- 8.2.1 Taking Care of Small Jumps -- 8.2.2 Series Representation: A General Framework -- 8.2.3 Rosi ´ nsky Rejection Method -- 8.2.4 α-Stable Processes -- 8.3 Tempered Stable Processes -- 8.3.1 Kim-Rachev Tempered Stable Case -- 8.3.2 Classical Tempered Stable Case -- 8.4 Tempered Infinitely Divisible Processes -- 8.4.1 Rapidly Decreasing Tempered Stable Case -- 8.4.2 Modified Tempered Stable Case -- 8.5 Time-Changed Brownian Motion -- 8.5.1 Classical Tempered Stable Processes -- 8.5.2 Variance Gamma and Skewed Variance Gamma Processes -- 8.5.3 Normal Tempered Stable Processes -- 8.5.4 Normal Inverse Gaussian Processes -- 8.6 Monte Carlo Methods -- 8.6.1 Variance Reduction Techniques.. - 8.6.2 A Nonparametric Monte Carlo Method -- 8.6.3 A Monte Carlo Example -- Appendix -- References -- CHAPTER 9 Multi-Tail t-Distribution -- 9.1 Introduction -- 9.2 Principal Component Analysis -- 9.2.1 Principal Component Tail Functions -- 9.2.2 Density of a Multi-Tail t Random Variable -- 9.3 Estimating Parameters -- 9.3.1 Estimation of the Dispersion Matrix -- 9.3.2 Estimation of the Parameter Set -- 9.4 Empirical Results -- 9.4.1 Comparison to Other Models -- 9.4.2 Two-Dimensional Analysis -- 9.4.3 Multi-Tail t Model Check for the DAX -- 9.5 Summary -- References -- CHAPTER 10 Non-Gaussian Portfolio Allocation -- 10.1 Introduction -- 10.2 Multifactor Linear Model -- 10.3 Modeling Dependencies -- 10.4 Average Value-at-Risk -- 10.5 Optimal Portfolios -- 10.6 The Algorithm -- 10.7 An Empirical Test -- 10.8 Summary -- References -- CHAPTER 11 Normal GARCH models -- 11.1 Introduction -- 11.2 GARCH Dynamics with Normal Innovation -- 11.3 Market Estimation -- 11.4 Risk-Neutral Estimation -- 11.4.1 Out-of-Sample Performance -- 11.5 Summary -- References -- CHAPTER 12 Smoothly Truncated Stable GARCH Models -- 12.1 Introduction -- 12.2 A Generalized NGARCH Option Pricing Model -- 12.3 Empirical Analysis -- 12.3.1 Results under the Objective Probability Measure -- 12.3.2 Explaining S& -- P 500 Option Prices -- 12.4 Summary -- References -- CHAPTER 13 Infinitely Divisible GARCH Models -- 13.1 Stock Price Dynamic -- 13.2 Risk-Neutral Dynamic -- 13.3 Non-Normal Infinitely Divisible GARCH -- 13.3.1 Classical Tempered Stable Model -- 13.3.2 Generalized Tempered Stable Model -- 13.3.3 Kim-Rachev Model -- 13.3.4 Rapidly Decreasing Tempered Stable Model -- 13.3.5 Inverse Gaussian Model -- 13.3.6 Skewed Variance Gamma Model -- 13.3.7 Normal Inverse Gaussian Model -- 13.4 Simulate Infinitely Divisible GARCH -- Appendix -- References.. - CHAPTER 14 Option Pricing with Monte Carlo Methods -- 14.1 Introduction -- 14.2 Data Set -- 14.2.1 Market Estimation -- 14.3 Performance of Option Pricing Models -- 14.3.1 In-Sample -- 14.3.2 Out-of-Sample -- 14.4 Summary -- References -- CHAPTER 15 American Option Pricing with Monte Carlo Methods -- 15.1 American Option Pricing in Discrete Time -- 15.2 The Least Squares Monte Carlo Method -- 15.3 LSM Method in GARCH Option Pricing Model -- 15.4 Empirical Illustration -- 15.5 Summary -- References -- Index.. - FINANCIAL MODELS WITH LéVY PROCESSES AND VOLATILITY CLUSTERING The failure of financial models has been identified by some market observers as a major contributor to the global financial crisis. More specifically, it's been argued that the underlying assumption made in most of these models-that distributions of prices and returns are normally distributed-have been responsible for their undoing. Financial crises and black swan events may not be precisely predictable by models, but improving the reliability and flexibility of those models is essential for both financial practitioners and academics intent on limiting the impact of major market crashes. In Financial Models with Lévy Processes and Volatility Clustering, authors Svetlozar Rachev, Young Shin Kim, Michele Leonardo Bianchi, and Frank Fabozzi focus on the application of non-normal distributions for modeling the behavior of stock price returns. Opening with a brief introduction to the basics of probability distributions, this practical resource quickly moves on to: Address a wide array of methods for the simulation of infinitely divisible distributions and Lévy processes with a view toward option pricing. Discuss two approaches to deal with non-normal multivariate distributions, providing insight into portfolio allocation assuming a multi-tail t distribution and a non-Gaussian multivariate model. Examine discrete time option pricing models with volatility clustering-namely non-Gaussian GARCH models. Provide guidance on pricing American options with Monte Carlo methods. If you want to gain a better understanding of how financial models can be used to capture the dynamics of economic and financial variables, Financial Models with Lévy Processes and Volatility Clustering is the best place to start.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 9780470937167
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| ISBN(galt) |
