Download or read book American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution written by Lars Stentoft and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose a feasible way to price American options in a model with time-varying volatility and conditional skewness and leptokurtosis, using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk-neutral dynamics can be obtained in this model, we interpret the effect of the risk-neutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model out-performs the Gaussian case for pricing options on the three large US stocks as well as a major index. In particular, improvements are found when it comes to explaining the smile in implied standard deviations.

Download or read book Handbook Of Financial Econometrics Mathematics Statistics And Machine Learning In 4 Volumes written by Cheng Few Lee and published by World Scientific. This book was released on 2020-07-30 with total page 5053 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

Download or read book Financial Models with Levy Processes and Volatility Clustering written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Download or read book Option Pricing Using Realized Volatility written by Lars Stentoft and published by . This book was released on 2008 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate dynamics to be used for option pricing purposes in this framework, and we show that our model explains some of the mispricings found when using traditional option pricing models based on interdaily data. We then show explicitly that a Generalized autoregressive Conditional Heteroskedastic model with Normal Inverse Gaussian distributed innovations is the corresponding benchmark model when only daily data is used. Finally, we perform an empirical analysis using stock options for three large American companies, and we show that in all cases our model performs significantly better than the corresponding benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes.

Download or read book What We Can Learn from Pricing 139 879 Individual Stock Options written by Lars Stentoft and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The GARCH framework has been used for option pricing with quite some success. While the initial work assumed conditional Gaussian innovations, recent contributions relax this assumption and allow for more flexible parametric specifications of the underlying distribution. However, until now the empirical applications have been limited to index options or options on only a few stocks and this using only few potential distributions and variance specifications. In this paper we test the GARCH framework on 30 stocks in the Dow Jones Industrial Average using two classical volatility specifications and 7 different underlying distributions. Our results provide clear support for using an asymmetric volatility specification together with non-Gaussian distribution, particularly of the Normal Inverse Gaussian type, and statistical tests show that this model is most frequently among the set of best performing models.

Download or read book Econometric Methods and Their Applications in Finance Macro and Related Fields written by Kaddour Hadri and published by World Scientific. This book was released on 2014 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume aims at providing an outlet for some of the best papers presented at the 15th Annual Conference of the African Econometric Society, which is one of the OC chaptersOCO of the International Econometric Society. Many of these papers represent the state of the art in financial econometrics and applied econometric modeling, and some also provide useful simulations that shed light on the models'' ability to generate meaningful scenarios for forecasting and policy analysis. Contents: Financial Econometrics and International Finance: Modeling Interest Rates Using Reducible Stochastic Differential Equations: A Copula-Based Multivariate Approach (Ruijun Bu, Ludovic Giet, Kaddour Hadri and Michel Lubrano); Financial Risk Management Using Asymmetric Heavy-Tailed Distribution and Nonlinear Dependence Structures of Asset Returns Under Discontinuous Dynamics (Alaa El-Shazly); Modeling Time-Varying Dependence in the Term Structure of Interest Rates (Diaa Noureldin); Nonlinear Filtering and Market Implied Rating for a Jump-Diffusion Structural Model of Credit Risk (Alaa El-Shazly); Time-Varying Optimal Weights for International Asset Allocation in African and South Asian Markets (Dalia El-Edel); Econometric Theory and Methods: Econometric Methods for Ordered Responses: Some Recent Developments (Franco Peracchi); Which Quantile Is the Most Informative? Maximum Likelihood, Maximum Entropy and Quantile Regression (Anil K Bera, Antonio F Galvao Jr., Gabriel V Montes-Rojas, Sung Y Park); The Experimetrics of Fairness (Anna Conte and Peter Moffatt); Uniform in Bandwidth Tests of Specification for Conditional Moment Restrictions Models (Pascal Lavergne and Pierre Nguimkeu); Joint LM Test for Homoscedasticity in a Two Way Error Components Model (Eugene Kouassi, Joel Sango, J M BossonBrou and Kern O Kymn); An Approximation to the Distribution of the Pooled Estimator When the Time Series Equation Is One of a Complete System (Ghazal Amer and William Mikhail); Monetary, Labor, Environmental and Other Econometric Applications: Monetary Policy and the Role of the Exchange Rate in Egypt (Tarek Morsi and Mai El-Mossallamy); International Migration, Remittances and Household Poverty Status in Egypt (Rania Roushdy, Ragui Assaad and Ali Rashed); Determinants of Job Quality and Wages of the Working Poor: Evidence From 1998OCo2006 Egypt Labor Market Panel Survey (Mona Said); A Contract-Theoretic Model of Conservation Agreements (Heidi Gjertsen, Theodore Groves, David A Miller, Eduard Niesten, Dale Squires and Joel Watson); Household Environment and Child Health in Egypt (Mahmoud Hailat and Franco Peracchi); Modeling the Relationship between Natural Resource Abundance, Economic Growth, and the Environment: A Cross-Country Study (Hala Abou-Ali and Yasmine M Abdelfattah); Global Cement Industry: Competitive and Institutional Frameworks (Tarek H Selim and Ahmed S Salem); On the Occurrence of Ponzi Schemes in Presence of Credit Restrictions Penalizing Default (Abdelkrim Seghir); Is Targeted Advertising Always Beneficial? (Nada Ben Elhadj-Ben Brahim, Rim Lahmandi-Ayed and Didier Laussel). Readership: Graduate students and researchers in the fields of econometrics, economic theory, applied econometrics.

Download or read book Elements of Financial Risk Management written by Peter Christoffersen and published by Academic Press. This book was released on 2011-11-22 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this best-selling book expands its advanced approach to financial risk models by covering market, credit, and integrated risk. With new data that cover the recent financial crisis, it combines Excel-based empirical exercises at the end of each chapter with online exercises so readers can use their own data. Its unified GARCH modeling approach, empirically sophisticated and relevant yet easy to implement, sets this book apart from others. Five new chapters and updated end-of-chapter questions and exercises, as well as Excel-solutions manual, support its step-by-step approach to choosing tools and solving problems. Examines market risk, credit risk, and operational risk Provides exceptional coverage of GARCH models Features online Excel-based empirical exercises

Download or read book Handbook of Research Methods and Applications in Empirical Finance written by Adrian R. Bell and published by Edward Elgar Publishing. This book was released on 2013-01-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This impressive Handbook presents the quantitative techniques that are commonly employed in empirical finance research together with real-world, state-of-the-art research examples. Written by international experts in their field, the unique approach describes a question or issue in finance and then demonstrates the methodologies that may be used to solve it. All of the techniques described are used to address real problems rather than being presented for their own sake, and the areas of application have been carefully selected so that a broad range of methodological approaches can be covered. The Handbook is aimed primarily at doctoral researchers and academics who are engaged in conducting original empirical research in finance. In addition, the book will be useful to researchers in the financial markets and also advanced Masters-level students who are writing dissertations.

Download or read book American Option Pricing Under GARCH With Non Normal Innovations written by Jean-Guy Simonato and published by . This book was released on 2018 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: As it is well known from the time-series literature, GARCH processes with non-normal shocks provide better descriptions of stock returns than GARCH processes with normal shocks. However, in the derivatives literature, American option pricing algorithms under GARCH are typically designed to deal with normal shocks. We thus develop here an approach capable of pricing American options with non-normal shocks. The approach uses an equilibrium pricing model with shocks characterized by a Johnson Su distribution and a simple algorithm inspired from the quadrature approaches recently proposed in the option pricing literature. Numerical experiments calibrated to stock index return data show that this method provides accurate option prices under GARCH for non-normal and normal cases.

Download or read book Financial Modeling Under Non Gaussian Distributions written by Eric Jondeau and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.

Download or read book Risk Adjustments of Option Prices Under Time changed Dynamics written by Elisa Nicolato and published by . This book was released on 2014 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a closed-form expansion of option prices in terms of Black-Scholes prices and higher-order Greeks. We show how the true price of an option less its Black-Scholes price is given by a series of premiums on higher-order risks that are not priced under the Black-Scholes model assumptions. The expansion can be used for a broad class of option pricing models with dynamics governed by time-changed Brownian motions. Specifically, we study expansions for exponential Lévy models such as the Variance Gamma and the Normal Inverse Gaussian models as well as their stochastic volatility counterparts, e.g., the VGSV and NIGSV models. Moreover, we consider extensions of the expansion to a more general subclass of affine jump-diffusion models for which the pricing transform may not be known in closed form.

Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Download or read book Computational Finance written by George Levy and published by Butterworth-Heinemann. This book was released on 2004-01-27 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM contains ... "working computer code, demonstration applications, and also PDF versions of several research articles that are referred to in the book." -- d.j.

Download or read book Option Pricing in a Dynamic Variance Gamma Model written by Lorenzo Mercuri and published by . This book was released on 2014 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying to capture persistence of volatility shocks and also higher order conditional dynamics in a parsimonious way.We select an equivalent martingale measure by means of the conditional Esscher transform as in Buhlmann et al. (1996) and show that this change of measure leads to a similar dynamics of the mixing distribution. The model admits a recursive procedure for the computation of the characteristic function of the terminal logprice, thus allowing semianalytical pricing as in Heston and Nandi (2000). From an empirical point of view, we check the ability of this model to calibrate SPX option data and we compare it with the Heston and Nandi (2000) model and with the Christoffersen, Heston and Jacobs (2006) model, that is based on Inverse Gaussian innovations.

Download or read book Quarterly Journal of Business and Economics written by and published by . This book was released on 2007 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.

Download or read book Option Pricing with a Natural Equivalent Martingale Measure for Log symmetric Levy Price Processes written by Ying Oon Tan and published by . This book was released on 2013 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis examines the pricing of options when the stock price follows a log-symmetric Levy process. Models in continuous time and discrete time are considered. We identify situations when there is an equivalent change of measure that preserves the Levy property, symmetry and the family of symmetric distributions of the returns (log-returns if discrete time), and makes the discounted price process into a martingale. We call such measures natural equivalent martingale measures.In continuous time, when a natural equivalent martingale measure exists it is unique. It can be obtained by changing only the location or the scale parameter of the symmetric distribution if the Brownian component in present or absent, respectively, in the Levy process. The analogous natural equivalent martingale measure in discrete time always exists but not unique. It can be obtained by changing the location and the scale parameters of the symmetric distribution.Option pricing with natural equivalent martingale measure is arbitrage-free. We apply this approach to obtain new and elegant option pricing formulae for log-symmetric variance gamma and log-symmetric normal inverse Gaussian models.