A Closed-Form GARCH Option Pricing Model


Book Description

This paper develops a closed-form option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The single factor (one lag) version of this model contains Heston's (1993) stochastic volatility model as a diffusion limit and therefore unifies the discrete GARCH and continuous-time stochastic volatility literature of option pricing. The new model provides the first option formula for a random volatility model that is solely a function of observables; all the parameters can be easily estimated from the history of asset prices, observed at discreteintervals. Empirical analysis on Samp;P500 index options shows the single factor version of the GARCH model to be a substantial improvement over the Black-Scholes (1973) model. The GARCH model continues to substantially outperform the Black-Scholes model even when the Black-Scholes model is updated every period while the parameters of the GARCH model are held constant. The improvement is due largely to the ability of the GARCH model to describe the correlation of volatility with spot returns. This allows the GARCH model to capture strike price biases in the Black-Scholes model that give rise to the skew in implied volatilities in the index options market.




Option Pricing Models and Volatility Using Excel-VBA


Book Description

This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland




A Closed-Form GARCH Option Valuation Model


Book Description

This paper develops a closed-form option valuation formula for a spot asset whose variance follows a GARCH(p,q) process that can be correlated with the returns of the spot asset. It provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables. The single lag version of this model contains Heston's (1993) stochastic volatility model as a continuous-time limit. Empirical analysis on Samp;P500 index options shows that the out-of-sample valuation errors from the single lag version of the GARCH model are substantially lower than the ad hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) that uses a separate implied volatility for each option to fit to the smirk/smile in implied volatilties. The GARCH model remains superior even though the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices while the ad hoc Black-Scholes model is updated every period. The improvement is largely due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility.




Volatility and Time Series Econometrics


Book Description

A volume that celebrates and develops the work of Nobel Laureate Robert Engle, it includes original contributions from some of the world's leading econometricians that further Engle's work in time series economics




GARCH Models


Book Description

This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation and tests. The book also provides coverage of several extensions such as asymmetric and multivariate models and looks at financial applications. Key features: Provides up-to-date coverage of the current research in the probability, statistics and econometric theory of GARCH models. Numerous illustrations and applications to real financial series are provided. Supporting website featuring R codes, Fortran programs and data sets. Presents a large collection of problems and exercises. This authoritative, state-of-the-art reference is ideal for graduate students, researchers and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.




A Time Series Approach to Option Pricing


Book Description

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.




Missing Data Methods


Book Description

Part of the "Advances in Econometrics" series, this title contains chapters covering topics such as: Missing-Data Imputation in Nonstationary Panel Data Models; Markov Switching Models in Empirical Finance; Bayesian Analysis of Multivariate Sample Selection Models Using Gaussian Copulas; and, Consistent Estimation and Orthogonality.




Handbook of Recent Advances in Commodity and Financial Modeling


Book Description

This handbook includes contributions related to optimization, pricing and valuation problems, risk modeling and decision making problems arising in global financial and commodity markets from the perspective of Operations Research and Management Science. The book is structured in three parts, emphasizing common methodological approaches arising in the areas of interest: - Part I: Optimization techniques - Part II: Pricing and Valuation - Part III: Risk Modeling The book presents to a wide community of Academics and Practitioners a selection of theoretical and applied contributions on topics that have recently attracted increasing interest in commodity and financial markets. Within a structure based on the three parts, it presents recent state-of-the-art and original works related to: - The adoption of multi-criteria and dynamic optimization approaches in financial and insurance markets in presence of market stress and growing systemic risk; - Decision paradigms, based on behavioral finance or factor-based, or more classical stochastic optimization techniques, applied to portfolio selection problems including new asset classes such as alternative investments; - Risk measurement methodologies, including model risk assessment, recently applied to energy spot and future markets and new risk measures recently proposed to evaluate risk-reward trade-offs in global financial and commodity markets; and derivatives portfolio hedging and pricing methods recently put forward in the financial community in the aftermath of the global financial crisis.




Statistics and Data Analysis for Financial Engineering


Book Description

Financial engineers have access to enormous quantities of data but need powerful methods for extracting quantitative information, particularly about volatility and risks. Key features of this textbook are: illustration of concepts with financial markets and economic data, R Labs with real-data exercises, and integration of graphical and analytic methods for modeling and diagnosing modeling errors. Despite some overlap with the author's undergraduate textbook Statistics and Finance: An Introduction, this book differs from that earlier volume in several important aspects: it is graduate-level; computations and graphics are done in R; and many advanced topics are covered, for example, multivariate distributions, copulas, Bayesian computations, VaR and expected shortfall, and cointegration. The prerequisites are basic statistics and probability, matrices and linear algebra, and calculus. Some exposure to finance is helpful.