Non-Affine GARCH Option Pricing Models, Variance Dependent Kernels, and Diffusion Limits

Non-Affine GARCH Option Pricing Models, Variance Dependent Kernels, and Diffusion Limits
Author: Alex Badescu
Publisher:
Total Pages: 54
Release: 2017
Genre:
ISBN:

This paper investigates the pricing and weak convergence of an asymmetric non-affine, non-Gaussian GARCH model when the risk-neutralization is based on a variance dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a general setting and its weak limit is derived. We show how several GARCH diffusions, martingalized via well-known pricing kernels, are obtained as special cases and we derive necessary and sufficient conditions for the presence of financial bubbles. An extensive empirical analysis using both historical returns and options data illustrates the advantage of coupling this pricing kernel with non-Gaussian innovations.

The Role of Fat-tails, Multiple Variance Components, and Pricing Kernels in Option Pricing

The Role of Fat-tails, Multiple Variance Components, and Pricing Kernels in Option Pricing
Author: Kadir Gokhan Babaoglu
Publisher:
Total Pages:
Release: 2016
Genre:
ISBN:

My dissertation, composed of two chapters, explores the pricing of index and individual equity options contracts. These chapters make three modeling choices on (i) state variables, (ii) return innovations and (iii) the pricing kernel, and answer the question about what we can learn from stocks and options data. Both chapters specify a variance-dependent pricing kernel, which allows non-monotonicity when projected onto returns. While first chapter employs Inverse Gaussian distribution to capture fat-tailed dynamics of returns, second chapter chooses to model distribution of returns as a normal shock plus Compound Poisson jumps. Regarding the state variables, Chapter 1 uses long-run and short-run variance components, whereas Chapter 2 defines normal and jump variance components as the state variables. The first chapter nests multiple volatility components, fat tails and a variance-dependent pricing kernel in a single option model and compare their contribution to describing returns and option data. All three features lead to statistically significant model improvements. A variance-dependent pricing kernel is economically most important and improves option fit by 17% on average and more so for two-factor models. A second volatility component improves the option fit by 9% on average. Fat tails improve option fit by just over 4% on average, but more so when a variance-dependent pricing kernel is applied. Overall these three model features are complements rather than substitutes: the importance of one feature increases in conjunction with the others. Focusing on individual equity options, second chapter develops a new factor model that explores (i) if a separate beta for market jumps is needed, (ii) cross-sectional differences in jump betas of stocks, and (iii) the role of jump betas in explaining equity option prices. Differentiating between normal beta and jump beta, the model predicts that a stock with higher sensitivity to market jumps (normal shocks) have higher out-of-the-money (at-the-money) option prices. The results show that jump betas are needed to adequately explain equity options.

Closed-Form Variance Swap Prices Under General Affine GARCH Models and Their Continuous-Time Limits

Closed-Form Variance Swap Prices Under General Affine GARCH Models and Their Continuous-Time Limits
Author: Alex Badescu
Publisher:
Total Pages: 30
Release: 2017
Genre:
ISBN:

In this paper, we derive fully explicit closed-form expressions for the fair strike prices of discrete-time variance swaps under general affine GARCH type models that have been risk-neutralized with a family of variance dependent pricing kernels. The methodology relies on solving differential recursions for the coefficients of the joint cumulant generating function of the log price and the conditional variance processes. An alternative derivation is provided in the case of Gaussian innovations. Using standard assumptions on the asymptotic behavior of the GARCH parameters as the sampling frequency increases, we derive the diffusion limit of a Gaussian GARCH model and we further investigate the convergence of the variance swap prices to its continuous-time limit. Numerical examples on the term structure of the variance swap rates and on the convergence results are also presented.

Volatility and Correlation

Volatility and Correlation
Author: Riccardo Rebonato
Publisher: John Wiley & Sons
Total Pages: 864
Release: 2005-07-08
Genre: Business & Economics
ISBN: 0470091401

In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School

Option Pricing and Estimation of Financial Models with R

Option Pricing and Estimation of Financial Models with R
Author: Stefano M. Iacus
Publisher: John Wiley & Sons
Total Pages: 402
Release: 2011-02-23
Genre: Business & Economics
ISBN: 1119990203

Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.

Statistics of Financial Markets

Statistics of Financial Markets
Author: Jürgen Franke
Publisher: Springer Science & Business Media
Total Pages: 454
Release: 2004
Genre: Business & Economics
ISBN: 9783540216759

Extreme Value Theory (EVT), GARCH MODELS, Hypothesis Testing, Fitting Probability Distributions to Risk Factors and Portfolios.

Empirical Dynamic Asset Pricing

Empirical Dynamic Asset Pricing
Author: Kenneth J. Singleton
Publisher: Princeton University Press
Total Pages: 497
Release: 2009-12-13
Genre: Business & Economics
ISBN: 1400829232

Written by one of the leading experts in the field, this book focuses on the interplay between model specification, data collection, and econometric testing of dynamic asset pricing models. The first several chapters provide an in-depth treatment of the econometric methods used in analyzing financial time-series models. The remainder explores the goodness-of-fit of preference-based and no-arbitrage models of equity returns and the term structure of interest rates; equity and fixed-income derivatives prices; and the prices of defaultable securities. Singleton addresses the restrictions on the joint distributions of asset returns and other economic variables implied by dynamic asset pricing models, as well as the interplay between model formulation and the choice of econometric estimation strategy. For each pricing problem, he provides a comprehensive overview of the empirical evidence on goodness-of-fit, with tables and graphs that facilitate critical assessment of the current state of the relevant literatures. As an added feature, Singleton includes throughout the book interesting tidbits of new research. These range from empirical results (not reported elsewhere, or updated from Singleton's previous papers) to new observations about model specification and new econometric methods for testing models. Clear and comprehensive, the book will appeal to researchers at financial institutions as well as advanced students of economics and finance, mathematics, and science.

Handbook of Economic Forecasting

Handbook of Economic Forecasting
Author: Graham Elliott
Publisher: Elsevier
Total Pages: 667
Release: 2013-08-23
Genre: Business & Economics
ISBN: 0444627405

The highly prized ability to make financial plans with some certainty about the future comes from the core fields of economics. In recent years the availability of more data, analytical tools of greater precision, and ex post studies of business decisions have increased demand for information about economic forecasting. Volumes 2A and 2B, which follows Nobel laureate Clive Granger's Volume 1 (2006), concentrate on two major subjects. Volume 2A covers innovations in methodologies, specifically macroforecasting and forecasting financial variables. Volume 2B investigates commercial applications, with sections on forecasters' objectives and methodologies. Experts provide surveys of a large range of literature scattered across applied and theoretical statistics journals as well as econometrics and empirical economics journals. The Handbook of Economic Forecasting Volumes 2A and 2B provide a unique compilation of chapters giving a coherent overview of forecasting theory and applications in one place and with up-to-date accounts of all major conceptual issues. - Focuses on innovation in economic forecasting via industry applications - Presents coherent summaries of subjects in economic forecasting that stretch from methodologies to applications - Makes details about economic forecasting accessible to scholars in fields outside economics

Volatility

Volatility
Author: Torben Gustav Andersen
Publisher: Edward Elgar Publishing
Total Pages: 0
Release: 2018
Genre: Econometrics
ISBN: 9781788110617

Volatility ranks among the most active and successful areas of research in econometrics and empirical asset pricing finance over the past three decades. This two-volume collection of papers comprises some of the most influential published works from this burgeoning literature, both classic and contemporary. Topics covered include GARCH, stochastic and multivariate volatility models as well as forecasting, evaluation and high-frequency data. Together with an original introduction by the editors, this definitive compilation presents the most important milestones and contributions that helped pave the way to today's understanding of volatility.