Download or read book Risk Neutral Moment Based Estimation of Affine Option Pricing Models written by Bruno Feunou and published by . This book was released on 2017 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a novel methodology for estimating option pricing models based on risk-neutral moments. We synthesize the distribution extracted from a panel of option prices and exploit linear relationships between risk-neutral cumulants and latent factors within the continuous time affine stochastic volatility framework. We find that fitting the Andersen, Fusari, and Todorov (2015b) option valuation model to risk-neutral moments captures the bulk of the information in option prices. Our estimation strategy is effective, easy to implement, and robust, as it allows for a direct linear filtering of the latent factors and a quasi-maximum likelihood estimation of model parameters. From a practical perspective, employing risk-neutral moments instead of option prices also helps circumvent several sources of numerical errors and substantially lessens the computational burden inherent in working with a large panel of option contracts.
Download or read book Characteristic Function Based Estimation of Affine Option Pricing Models written by Yannick Dillschneider and published by . This book was released on 2019 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we derive explicit expressions for certain joint moments of stock prices and option prices within a generic affine stochastic volatility model. Evaluation of each moment requires weighted inverse Fourier transformation of a function that is determined by the risk-neutral and real-world characteristic functions of the state vector. Explicit availability of such moment expressions allows to devise a novel GMM approach to jointly estimate real-world and risk-neutral parameters of affine stochastic volatility models using observed individual option prices. Moreover, the moment expressions may be used to include option price information into other existing moment-based estimation approaches.
Download or read book Efficient Quasi Bayesian Estimation of Affine Option Pricing Models Using Risk neutral Cumulants written by Riccardo Brignone and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: We propose a general, accurate and fast econometric approach for the estimation of affine option pricing models. The algorithm belongs to the class of Laplace-Type Estimation (LTE) techniques and exploits Sequential Monte Carlo (SMC) methods. We employ functions of the risk-neutral cumulants given in closed form to marginalize latent states, and we address parameter estimation by designing a density tempered SMC sampler. We test our algorithm on simulated data by tackling the challenging inference problem of estimating an option pricing model which displays two stochastic volatility factors, allows for co-jumps between price and volatility, and stochastic jump intensity. Furthermore, we consider real data and estimate the model on a large panel of option prices. Numerical studies confirm the accuracy of our estimates and the superiority of the proposed approach compared to its natural benchmark
Download or read book Quantitative Energy Finance written by Fred Espen Benth and published by Springer Nature. This book was released on with total page 270 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 Advanced Option Pricing Models written by Jeffrey Owen Katz and published by McGraw Hill Professional. This book was released on 2005-03-21 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Option Pricing Models details specific conditions under which current option pricing models fail to provide accurate price estimates and then shows option traders how to construct improved models for better pricing in a wider range of market conditions. Model-building steps cover options pricing under conditional or marginal distributions, using polynomial approximations and “curve fitting,” and compensating for mean reversion. The authors also develop effective prototype models that can be put to immediate use, with real-time examples of the models in action.
Download or read book Option Pricing in Incomplete Markets written by Yoshio Miyahara and published by World Scientific. This book was released on 2012 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem
Download or read book Option Pricing for an Affine Jump Diffusion Model written by Zhiqiu Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of this thesis, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion (AJD) model. Let log stock price under risk-neutral measure follow an AJD model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work. In the second part of this thesis, we study the European option pricing problem when the underlying stock follows an AJD model whose jump interarrival time has a Cox-Ingersoll-Ross type intensity dynamics. An analytic formula of a European option pricing is derived using the Fourier inversion transform technique. We develop a Monte Carlo algorithm to simulate the dynamics of an AJD model. We observe AJD At-The-Money (ATM) European option prices using the Monte Carlo simulation converge to the Fourier analytic ones as the number of simulation paths increases.
Download or read book A Closed Form Approach to Valuing Risk Neutral Moments from Option Prices written by Aristogenis Lazos and published by . This book was released on 2018 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops closed-form solutions for the finite integrals in the volatility, cubic and quartic contracts in Bakshi, Kapadia and Madan (2003) which avoid discretization errors and do not involve interpolation and extrapolation. It compares the accuracy of the closed-form approach with the popular interpolation-extrapolation approach in the literature. Our results show that the closed-form approach provides more accurate estimates for skewness. This holds across different option pricing models and parameterization which have been shown to be favourable for the interpolation-extrapolation approach. Finally, our results show that the closed-form approach always extracts expectations consistent with the term structure of the volatility smirk whereas the interpolation-extrapolation approach fails several times.
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
Download or read book A Closed form GARCH Option Pricing Model written by Steven L. Heston and published by . This book was released on 1997 with total page 44 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. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces 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.
Download or read book Three Essays on Estimation of Risk Neutral Measures Using Option Pricing Models written by Seung Hwan Lee and published by . This book was released on 2008 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation develops two new parametric and nonparametric methods for estimating risk-neutral measures (RNM) which embody important information about market participants' sentiments concerning prices of the underlying asset in the future, and investigates empirical performance of parametric RNM estimation methods. The first essay, "Estimation of Risk Neutral Measures using the Generalized Two-Factor Log-Stable Option Pricing Model", constructs a simple representative agent model to provide a theoretical framework for the log-stable option pricing model and then implements a new parametric method for estimating the RNM using a generalized two-factor log-stable option pricing model. Under the generalized two-factor log-stable uncertainty assumption, the RNM for the log of price is a convolution of two exponentially tilted stable distributions. The generalized two-factor log-stable RNM provides a sufficiently accurate tool for estimating the RNM from observed option prices even if the log-stable assumption might not be satisfied. I estimate the RNM using the S & P 500 index options and find that the generalized two-factor log-stable model gives better performance than alternative models in fitting the observed option prices. The second essay, "Parametric Risk Neutral Measure Estimation Methods: A Horse Race", implements 12 parametric RNM estimation methods by means of the closed-form or characteristic function of RNM distributions and then compares the empirical performance under three criteria - -the root mean squared error (RMSE), likelihood ratio (LR), and the root mean integrated squared error (RMISE). The empirical results show that the generalized two-factor log-stable model outperforms other alternative parametric RNM estimation methods. The third essay, "Nonparametric Estimation of Risk-Neutral Measures using Quartic B-Spline CDFs with Power Tails", proposes a new nonparametric (BSP) method. I model a RNM cumulative distribution function (CDF) using quartic B-splines with power tails so that the resulting RNM probability density function (PDF) has continuity C2 and arbitrage-free properties. Since the number of knots is selected optimally in constructing the quartic B-spline RNM CDF, my method avoids both overfitting and oversmoothing. To improve computational efficiency and accuracy I introduce a 3-step RNM estimation procedure that transforms a nonlinear optimization problem into a convex quadratic program, which is efficiently solved by numerical optimization software.
Download or read book Option Pricing Models and Volatility Using Excel VBA written by Fabrice D. Rouah and published by Wiley. This book was released on 2007-03-22 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book A Semiparametric Estimation of Liquidity Effects on Option Pricing written by Eva Ferreira and published by . This book was released on 1999 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays on the Econometrics of Option Pricing written by Evgenii Vladimirov (Ph. D.) and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This dissertation is a collection of three essays that delve into the econometrics of option pricing. The primary objective of these essays is to develop and deploy diverse econometric techniques that enable the accurate extraction of valuable information embedded in option prices. Chapter 2 investigates jump contagion between international stock markets using options data. It introduces a multivariate option pricing model that assesses the contagious effects of market shocks. Chapter 3 tackles the challenge of estimating continuous-time option pricing models. It proposes a new filtering and estimation method for affine jump-diffusion models, enhancing computational efficiency and implementation ease. Finally, Chapter 4 develops a unified framework for non-parametric estimation of risk-neutral densities, option prices, and option sensitivities."--
Download or read book Empirical Dynamic Asset Pricing written by Kenneth J. Singleton and published by Princeton University Press. This book was released on 2009-12-13 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
