Download or read book A Class of Nonlinear Stochastic Volatility Models written by Jun Yu and published by . This book was released on 2013 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a class of nonlinear stochastic volatility models based on the Box-Cox transformation which offers an alternative to the one introduced in Andersen (1994). The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model, and has an advantage in the ease with which different specifications on stochastic volatility can be tested. In addition, the functional form of transformation which induces marginal normality of volatility is obtained as a byproduct of this general way of modeling stochastic volatility. The efficient method of moments approach is used to estimate model parameters. Empirical results reveal that the lognormal stochastic volatility model is rejected for daily index return data but not for daily individual stock return data. As a consequence, the stock volatility can be well described by the lognormal distribution as its marginal distribution, consistent with the result found in a recent literature (cf Andersen et al (2001a)). However, the index volatility does not follow the lognormal distribution as its marginal distribution.

Download or read book A Lognormal Type Stochastic Volatility Model With Quadratic Drift written by Peter Carr and published by . This book was released on 2019 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the instantaneous volatility level. The steady-state distribution of the instantaneous volatility belongs to the class of Generalized Inverse Gaussian distributions. We show that the quadratic term in the drift is crucial to avoid moment explosions and to preserve the martingale property of the stock price process. Using a conveniently chosen change of measure, we relate the model to the class of polynomial diffusions. This remarkable relation allows us to develop a highly accurate option price approximation technique based on orthogonal polynomial expansions.

Download or read book A Normal Stochastic Volatility Model written by Majed Sidani and published by . This book was released on 2014 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: I derive a closed form formula for pricing a European style call option assuming stochastic volatility and normal dynamics for the underlying. The model differs from the Heston model in the underlying dynamics only - normal as opposed to lognormal.

Download or read book Log Normal Stochastic Volatility Model written by Artur Sepp and published by . This book was released on 2016 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: While empirical studies have established that the log-normal stochastic volatility (SV) model is superior to its alternatives, the model does not allow for the analytical solutions available for affine models. To circumvent this, we show that the joint moment generating function (MGF) of the log-price and the quadratic variance (QV) under the log-normal SV model can be decomposed into a leading term, which is given by an exponential-affine form, and a residual term, whose estimate depends on the higher order moments of the volatility process. We prove that the second-order leading term is theoretically consistent with the expected values and covariance matrix of the log-price and the quadratic variance. We further extend this approach to the log-normal SV model with jumps. We use Fourier inversion techniques to value vanilla options on the equity and the QV and, by comparison to Monte Carlo simulations, we show that the second-order leading term is precise for the valuation of vanilla options. We generalize the affine decomposition to other non-affine stochastic volatility models with polynomial drift and volatility functions, and with jumps in the volatility process.

Download or read book Empirical Calibration and Minimum Variance Delta Under Log Normal Stochastic Volatility Dynamics written by Artur Sepp and published by . This book was released on 2016 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider calibration of log-normal stochastic volatility model and computation of option delta consistently with statistical dynamics of the asset price and its implied volatility surface. We introduce the concept of volatility skew-beta which serves as an empirical adjustment for empirical option delta. We show how to calibrate the model and make it consistent with any dynamics of implied volatility under the statistical measure and reproduce empirical option delta. The calibrated model minimizes realized volatility of delta-hedging P&L-s, especially so for non-vanilla options. We present empirical investigation using implied and realized volatilities of four major stock indices (S&P 500, FTSE 100, Nikkei 225, and STOXX 50) to validate the assumption about log-normality of both implied and realized volatilities.

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c

Download or read book New Methods for Performing Efficient Inference for Linear and Log normal Stochastic Volatility Models written by Chak Kei Jack Wong and published by . This book was released on 1999 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Roughness in Spot Variance written by Anine E. Bolko and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.

Download or read book Hyperbolic Normal Stochastic Volatility Model written by Jaehyuk Choi and published by . This book was released on 2019 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's SU distribution -- a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.

Download or read book Stochastic Volatility and Realized Stochastic Volatility Models written by Makoto Takahashi and published by Springer Nature. This book was released on 2023-04-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.

Download or read book Time Series Models written by D.R. Cox and published by CRC Press. This book was released on 2020-11-26 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis prediction and interpolation of economic and other time series has a long history and many applications. Major new developments are taking place, driven partly by the need to analyze financial data. The five papers in this book describe those new developments from various viewpoints and are intended to be an introduction accessible to readers from a range of backgrounds. The book arises out of the second Seminaire European de Statistique (SEMSTAT) held in Oxford in December 1994. This brought together young statisticians from across Europe, and a series of introductory lectures were given on topics at the forefront of current research activity. The lectures form the basis for the five papers contained in the book. The papers by Shephard and Johansen deal respectively with time series models for volatility, i.e. variance heterogeneity, and with cointegration. Clements and Hendry analyze the nature of prediction errors. A complementary review paper by Laird gives a biometrical view of the analysis of short time series. Finally Astrup and Nielsen give a mathematical introduction to the study of option pricing. Whilst the book draws its primary motivation from financial series and from multivariate econometric modelling, the applications are potentially much broader.

Download or read book Bayesian Analysis of Stochastic Volatility Models written by Asma Graja and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Time varying volatility is a characteristic of many financial series. An alternative to the popular ARCH framework is a Stochastic Volatility model which is harder to estimate than the ARCH family. In this paper we estimate and compare two classes of Stochastic Volatility models proposed in financial literature: the Log normal autoregressive model with some extensions and the Heston model. The basic univariate Stochastic Volatility model is extended to allow for the quot;leverage effectquot; via correlation between the volatility and the mean innovations and for fat tails in the mean equation innovation.A Bayesian Markov Chain Monte Carlo algorithm developed in Jacquier, Polson and Rossi 2004 is analyzed and applied to a large data base of the French financial market. Moreover, explicit expression for the parameter's estimators is found via Monte Carlo technique.

Download or read book A New Class of Stochastic Volatility Models with Jumps written by Mikhail Chernov and published by . This book was released on 2012 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and log-normal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jump-diffusions previously considered in empirical work and includes the affine class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for non-affine random intensity jump components. We attain the generality of our specification through a generic Levy process characterization of the jump component. The processes we introduce share the desirable feature with the affine class that they yield analytically tractable and explicit option pricing formula. The non-affine class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to affine random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the Samp;P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisely. The non-affine random intensity jump processes are more parsimonious than the affine class and appear to fit the data much better.

Download or read book Quantitative Analysis Derivatives Modeling and Trading Strategies written by Yi Tang and published by World Scientific. This book was released on 2007 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses selected practical applications and recent developments in the areas of quantitative financial modeling in derivatives instruments, some of which are from the authorsOCO own research and practice. While the primary scope of this book is the fixed-income market (with further focus on the interest rate market), many of the methodologies presented also apply to other financial markets, such as the credit, equity, and foreign exchange markets. This book, which assumes that the reader is familiar with the basics of stochastic calculus and derivatives modeling, is written from the point of view of financial engineers or practitioners, and, as such, it puts more emphasis on the practical applications of financial mathematics in the real market than the mathematics itself with precise (and tedious) technical conditions. It attempts to combine economic insights with mathematics and modeling so as to help the reader develop intuitions. In addition, the book addresses the counterparty credit risk modeling, pricing, and arbitraging strategies, which are relatively recent developments and are of increasing importance. It also discusses various trading structuring strategies and touches upon some popular credit/IR/FX hybrid products, such as PRDC, TARN, Snowballs, Snowbears, CCDS, credit extinguishers."

Download or read book Displaced Lognormal and Displaced Heston Volatility Skews Analysis and Applications to Stochastic Volatility Simulations written by Dan Wang and published by . This book was released on 2010 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finally we discuss the convergency of the discretisation schemes of the stochastic processes encountered in the Monte Carlo simulations. Under some regularity conditions, we give a partial strong convergency result for the stochastic volatility process. Moreover, we give a strong convergency result for the mean-reverting CEV process.

Download or read book Handbook of Volatility Models and Their Applications written by Luc Bauwens and published by John Wiley & Sons. This book was released on 2012-03-22 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.