Download or read book From Moving Average Local and Stochastic Volatility Models to 2 Factor Stochastic Volatility Models written by Oleg Kovrizhkin and published by . This book was released on 2008 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the following models:1. Generalization of a local volatility model rolled with a moving average of the spot: dS = mu Sdt + sigma(S/A)SdW$ where A(t) is a moving average of spot S.2. Generalization of Heston pure stochastic volatility model rolled with a moving average of the stochastic volatility: dS = mu Sdt + sigma SdW, dsigma^2 = k(theta - sigma^2)dt + gamma sigma dZ where theta(t) is a moving average of variance sigma^2.3. Generalization of a full stochastic volatility with the process for volatility depending on both sigma and S and rolled with a moving average of S: dS = mu Sdt + sigma SdW, dsigma = a(sigma, S/A)dt + b(sigma, S/A)dZ,corr(dW, dZ) = rho(sigma, S/A)$, where A(t) is a moving average of the spot S. We will generalize these and other ideas further and show that they lead to a 2-factor pure stochastic volatility model: dS = mu Sdt + sigma SdW$, sigma = sigma(v_1, v_2), dv_1 = a_1(v_1, v_2)dt + b_1(v_1, v_2)dZ_1,dv_2 = a_2(v_1, v_2)dt + b_2(v_1, v_2)dZ_2, corr(dW, dZ_1) = rho_1(v_1, v_2), corr(dW, dZ_2) = rho_2(v_1, v_2), corr(dZ_1, dZ_2) = rho_3(v_1, v_2) and give examples of analytically solvable models, applicable for multicurrency models consistent with cross currency pairs dynamics in FX. We also consider jumps and stochastic interest rates.

Download or read book Bayesian Analysis of Moving Average Stochastic Volatility Models written by Stefanos Dimitrakopoulos and published by . This book was released on 2017 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a moving average stochastic volatility in mean model and a moving average stochastic volatility model with leverage. For parameter estimation, we develop efficient Markov chain Monte Carlo algorithms and illustrate our methods, using simulated data and a real data set. We compare the proposed specifications against several competing stochastic volatility models, using marginal likelihoods and the observed-data Deviance information criterion. We find that the moving average stochastic volatility model with leverage has better fit to our daily return series than various standard benchmarks.

Download or read book Multivariate Continuous Time Stochastic Volatility Models Driven by a L vy Process written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Several multivariate stochastic models in continuous time are introduced and their probabilistic and statistical properties are studied in detail. All models are driven by Lévy processes and can generally be used to model multidimensional time series of observations. In this thesis the focus is on various stochastic volatility models for financial data. Firstly, multidimensional continuous-time autoregressive moving-average (CARMA) processes are considered and, based upon them, a multivariate continuous-time exponential GARCH model (ECOGARCH). Thereafter, positive semi-definite Ornstein-Uhlenbeck type processes are introduced and the behaviour of the square root (and similar transformations) of stochastic processes of finite variation, which take values in the positive semi-definite matrices and can be represented as the sum of an integral with respect to time and another integral with respect to an extended Poisson random measure, is analysed in general. The positive semi-definite Ornstein-Uhlenbeck type processes form the basis for the definition of a multivariate extension of the popular stochastic volatility model of Barndorff-Nielsen and Shephard. After a detailed theoretical study this model is estimated for some observed stock price series. As a further model with stochastic volatility multivariate continuous time GARCH (COGARCH) processes are introduced and their probabilistic and statistical properties are analysed.

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.

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 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 Modelling and Simulation of Stochastic Volatility in Finance written by Christian Kahl and published by Universal-Publishers. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.

Download or read book A Simple Test for GARCH Against a Stochastic Volatility Model written by Philip Hans Franses and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: GARCH models and Stochastic Volatility (SV) models can both be used to describe unobserved volatility in asset returns. We consider the issue of testing a GARCH model against an SV model. For that purpose, we propose a new and parsimonious GARCH-t model with an additional restricted moving average term, which can capture SV model properties. We discuss model representation, parameter estimation, and our simple test for model selection. Furthermore, we derive the theoretical moments and the autocorrelation function of our new model. We illustrate our model and test for nine daily stock-return series.

Download or read book Moving Average Stochastic Volatility Models with Application to Inflation Forecast written by Joshua C. C. Chan and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modeling Stochastic Volatility with Application to Stock Returns written by Mr.Noureddine Krichene and published by International Monetary Fund. This book was released on 2003-06-01 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic volatility model where volatility was driven solely by a latent variable called news was estimated for three stock indices. A Markov chain Monte Carlo algorithm was used for estimating Bayesian parameters and filtering volatilities. Volatility persistence being close to one was consistent with both volatility clustering and mean reversion. Filtering showed highly volatile markets, reflecting frequent pertinent news. Diagnostics showed no model failure, although specification improvements were always possible. The model corroborated stylized findings in volatility modeling and has potential value for market participants in asset pricing and risk management, as well as for policymakers in the design of macroeconomic policies conducive to less volatile financial markets.

Download or read book Local Stochastic Volatility written by Lorenzo Bergomi and published by . This book was released on 2017 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine local-stochastic volatility models and derive a simple condition such models need to obey so that the carry P&L of a delta-hedged/vega-hedged position makes sense in a trading context.We give examples of admissible and non-admissible models and discuss the issue of the delta position in the hedge portfolio.We end with a characterization of the break-even levels of the local volatility model - itself in the admissible class.

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by . This book was released on 2016 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Chapter 2 of Stochastic Volatility Modeling, published by CRC/Chapman & Hall.In this chapter the local volatility model is surveyed as a market model for the underlying together with its associated vanilla options.First, relationships of implied to local volatilities are derived, as well as approximations for skew and curvature. Exact and approximate techniques for taking dividends into account are presented.We then turn to the dynamics of the local volatility model. We introduce the Skew Tickiness Ratio (SSR) and derive approximate formulas for the SSR and volatilities of volatilities in the local volatility model.We also examine future skews.We then consider the delta and carry P&L of a hedged option position. We derive the expression of the market-model delta of the local volatility model and discuss the relationship between sticky-strike and market-model deltas. We characterize the gamma/theta break-even levels of a hedged position and show that the local volatility model is indeed a market model.We then derive the expression of the vega-hedge portfolio.Markov-functional models are considered next.Finally, we survey the Uncertain Volatility Model and its usage.A digest summarizes key points.

Download or read book Turbo Charged Local Stochastic Volatility Models written by Ghislain Vong and published by . This book was released on 2013 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article presents an alternative formulation of the standard Local Stochastic Volatility model (LSV) widely used for the pricing and risk-management of FX derivatives and to a lesser extent of equity derivatives. In the standard model, calibration is achieved by solving a non-linear two-factor Kolmogorov forward PDE, where a minimum number of vol points is required to achieve convergence of a finite difference implementation. In contrast, we propose to model the volatility process by a Markov chain defined over an arbitrary small number of states, so that calibration and pricing are achieved by solving a coupled system of one-factor PDEs. The practical benefits are twofolds: existing one-factor PDE solvers can be recycled to model stochastic volatility, while the reduction in number of discretisation points implies a speedup in execution time that enables real-time risk-management of large derivatives position.

Download or read book Two Factor Stochastic Volatility with Embedded Local Volatility written by Adil Reghai and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is intended to introduce an extension of the stochastic volatility model introduced by Pat Hagan. It adds to it two important features: a second factor and mean reversion. It is also a response to the smile dynamics problem taking into account very important features.

Download or read book Extremes of L vy Driven Moving Average Processes with Applications in Finance written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical volatility changes in time and exhibits tails, which are heavier than those of normal distributions. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and non-classical stochastic volatility models with respect to their extreme behavior: subexponential Lévy driven MA processes in the maximum domain of attraction of the Gumbel distribution, regularly varying mixed MA processes, Ornstein-Uhlenbeck processes with exponentially decreasing tails and COGARCH processes. The basic volatility models of this thesis are subexponential Lévy driven MA processes $Y(t)=\int_{-\infty}^{\infty}f(t-s)\, dL(s)$ for $t\in \R$ where f is a deterministic function and L is a Lévy process. In Chapter 1 we study the extremal behavior of subexponential MA processes in the maximum domain of attraction of the Gumbel distribution and in Chapter 2 of the Fréchet distribution. The behavior is quite different in these different regimes. For both classes we give sufficient conditions for the kernel function f, such that a stationary version of the MA process Y exists, which preserves the infinitely divisibility of L. We calculate the tail behavior of the stationary distribution, which is again subexponential and in the same maximum domain of attraction as the driving Lévy process L. Hence they capture heavy tails and volatility jumps. Our investigation on the extremal behavior of Y is based on a discrete-time skeleton of Y chosen to incorporate those times, where large jumps of the Lévy process L and extremes of the kernel function f occur. Adding marks to this discrete-time skeleton, we obtain, by the weak limit of marked point processes, complete information about the extremal behavior. A complementary result guarantees the convergence of running maxima. Both models have volatility clusters. Regularly varying MA processes have long high level excursion in contrast to subexp.

Download or read book Multiple Time Scales Stochastic Volatility Modeling Method in Stochastic Local Volatility Model Calibration written by Fan Wang and published by . This book was released on 2013 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study carefully the stochastic local volatility (SLV) model for pricing barrier options in foreign exchange or equity market. We first discuss the advantage and disadvantage of popular models such as stochastic volatility and local volatility that have been used for pricing the same products, then introduce the necessities to build a hybrid SLV model. We classified the calibration process of SLV model into two major parts according to parameters' different nature, and point out the slowness of the calibration procedure is mainly caused by solving the lever-age surface from Kolmogorov forward equation via the iteration method. Our major contribution is to apply the fast mean reversion volatility modeling technique and singular/regular perturbation analysis developed by Fouque, Papanicolaou, Sircar and Sølna in [24, 27, 26] to the forward equation, which gives a starting point which is proved to be close to the true solution, so that the iteration time is significantly reduced. Besides, we developed target functions specifically designed for processing exotic option quotes and give suitable numerical methods for each step of the calibration.

Download or read book Stochastic Volatility Models with ARMA Innovations written by Bo Zhang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: