Download or read book Stochastic Volatility Models written by Jian Yang and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Likelihood Estimation of Stochastic Volatility Models written by Gleb Sandmann and published by . This book was released on 1996 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Likelihood Estimation of Stochastic Volatility Models written by Yacine Ait-Sahalia and published by . This book was released on 2009 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop and implement a new method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by the implied volatility of a short dated at-the-money option. We find that the approximation results in a negligible loss of accuracy. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine model of Heston (1993) and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.
Download or read book Maximum Likelihood Estimation of Stochastic Volatility Models written by Yacine Aït-Sahalia and published by . This book was released on 2004 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop and implement a new method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by the implied volatility of a short dated at-the-money option. We find that the approximation results in a negligible loss of accuracy. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine model of Heston (1993) and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Download or read book Stochastic Volatility Models and Simulated Maximum Likelihood Estimation written by Ji Eun Choi and published by . This book was released on 2011 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial time series studies indicate that the lognormal assumption for the return of an underlying security is often violated in practice. This is due to the presence of time-varying volatility in the return series. The most common departures are due to a fat left-tail of the return distribution, volatility clustering or persistence, and asymmetry of the volatility. To account for these characteristics of time-varying volatility, many volatility models have been proposed and studied in the financial time series literature. Two main conditional-variance model specifications are the autoregressive conditional heteroscedasticity (ARCH) and the stochastic volatility (SV) models. The SV model, proposed by Taylor (1986), is a useful alternative to the ARCH family (Engle (1982)). It incorporates time-dependency of the volatility through a latent process, which is an autoregressive model of order 1 (AR(1)), and successfully accounts for the stylized facts of the return series implied by the characteristics of time-varying volatility. In this thesis, we review both ARCH and SV models but focus on the SV model and its variations. We consider two modified SV models. One is an autoregressive process with stochastic volatility errors (AR--SV) and the other is the Markov regime switching stochastic volatility (MSSV) model. The AR--SV model consists of two AR processes. The conditional mean process is an AR(p) model, and the conditional variance process is an AR(1) model. One notable advantage of the AR--SV model is that it better captures volatility persistence by considering the AR structure in the conditional mean process. The MSSV model consists of the SV model and a discrete Markov process. In this model, the volatility can switch from a low level to a high level at random points in time, and this feature better captures the volatility movement. We study the moment properties and the likelihood functions associated with these models. In spite of the simple structure of the SV models, it is not easy to estimate parameters by conventional estimation methods such as maximum likelihood estimation (MLE) or the Bayesian method because of the presence of the latent log-variance process. Of the various estimation methods proposed in the SV model literature, we consider the simulated maximum likelihood (SML) method with the efficient importance sampling (EIS) technique, one of the most efficient estimation methods for SV models. In particular, the EIS technique is applied in the SML to reduce the MC sampling error.
Download or read book High and Low frequency Exchange Rate Volatility Dynamics written by Sassan Alizadeh and published by . This book was released on 2001 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. The good properties of the range imply that range-based Gaussian quasi-maximum likelihood estimation produces simple and highly efficient estimates of stochastic volatility models and extractions of latent volatility series. We use our method to examine the dynamics of daily exchange rate volatility and discover that traditional one-factor models are inadequate for describing simultaneously the high- and low-frequency dynamics of volatility. Instead, the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor.
Download or read book Range Based Estimation of Stochastic Volatility Models written by Sassan Alizadeh and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. The good properties of the range imply that range-based Gaussian quasi-maximum likelihood estimation produces simple and highly efficient estimates of stochastic volatility models and extractions of latent volatility series. We use our method to examine the dynamics of daily exchange rate volatility and discover that traditional one-factor models are inadequate for describing simultaneously the high- and low-frequency dynamics of volatility. Instead, the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor.
Download or read book Asymmetric Stochastic Volatility Models written by Xiuping Mao and published by . This book was released on 2016 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we derive the statistical properties of a general family of Stochastic Volatility (SV) models with leverage effect which capture the dynamic evolution of asymmetric volatility in financial returns. We provide analytical expressions of moments and autocorrelations of power-transformed absolute returns. Moreover, we use an Approximate Bayesian Computation (ABC) filter-based Maximum Likelihood (ML) method to estimate the parameters of the SV models. In Monte Carlo simulations we show that the ABC filter-based ML accurately estimates the parameters of a very general specification of the log-volatility with standardized returns following the Generalized Error Distribution (GED). The results are illustrated by analyzing series of daily S&P 500 and MSCI World returns.
Download or read book Maximum Likelihood Approach for Stochastic Volatility Models written by Jordi Camprodon Masnou and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Volatility written by Scott Ian White and published by . This book was released on 2006 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Range based Estimation of Stochastic Volatility Models Or Exchange Rate Dynamics are More Interesting Than You Think written by Sassan Alizadeh and published by . This book was released on 2000 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comparing Estimation Procedures for Stochastic Volatility Models of Short Term Interest Rates written by Ramaprasad Bhar and published by . This book was released on 2009 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper compares the performance of three maximum likelihood estimation procedures -quasi-maximum likelihood, Monte Carlo likelihood and the particle filter to estimate stochastic volatility models of short term interest rates. The procedures are compared in an empirical study of interest rate volatility where a number of diagnostic tests in- and out-of-sample are utilized to evaluate both model specification and estimation procedure. Empirically, the results suggest interest rates follow the Cox-Ingersoll-Ross model with stochastic volatility and that volatility increases after Federal Open Market Committee meetings. Overall, the Monte Carlo likelihood procedure provided the best results.
Download or read book Quasi Maximum Likelihood Inference for Stochastic Volatility Models written by Maddalena Cavicchioli and published by . This book was released on 2015 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper we consider the Quasi Maximum Likelihood (QML) procedure for the estimation of stationary Stochastic Volatility models. We prove the consistency of the QML estimators and compute explicitly their asymptotic variances. This allows us to obtain also consistent estimators of the asymptotic variances in explicit forms. The knowledge of the asymptotic variance-covariance matrix of the QML estimators gives a concrete possibility for the use of the classical testing procedures. Our results are related to those obtained in Ruiz (1994) and Bartolucci and De Luca (2001) (2003).
Download or read book Estimation of the Dynamic Stochastic Volatility Model for Asset Price Determination by Simulated Maximum Likelihood written by Jon Danielsson and published by . This book was released on 1991 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Empirical Analysis of Stochastic Volatility Models written by Adrien-Paul Lambillon and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to explain and apply the stochastic volatility models of Heston and GARCH to model the S&P 500 index volatility. The maximum likelihood estimate of the CIR process in the volatility equation of the Heston model and GARCH(1,1) with different underlying distributions are compared. It is shown that the model with strongest mean reversion, the CIR model, is the best volatility estimation for the overall period. For periods of volatility clustering, however, GARCH models capture the behaviour more accurately.
