Download or read book Alternative Formulations of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy Tailed Errors written by Philippe J. Deschamps and published by . This book was released on 2016 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates three formulations of the leverage effect in a stochastic volatility model with a skewed and heavy-tailed observation distribution. The first formulation is the conventional one, where the observation and evolution errors are correlated. The second is a hierarchical one, where log-volatility depends on the past log-return multiplied by a time-varying latent coefficient. In the third formulation, this coefficient is replaced by a constant. The three models are compared with each other and with a GARCH formulation, using Bayes factors. MCMC estimation relies on a parametric proposal density estimated from the output of a particle smoother. The results, obtained with recent S&P500 and Swiss Market Index data, suggest that the last two leverage formulations strongly dominate the conventional one. The performance of the MCMC method is consistent across models and sample sizes, and its implementation only requires a very modest (and constant) number of filter and smoother particles.
Download or read book Alternative Asymmetric Stochastic Volatility Models written by Manabu Asai and published by . This book was released on 2010 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Leverage in a Stochastic Volatility Model written by Jun Yu and published by . This book was released on 2013 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications co-exist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods reveal that the specification of Jacquier et al is inferior. Simulation experiments are conducted to study the sampling properties of the Bayes MCMC for the conventional model.
Download or read book A Stochastic Volatility Model with Fat Tails Skewness and Leverage Effects written by Daniel R. Smith and published by . This book was released on 2007 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a new stochastic volatility model that captures the three most important features of stock index returns: negative correlation between returns and future volatility, excess kurtosis and negative skewness. We estimate the model parameters by maximum likelihood using a numerical integration-based filter to deal with the latent nature of volatility. In this approach different models are defined by varying the joint density of returns and future volatility conditional on current volatility. Our innovation is to construct the joint conditional density using a copula. This approach is tremendously flexible and allows the econometrician to choose the marginal distribution of both returns and volatility independently and then stitch them together using a copula, which is also chosen independently, to form the joint density. We also develop conditional moment-based model specification tests for the extent to which the various stochastic volatility models are able to capture the skewness and excess kurtosis we observe in practice. The parameter estimates and conditional moment tests indicate that leverage effects, excess kurtosis and skewness are all crucial for modeling stock returns.
Download or read book Incorporation of a Leverage Effect in a Stochastic Volatility Model written by Ole Eiler Barndorff-Nielsen and published by . This book was released on 1998 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Research Report written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non linear Filtering for Stochastic Volatility Models with Heavy Tails and Leverage written by Adam Clements and published by . This book was released on 2005 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Stochastic Volatility Model with Leverage Effect and Regime Switching written by Hong Jiang and published by . This book was released on 2014 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic volatility models written by Roman Liesenfeld and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study About the Existence of the Leverage Effect in Stochastic Volatility Models written by Ionut Florescu and published by . This book was released on 2018 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The empirical relationship between the return of an asset and the volatility of the asset has been well documented in the financial literature. Named the leverage e ffect or sometimes risk-premium effect, it is observed in real data that, when the return of the asset decreases, the volatility increases and vice-versa.Consequently, it is important to demonstrate that any formulated model for the asset price is capable to generate this eff ect observed in practice. Furthermore, we need to understand the conditions on the parameters present in the model that guarantee the apparition of the leverage effect. In this paper we analyze two general speci cations of stochastic volatility models and their capability of generating the perceived leverage effect. We derive conditions for the apparition of leverage e ffect in both of these stochastic volatility models. We exemplify using stochastic volatility models used in practice and we explicitly state the conditions for the existence of the leverage effect in these examples.
Download or read book Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model written by Dinghai Xu and published by . This book was released on 2010 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation for Mean reverting Stochastic Volatility Models with a Leverage Effect written by Agnès Grimaud and published by . This book was released on 2006 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Leverage Effect in Stochastic Volatility written by Amaan Mehrabian and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A striking empirical feature of many financial time series is that when the price drops, the future volatility increases. This negative correlation between the financial return and future volatility processes was initially addressed in Black 76 and explained based on financial leverage, or a firm's debt-to-equity ratio: when the price drops, financial leverage increases, the firm becomes riskier, and hence, the future expected volatility increases. The phenomenon is, therefore, traditionally been named the leverage effect. In a discrete time Stochastic Volatility (SV) model framework, the leverage effect is often modelled by a negative correlation between the innovation processes of return and volatility equations. These models can be represented as state space models in which the returns and the volatilities are considered as the observed and the latent state variables respectively. Including the leverage effect in the SV model not only results in a better fit ...
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 Multiple Time Scales in Volatility and Leverage Correlations written by Josep Perelló and published by . This book was released on 2013 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
