Alternative Formulations of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors PDF Download
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Author: Philippe J. Deschamps
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
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.
Author: Philippe J. Deschamps
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Book Description
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.
Author: Manabu Asai
Publisher:
ISBN:
Category : Foreign exchange rates
Languages : en
Pages : 25
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Author: Jun Yu
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ISBN:
Category :
Languages : en
Pages : 16
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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.
Author: Daniel R. Smith
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ISBN:
Category :
Languages : en
Pages : 24
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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.
Author: Ole Eiler Barndorff-Nielsen
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ISBN:
Category :
Languages : en
Pages : 18
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Author:
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ISBN:
Category :
Languages : en
Pages :
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Author: Adam Clements
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ISBN:
Category : Economics
Languages : en
Pages : 20
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Author: Hong Jiang
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ISBN:
Category : Asset-liability management
Languages : en
Pages : 125
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Author: Roman Liesenfeld
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ISBN:
Category :
Languages : de
Pages : 0
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Author: Ionut Florescu
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ISBN:
Category :
Languages : en
Pages : 25
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Book Description
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.
