Alternative Formulations of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors

2015 ◽  
Author(s):  
Philippe J. Deschamps
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Leverage Effect ◽  
Volatility Model ◽  
Heavy Tailed

scholarly journals Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets

2013 ◽  
Vol 45 (02) ◽  
pp. 545-571 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Simulation Method ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Leverage Effect ◽  
Order Structure ◽  
Spot Prices ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility

Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

scholarly journals A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 689
Author(s):  
Łukasz Lenart ◽  
Anna Pajor ◽  
Łukasz Kwiatkowski
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Financial Time Series ◽  
Stochastic Volatility Model ◽  
Mcmc Methods ◽  
Statistical Framework ◽  
Typical Data ◽  
Volatility Model ◽  
Density Forecasting ◽  
Heavy Tailed

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.

scholarly journals MULTIVARIATE ECOGARCH PROCESSES

2010 ◽  
Vol 27 (2) ◽  
pp. 344-371 ◽  
Author(s):  
Stephan Haug ◽  
Robert Stelzer
Keyword(s):  
Stochastic Volatility ◽  
Continuous Time ◽  
Stochastic Volatility Model ◽  
Leverage Effect ◽  
Mixing Properties ◽  
Multivariate Extension ◽  
Volatility Model

A multivariate extension of the exponential continuous time GARCH (p, q) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated, and ways to model a component-wise leverage effect are presented.

Estimation of SV Model with Leverage Effect Based on MCMC Technique

2014 ◽  
Vol 530-531 ◽  
pp. 605-608
Author(s):  
Xiao Cui Yin
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stock Index ◽  
Leverage Effect ◽  
Model Parameters ◽  
Convergence Diagnostics ◽  
Volatility Model ◽  
Mcmc Simulation ◽  
Series Convergence

This paper is to study the estimation of stochastic volatility model with leverage effect using Bayesian approach and Markov Chain Monte Carlo (MCMC) simulation technique. The data used is China's Shenzheng stock index. Estimations of model parameters are achieved by using MCMC technique in Openbugs Software, results show that there is leverage effect in Shenzheng stock series, convergence diagnostics suggest that parameters of the model are convergent.

scholarly journals A CORRELATED STOCHASTIC VOLATILITY MODEL MEASURING LEVERAGE AND OTHER STYLIZED FACTS

2002 ◽  
Vol 05 (05) ◽  
pp. 541-562 ◽  
Author(s):  
JAUME MASOLIVER ◽  
JOSEP PERELLÓ
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
Leverage Effect ◽  
Stylized Facts ◽  
Uhlenbeck Process ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Negative Skewness

We analyze a stochastic volatility market model in which volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. In the framework of this model we exactly calculate the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.

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