Publication: Asymmetric stochastic volatility models
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Publication date
2015-04-30
Defense date
2015-03-13
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Tutors
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Abstract
This dissertation focuses on the analysis of Stochastic Volatility (SV) models with leverage effect.
We propose a general family of asymmetric SV (GASV) models and consider in detail two particular
specifications within this family. The first one is the Threshold GASV (T-GASV) model which
nests some of the most famous asymmetric SV models available in the literature with the errors
being either Normal or GED.We also propose score driven GASV models with different assumptions
about the error distribution, namely the Normal, Student-t or GED distributions, where the volatility
is driven by the score of the lagged return distribution conditional on the volatility. Closed-form
expressions of some statistical moments of interest of these two GASV models are derived and
analyzed. We show that some of the parameters of these models cannot be properly identified by
the moments usually considered when describing the stylized facts of financial returns, namely,
excess kurtosis, autocorrelations of squares and cross-correlations between returns and future
squared returns. As a byproduct, we obtain the statistical properties of those nested popular
asymmetric SV models, some of which were previously unknown in the literature. By comparing
the properties of these models, we are able to establish the advantages and limitations of each of
them and give some guidelines about which model to implement in practice.
We also propose the Stochastic News Impact Surface (SNIS) to represent the asymmetric
response of volatility to positive and negative shocks in the context of SV models. The SNIS
is useful to show the added flexibility of SV models over GARCH models when representing
conditionally heteroscedastic time series with leverage effect. Analyzing the SNIS, we find that
the asymmetric impact of the level disturbance on the volatility can be different depending on the
volatility disturbance. Finally, we analyze the finite sample properties of a MCMC estimator of the parameters and
volatilities of some restricted GASV models. Furthermore, estimating the restricted T-GASV
model using this MCMC estimator, we show that one can correctly identify the true nested
specifications which are popularly implemented in empirical applications.
All the results are illustrated by Monte Carlo experiments and by fitting the models to both
daily and weekly financial returns.
Description
Mención Internacional en el tÃtulo de doctor
Keywords
Modelo estocástico, Volatilidad