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Number of results: 7
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Abstract

In this paper we show that in the lognormal discrete-time stochastic volatility model with predictable conditional expected returns, the conditional expected value of the discounted payoff of a European call option is infinite. Our empirical illustration shows that the characteristics of the predictive distributions of the discounted payoffs, obtained using Monte Carlo methods, do not indicate directly that the expected discounted payoffs are infinite.
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Abstract

This paper presents some new results on exogeneity in models with latent variables. The concept of exogeneity is extended to the class of models with latent variables, in which a subset of parameters and latent variables is of interest. Exogeneity is discussed from the Bayesian point of view. We propose sufficient weak and strong exogeneity conditions in the vector error correction model (VECM) with stochastic volatility (SV) disturbances. Finally, an empirical illustration based on the VECM-SV model for the daily growth rates of two main official Polish exchange rates: USD/PLN and EUR/PLN, as well as EUR/USD from the international Forex market is presented. The exogeneity of the EUR/USD rate is examined. The strong exogeneity hypothesis of the EUR/USD rate is not rejected by the data.
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Abstract

The aim of this paper is to examine the empirical usefulness of two new MSF – Scalar BEKK(1,1) models of n-variate volatility. These models formally belong to the MSV class, but in fact are some hybrids of the simplest MGARCH and MSV specifications. Such hybrid structures have been proposed as feasible (yet non-trivial) tools for analyzing highly dimensional financial data (large n). This research shows Bayesian model comparison for two data sets with n = 2, since in bivariate cases we can obtain Bayes factors against many (even unparsimonious) MGARCH and MSV specifications. Also, for bivariate data, approximate posterior results (based on preliminary estimates of nuisance matrix parameters) are compared to the exact ones in both MSF-SBEKK models. Finally, approximate results are obtained for a large set of returns on equities (n = 34).
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Abstract

The paper refines Lenk’s concept of improving the performance of the computed harmonic mean estimator (HME) in three directions. First, the adjusted HME is derived from an exact analytical identity. Second, Lenk’s assumption concerning the appropriate subset A of the parameter space is significantly weakened. Third, it is shown that, under certain restrictions imposed on A, a fundamental identity underlying the HME also holds for improper prior densities, which substantially extends applicability of the adjusted HME.
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Abstract

The s-period ahead Value-at-Risk (VaR) for a portfolio of dimension n is considered and its Bayesian analysis is discussed. The VaR assessment can be based either on the n-variate predictive distribution of future returns on individual assets, or on the univariate Bayesian model for the portfolio value (or the return on portfolio). In both cases Bayesian VaR takes into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. In the case of a large portfolio, the applicability of the n-variate approach to Bayesian VaR depends on the form of the statistical model for asset prices. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this multivariate approach and the much simpler univariate approach based on modelling volatility of the value of a given portfolio.
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Abstract

Hybrid MSV-MGARCH models, in particular the MSF-SBEKKspecification, proved useful in multivariate modelling of returns on financialand commodity markets. The initial MSF-MGARCH structure, called LN-MSF-MGARCH here, is obtained by multiplying the MGARCH conditionalcovariance matrixHtby a scalar random variablegtsuch that{lngt, t∈Z}is aGaussian AR(1) latent process with auto-regression parameterφ. Here we alsoconsider an IG-MSF-MGARCH specification, which is a hybrid generalisationof conditionally StudenttMGARCH models, since the latent process{gt}is nolonger marginally log-normal (LN), but forφ= 0it leads to an inverted gamma(IG) distribution forgtand to thet-MGARCH case. Ifφ6= 0, the latentvariablesgtare dependent, so (in comparison to thet-MGARCH specification)we get an additional source of dependence and one more parameter. Dueto the existence of latent processes, the Bayesian approach, equipped withMCMC simulation techniques, is a natural and feasible statistical tool to dealwith MSF-MGARCH models. In this paper we show how the distributionalassumptions for the latent process together with the specification of theprior density for its parameters affect posterior results, in particular theones related to adequacy of thet-MGARCH model. Our empirical findingsdemonstrate sensitivity of inference on the latent process and its parameters,but, fortunately, neither on volatility of the returns nor on their conditionalcorrelation. The new IG-MSF-MGARCH specification is based on a morevolatile latent process than the older LN-MSF-MGARCH structure, so thenew one may lead to lower values ofφ– even so low that they can justify thepopulart-MGARCH model.
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