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1

BAYESIAN SV MODELS IN THE ANALYSIS OF CONDITIONAL CORRELATION

100%

Pajor A.

Przegląd Statystyczny

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2006

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vol. 53

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issue 1

69-89

EN

The paper presents four specifications of Bivariate Stochastic Volatility process: the Basic Stochastic Volatility process (BSV), the Stochastic Discount Factor process (SDF), the SV with the Cholesky decomposition (TSV), and the SV with the spectral decomposition (JSV). The multivariate SV models are characterised by treating the volatilities (the conditional variances) as unobserved variables. The SDF model assumes that the conditional covariances are stochastic but the conditional correlations among the series are constant over time - the dynamic of the conditional variances and covariance is described by one stochastic process. The TSV and JSV models assume that the conditional correlation is time-varying and stochastic. In the TSV model the conditional covariance matrix is modelled using three separate stochastic processes, while in the JSV model there are only two separate processes. In this paper the bivariate stochastic volatility models are used to describe the daily exchange rate of the euro against the Polish zloty and the daily exchange rate of the US dollar against the Polish zloty. The general methods of the Bayesian inference and model selection are used to select the best bivariate SV model. The results presented here indicate that the conditional correlation coefficient changes over .time. The TSV model outperforms other models. The assumption of zero conditional correlation is strongly rejected by the data. The BSV model turned out to be the worst one. The results presented in this paper are obtained by Monte Carlo Markov chain. The Metropolis-Hastings algorithm is used within the Gibbs sampler.

2

BIVARIATE BAYESIAN VECM-SV MODELS FOR POLISH EXCHANGE RATES

100%

Pajor A.

Przegląd Statystyczny

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2006

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vol. 53

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issue 3

9-26

EN

In the paper three series of daily growth rates (of PLN/USD, PLN/EUR and EUR/USD over a period: 02.01.2002 -31.12.2004) are used to investigate the effect of the Forex market on the Polish exchange rates. In modelling of the official daily PLN/USD and PLN/EUR exchange rates the relationship: (PLN/USD)/(PLN/EUR) ~ EUR/USD is introduced. We assume that this relation (in log terms) is a cointegration equation in the sense of Engle and Granger and that the EUR/USD exchange rate is weakly exogenous in the Bayesian sense (for inferences on the parameters and on the latent variables, which describe two Polish exchange rates). Under this assumption we build five models with the error correction mechanism (ECM) and with the disturbances, which follow bivariate SV processes. The stochastic volatility processes differ in assumptions on the conditional correlation and in the number of latent processes. The best model assumes that the conditional correlation is time-varying, stochastic, and that the conditional covariance matrix is described by three separate stochastic processes. We show that the presence of the EUR/USD exchange rate and of the ECM term has serious effect on the Polish exchange rates. It reduces volatility and leads to increase in the posterior mean of the conditional correlations.

3

BAYESIAN ANALYSIS OF EUROPEAN CALL OPTION AND DELTA-NEUTRAL HEDGE USING GARCH AND CSV PROCESSES

63%

Pipien M., Pajor A.

Przegląd Statystyczny

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2005

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vol. 52

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issue 3

37-63

EN

The main goal of this article was to present an application of GARCH (Generalised Auto Regressive Conditionally Heteroscedastic) and CSV (Correlated Stochastic Volatility) processes in modelling the volatility of the daily returns of PLN/USD exchange rate and pricing the European call option for this exchange rate. The authors offer the Bayesian interpretation of commonly used methods of volatility assessment as well as predictive consequences of different volatility models. They also consider Bayesian estimation of the delta coefficient for the European call option. From the Bayesian point of view posterior distribution of delta enables to predict the cost of so called delta-neutral hedging strategy. They show the predictive distributions of the cost of this strategy as well as the cost of its managing.

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3 Przegląd Statystyczny

3 Pajor A.

1 Pipien M.

2 2006

1 2005

BAYESIAN SV MODELS IN THE ANALYSIS OF CONDITIONAL CORRELATION

BIVARIATE BAYESIAN VECM-SV MODELS FOR POLISH EXCHANGE RATES

BAYESIAN ANALYSIS OF EUROPEAN CALL OPTION AND DELTA-NEUTRAL HEDGE USING GARCH AND CSV PROCESSES