Prague Economic Papers 2013, 22(2):251-283 | DOI: 10.18267/j.pep.451

Estimating Correlated Jumps and Stochastic Volatilities

Jiøí Witzany
University of Economics, Prague, nám. W. Churchilla 4, CZ - 130 67 Praha 3 (jiri.witzany@vse.cz).

We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model's parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on the two most important Czech domestic financial market time series of the FX (CZK/EUR) and stock (PX index) returns. Four bivariate models with and without jumps and/or stochastic volatility are compared using the deviance information criterion (DIC) confirming importance of incorporation of jumps and stochastic volatility into the model.

Keywords: value at risk, jump-diffusion, stochastic volatility, MCMC, Monte Carlo
JEL classification: C11, C15, G1

Published: January 1, 2013  Show citation

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Witzany, J. (2013). Estimating Correlated Jumps and Stochastic Volatilities. Prague Economic Papers, 22(2), 251-283. doi: 10.18267/j.pep.451
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