Estimating Correlated Jumps and Stochastic Volatilities

IES Working Paper No. 35/2011

36 Pages Posted: 19 Aug 2011 Last revised: 18 Nov 2011

See all articles by Jiri Witzany

Jiri Witzany

University of Economics in Prague

Date Written: June 18, 2011

Abstract

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: jump-diffusion, stochastic volatility, MCMC, Value at Risk, Monte Carlo

JEL Classification: C11, C15, G1

Suggested Citation

Witzany, Jiri, Estimating Correlated Jumps and Stochastic Volatilities (June 18, 2011). IES Working Paper No. 35/2011. Available at SSRN: https://ssrn.com/abstract=1911996 or http://dx.doi.org/10.2139/ssrn.1911996

Jiri Witzany (Contact Author)

University of Economics in Prague ( email )

Winston Churchilla Sq. 4
Prague 3, 130 67
Czech Republic

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