Stochastic Volatility Jumps Model with Dependent Jumps

Young-su Kang

Abstract

This paper explores volatility forecasting using the Stochastic Volatility with Jumps (SVJ) model with dependent jumps implemented by particle learning methods. Previous studies show that the performance from the SVJ model outperforms the GARCH and the Stochastic Volatility (SV) model when there is a dramatic change in the volatility of returns. This paper suggests ways to improve the performance of the SVJ model by making the independent jump process dependent on macroeconomic variables.

Dependent jump component shows how volatility clustering can be incorporated into the SVJ model. The model is implemented by particle learning method as an alternative to Markov Chain Monte Carlo (MCMC) method for computational efficiency and fast updates in nonlinear settings.

I have referred to the S&P 500 Index and NASDAQ-100 Index from year 2002 to compare how each model captures the change in volatility. Out of sample forecasting for the testing period from 2006 to 2007 and model selection criterion are employed to compare the performance of volatility forecast models.