Improvement of Real-GJR Model using Jump Variables on High Frequency Data

Abstract

Volatility is a key indicator in assessing risk when making investment decisions. In the world of financial markets, volatility reflects the degree to which the value of a financial asset fluctuates over a given period. The most common way to measure the future loss potential of an investment is through volatility. Focusing on the Realized GJR (RealGJR) volatility model, which consists of return, conditional volatility, and measurement equations, this study proposes the RealGJR-CJ model developed by decomposing the exogenous variable in the volatility equation of RealGJR into continuous C and discontinuous (jump) J variables. The decomposition of exogenous variables makes the RealGJR-CJ model follow realistic financial markets, where the asset volatility is a continuous process with some jump components. As an empirical illustration, the models are applied to an index in the Japanese stock market, namely Tokyo Stock Price Index, covering from January 2004 to December 2011. The observed exogenous variable in the volatility equation of RealGJR models is Realized Volatility (RV), which is calculated using intraday data with time intervals of 1 and 5 minutes. Adaptive Random Walk Metropolis method was employed in Markov Chain Monte Carlo algorithm to estimate the model parameters by updating the parameters during sampling based on previous samples from the chain. From the results of running the MCMC algorithm 20 times, the mean of the information criteria of competing models is significantly different based on standard deviation and the result suggests that the model with continuous and jump variables can improve the model without jump. The best fit model is provided by RealGJR-CJ with the adoption of 1-minute RV data.