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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Prosiding University Research Colloquium
Alfagustina, Yumita Cristin
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Humanities Computer Science & IT Environmental Science Law, Crime, Criminology & Criminal Justice Mathematics Medicine & Pharmacology

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Improvement of Real-GJR Model using Jump Variables on High Frequency Data Nugroho, Didit Budi; Wulandari, Nadya Putri; Alfagustina, Yumita Cristin; Parhusip, Hanna Arini; Tita, Faldy; Susanto, Bambang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.24294

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. 
Study on The Continuous-Jump Behavior of Asset Return Volatility Through The GJR Model Alfagustina, Yumita Cristin; Nugroho, Didit Budi; Tita, Faldy
Prosiding University Research Colloquium Proceeding of The 17th University Research Colloquium 2023: Bidang MIPA dan Kesehatan
Publisher : Konsorsium Lembaga Penelitian dan Pengabdian kepada Masyarakat Perguruan Tinggi Muhammadiyah 'Aisyiyah (PTMA) Koordinator Wilayah Jawa Tengah - DIY

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Generalized Auto-Regressive Conditional Heteroskeasticity (GARCH) is a model used to predict the volatility of returns. Volatility is a statistical measure of the movement of returns for securities (financial instruments that can only be traded through markets or securities companies) or certain market indices. Then the GARCH model was further developed into an asymmetric form, namely conditional volatility and returns have a relationship, namely the GJR model which is an abbreviation of the name (Glosten- Jagannathan-Runkle). This research focuses on the GJR-X by adding high-frequency exogenous variables in volatility process and on the GARCH-CJ which is a decomposition of the exogenous variable X, namely the continuous component C (Continuous) and the jump J (Jump). TOPIX data (Tokyo Stock Price Index) is the real data used in this study. To estimate the model parameters, the ARWM (Adaptive Random Walk Metropolis) method will be used with the MCMC (Markov Chain Monte Carlo) algorithm. First, it was found that the ARWM method is good at estimating parameters. Second, the AIC value of GJR-CJ was smaller than that of GJR-X, which means that GJR-CJ had better data fitting.
Co-Authors Bambang Susanto Didit Budi Nugroho Faldy Tita Hanna Arini Parhusip Wulandari, Nadya Putri