Abstract
Price volatility of stocks is an important issue in stock markets. It should also be taken into account that the stochastic nature of volatility affects decision-makers’ minds to a great extent. Therefore, predicting price volatility could help them make proper decisions. In this paper, a new multivariate fractionally integrated generalised autoregressive conditional heteroscedasticity (MFIGARCH) model is proposed to handle the price volatility in stocks. In this model, a long-term parameter is considered and estimated along with other parameters. In estimating the parameters of this nonlinear model, the maximum likelihood estimation method, which could be solved by standard econometric packages, is applied. However, these packages are no longer efficient when the size of the model increases. Thus meta-heuristic approaches, which stochastically seek optimal or near-optimal solutions, were used. In this paper, the well-known Particle Swarm Optimisation (PSO) meta-heuristic method is used for solving the suggested multivariate FIGARCH model. Hence the main objective of this paper is to introduce a new model for addressing the stock price volatility (i.e., the development of FIGARCH to create the MFIGARCH model) and to apply an efficient estimation method (i.e. PSO) for finding the parameters of the problem.
Highlights
Studying price volatility in stock markets indicates that the volatility of a stock depends greatly on both the volatility of other stocks and that of the same stock in previous periods
To investigate the performance of the proposed multivariate fractionally integrated GARCH (FIGARCH) model estimated by Particle Swarm Optimisation (PSO), three stock indices – those of the automobile industry, leasing, and machinery and equipment – were considered
generalised ARCH (GARCH) approaches are theoretically preferred for estimating the variance and covariance matrix, the FIGARCH model needs many parameters
Summary
Studying price volatility in stock markets indicates that the volatility of a stock depends greatly on both the volatility of other stocks and that of the same stock in previous periods. Some typical applications of the multivariate GARCH (MGARCH) model are in optimising portfolios [2], pricing assets and derivatives [3], computing the value at risk [4,5], hedging futures [6], transmitting volatility and allocating asset [7], estimating systemic risk in banking [8], determining leverage effect [9], estimating volatility momentum function [3,10,11], nonlinear programming [12], avoiding currency exposure risk [13,14], calculating property portfolio minimum capital risk [15], ascertaining incorrect tests of MGARCH models [16], modelling changing variance in an exchange rate structure [17], and analysing individual financial markets [18]
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