Abstract
This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by fractional Brownian motions, combined with Poisson processes and modulated by continuous-time homogeneous Markov chains. The calibration is carried out by estimating the Jump Generalized Autoregressive Conditional Heteroscedasticity (Jump-GARCH) and Markov regime-switching models of each precious metal, as well as computing their Hurst exponents. The novelty in this research is the use of non-linear, non-normal, multi-factor, time-varying risk stochastic models, useful for an investors’ decision-making process when they intend to include precious metals in their portfolios as safe-haven assets. The main empirical results are as follows: (1) all metals stay in low volatility most of the time and have long memories, which means that past returns have an effect on current and future returns; (2) silver and platinum have the largest jump sizes; (3) silver’s negative jumps have the highest intensity; and (4) silver reacts more than gold and platinum, and it is also the most volatile, having the highest probability of intensive jumps. Gold is the least volatile, as its percentage of jumps is the lowest and the intensity of its jumps is lower than that of the other two metals. Finally, a set of recommendations is provided for the decision-making process of an average investor looking to buy and sell precious metals.
Highlights
It is well known that gold and silver behave as safe-haven investment instruments.Investors usually use gold and silver to hedge economic slowdown or crisis periods since they perform better than stocks and other financial assets in conditions of high volatility [1,2]
The first equation explains the dynamic of the metal returns in terms of a trend plus idiosyncratic volatility, which is associated with fractional Brownian motion
The second equation states that volatility is stochastic and is explained through a mean reverting process, plus the volatility of volatility associated with fractional Brownian motion, plus a term of Poisson jumps with expected jump size γ
Summary
Investors usually use gold and silver to hedge economic slowdown or crisis periods since they perform better than stocks and other financial assets in conditions of high volatility [1,2]. This paper attempts to model the dynamics of gold, silver, and platinum returns from 1994 to 2019 using a stochastic volatility model that combines fractional jump-diffusion processes with continuous-time homogeneous Markov chains. This paper is organized as follows: the Section presents a short overview of three precious metals (gold, silver, and platinum); Section 3 states the main assumptions and sets up the model; Section 4 describes the data; Section 5 carries out the calibration of the proposed stochastic volatility model and discusses the empirical results obtained; Section 6 provides the conclusions and acknowledges the limitations of this study.
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