In light of the special roles of the price of gold on the technological and economic development as well as social aspects of human society, it is of great importance and necessity to develop a series of statistical models that, based on sound reflection of the current structure of the gold market, are able to provide valuable references for trends of the gold price. In fact, the gold price is influenced by a variety of economic factors. For forecasting purposes, it is useful to study the shortand long-run effect of direct and indirect economic factors towards the supply and demand of gold and thus the spot price of gold. To this point, this paper focuses on analyzing the individual and mutual impact of influencing factors on the gold price and, simultaneously, providing a short-term forecast of the price of gold based on the relationships with other major macroeconomic variables. While these relationships are modeled with multiple regression, forecasts of individual factors are obtained under multivariate time series models. The forecasting results are found to be accurate in a relative sense, confirming the significant impact of the factors chosen while indicating the validity of the modeling idea applied.

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This paper proposes a novel analytical pricing-hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Directly targeting the instantaneous variance of a risky asset, our model consists of a generalized fractional Ornstein-Uhlenbeck process driven by a Lévy subordinator and an independent sinusoidalcomposite Lévy process, and allows the characteristic function of average forward variance to be obtainable in semiclosed form, without having to invoke any geometric-mean approximations. Pricing-hedging formulae are proposed for a general class of power-type derivatives, in the spirit of numerical Fourier transform. A comparative empirical study is conducted on two independent recent data sets on Volatility Index options, before and during the COVID-19 pandemic, to demonstrate that the proposed framework is highly amenable to efficient model calibration under various choices of kernels. The price dynamics of the underlying asset can be readily considered and the possibility of studying rough volatility of volatility is given as well.

In this article, the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite-activity subordinators induced by the probability distribution of the running average process and determine their jump intensity measures. Special cases including gamma processes and inverse Gaussian processes are discussed. Then we derive easily implementable formulas for the distribution functions, cumulants, and moments, as well as provide explicit estimates for their asymptotic behaviors. Numerical experiments are conducted for illustrating the applicability and efficiency of the proposed formulas. Two important extensions of the running average process and its equi-distributed subordinator are subsequently examined, with concrete applications to structural degradation modeling with memory and financial derivatives pricing in the presence of enhanced asymmetric leptokurtic feature, where their advantages relative to various existing models are highlighted together with the mention of Euler discretization and compound Poisson approximation techniques.