Statistical modeling of gold price data using generalized extreme value distribution: an inference based on parametric and nonparametric bootstrap confidence interval

This study applies Extreme Value Theory (EVT) to model and quantify the risk associated with gold price fluctuations in the Malaysian market. Using daily gold price data from February 2010 to May 2023, the monthly maxima of negative daily log returns are modeled using the Generalized Extreme Value (GEV) distribution, with parameters estimated using Maximum Likelihood Estimation (MLE). Value-at-Risk (VaR) estimates for high quantiles are obtained from the fitted GEV model. To quantify the uncertainty of these estimates, the parametric and nonparametric bootstrap methods are used for constructing confidence intervals (CIs). Simulation study conducted across varying return periods (10, 20, 50, and 100 months), sample sizes (50, 100, 150, and 200), and GEV shape parameters (0.1, 0.2, 0.3, and 0.4), reveals that the nonparametric bootstrap method generally outperforms its parametric counterpart. This superiority is particularly evident for larger sample sizes and longer return periods, as demonstrated by narrower confidence intervals and lower error metrics. Applied to the Malaysian gold price data, the analysis yields VaR estimates ranging from 3.16% for a 10-month return period to 5.96% for a 100-month return period, with corresponding probabilities of exceedance decreasing from 10% to 1%. These results highlight the potential for significant losses in gold investments over longer time horizons with correspondingly decreasing probabilities of occurrence, while also demonstrating the effectiveness of EVT and bootstrap techniques in capturing and quantifying the uncertainty associated with extreme market events.

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