Modelling Currency in Circulation in Ghana: An Application of Extreme Value Theory

Abstract

This study aims to model Currency in circulation (CiC), ascertain the volatility characteristics, evaluate the risk, and predict the future volatility of CiC in Ghana. CiC influences inflation, monetary policy, and overall economic stability. This will help the Bank of Ghana in achieving and maintaining price stability, formulate and implement monetary policy instruments to influence interest rates, and manage liquidity. Leveraging 415 data points spanning from 1990 to 2024, the analysis reveals that the CiC data exhibit heavy-tailed characteristics, positive skewness, and high kurtosis. These features indicate the presence of significant outliers and extreme events that may not be adequately captured by conventional models. The analysis employs both the Generalized Pareto Distribution (GPD) and the Generalized Extreme Value (GEV) models through block maxima and threshold-based methodologies. These models, grounded in extreme value theory (EVT), enable robust estimation of the probabilities and magnitudes of extreme events.  This approach effectively estimates tail risk measures, particularly Value-at-Risk (VaR) and Expected Shortfall (ES). The CiC exhibits high volatility, as evidenced by the elevated standard deviations of the scale parameters, specifically 0.08296 and 1.8263. The fitted GPD models yield insights into the likelihood and severity of extreme events, underscoring the risks associated with extreme but impactful occurrences in both directions (gains and losses). The VaR estimates, computed at the 99th percentile, are 54.81% for monthly positive returns and 44.17% for negative returns. The Expected Shortfall estimates are 676.79% for monthly positive returns and 194.24% for negative returns.