DISTRIBUTIONAL PROPERTIES OF NAIRA EXCHANGE RATE VOLATILITY: AN INVERSE GAMMA PERSPECTIVE.

Abstract

This study investigates the distributional properties of monthly exchange rate volatility of the Nigerian Naira, with particular emphasis on inverse gamma behavior. Monthly exchange rate data for the Naira against the US Dollar (USD), Euro (EUR), and Pounds Sterling (GBP) from January 2020 to December 2024 are analyzed. Exchange rate volatility is proxied using squared logarithmic returns. Descriptive statistics indicate that the volatility series are strictly positive, highly right-skewed, and extremely leptokurtic, with skewness values exceeding 5 and kurtosis values above 30 for all currencies, confirming pronounced heavy-tailed behavior. The inverse gamma distribution is estimated using maximum likelihood techniques, and goodness-of-fit is assessed using the Kolmogorov–Smirnov test and graphical diagnostics. The Kolmogorov–Smirnov test rejects the null hypothesis of an exact inverse gamma distribution for all currency pairs; however, quantile–quantile plots show strong alignment between empirical and theoretical quantiles in the upper tail. Comparative volatility analysis reveals that the Naira–Pounds Sterling exchange rate exhibits the highest volatility, followed by the Naira–Euro and the Naira–US Dollar exchange rates. Although alternative distributions such as the gamma and lognormal achieve higher log-likelihood values, the inverse gamma distribution remains useful for capturing extreme exchange rate volatility, which is of primary interest in financial risk analysis.