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The Radial Basis Functions (RBF) interpolation is a popular approximation technique used to smooth scattered data in various dimensions. This study uses RBF interpolation to interpolate the volatility skew of the S&P500 index options. The interpolated skews are used to construct the risk-neutral densities of the index and its local volatility surface. The RBF interpolation is contrasted throughout the study with the cubic spline interpolation. An analysis of the densities and the local volatility shows that RBF are an effective and practical tool for interpolating the implied volatility surface.

This study examines the relationship between international trade and exchange rate uncertainty in Eswatini. The specific objectives were to establish the nature of relationship between import and exchange rate uncertainty, relationship between export trade and exchange rate uncertainty, and the causal relationship between import, export and exchange rate uncertainty. Annual data ranging from 1972 to 2018 were collected and analyzed using Engle–Granger cointegration and Granger causality techniques. Exchange rate uncertainty is measured using symmetric GARCH (1,1) model of the nominal exchange rate. Estimates from the augmented Dickey–Fuller (ADF) unit root test indicate that all the data were stationary at first difference. The cointegration results show evidence of long-run relationship between import and exchange rate uncertainty. The results also show that export is significantly related to exchange rate uncertainty in the long-run. Granger causality results evince the existence of a unidirectional causality from export to exchange rate uncertainty, and a bidirectional causal relationship between import and exchange rate uncertainty. The magnitude of influence of exchange rate uncertainty, however, is greater than that of import. The study recommends amongst others that monetary authorities should develop strategies that will stimulate demand for local goods so as to boost the influence of import on exchange rate uncertainty.