Analysis of Short-Term Interest Rate Models with Stochastic Volatility

The examination of short-term interest-rate behaviour is of critical importance in financial analysis, risk management, and in formulating monetary policy. Fluctuations in financial markets in recent times have emphasised the need for strong and reliable models that can effectively model behaviors and dynamics involved in short-term interest-rate fluctuations. Conventional approaches, including Vasicek’s, have been universally embraced; yet such techniques often face difficulty in explaining clustering and autocorrelated volatility in real-world data. This study explores short-term interest rate models with stochastic volatility and evaluates their effectiveness in comparison to Autoregressive Conditional Heteroskedasticity (ARCH) and Generalised ARCH (GARCH) models. Using historical data from Nigerian financial instruments, we carried out Ljung-Box Q-statistic and ARCH tests to examine autocorrelation and volatility clustering. Results indicate that the data exhibits strong autocorrelation and significant volatility clustering. The predictive performance of our stochastic volatility model was measured by 10-day ahead volatility forecasts, which reached the sum of squared deviations of 1.3095, while ARCH had 2.0001 and GARCH had 2.1433. Our findings suggest that the stochastic volatility model outperforms the traditional ones, such as ARCH and GARCH, for interest rate change forecasting. Based on the performance realised, observed stochastic volatility models are recommended to better forecast interest rates, particularly for the emerging markets, where financial data could be volatile.