A Hybrid Particle Swarm Optimization to Forecast Implied Volatility Risk

The application of optimization methods to prediction issues is a continually exploring field. In line with this, this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a forecasting perspective. The complex characteristics of implied volatility risk index such as non-linearity structure, time-varying and non-stationarity motivate us to apply a nonlinear polynomial Hammerstein model with known structure and unknown parameters. We use the Hybrid Particle Swarm Optimization (HPSO) tool to identify the model parameters of nonlinear polynomial Hammerstein model. Findings indicate that, following a nonlinear polynomial behaviour cascaded to an autoregressive with exogenous input (ARX) behaviour, the fear index in US financial market is significantly affected by COVID-19-infected cases in the US, COVID-19-infected cases in the world and COVID-19-infected cases in China, respectively. Statistical performance indicators provided by the developed models show that COVID-19-infected cases in the US are particularly powerful in predicting the Cboe volatility index compared to COVID-19-infected cases in the world and China (MAPE (2.1013%); R2 (91.78%) and RMSE (0.6363 percentage points)). The proposed approaches have also shown good convergence characteristics and accurate fits of the data.