Extending the Heston Model to Forecast Motor Vehicle Collision Rates

Abstract

We present an alternative approach to the forecasting of motor vehicle collision rates. We adopt an oft-used tool in mathematical finance, the Heston Stochastic Volatility model, to forecast the short-term and long-term evolution of motor vehicle collision rates. We incorporate a number of extensions to the Heston model to make it fit for modelling motor vehicle collision rates. We incorporate the temporally-unstable and non-deterministic nature of collision rate fluctuations, and introduce a parameter to account for periods of accelerated safety. We also adjust estimates to account for the seasonality of collision patterns. Using these parameters, we perform a short-term forecast of collision rates and explore a number of plausible scenarios using long-term forecasts. The short-term forecast shows a close affinity with realised rates (over 95% accuracy), and outperforms forecasting models currently used in road safety research (Vasicek, SARIMA, SARIMA-GARCH). The long-term scenarios suggest that modest targets to reduce collision rates (1.83% annually) and targets to reduce the fluctuations of month-to-month collision rates (by half) could have significant benefits for road safety. The median forecast in this scenario suggests a 50% fall in collision rates, with 75% of simulations suggesting that an effective change in collision rates is observed before 2044. The main benefit the model provides is eschewing the necessity for setting unreasonable safety targets that are often missed. Instead, the model presents the effects that modest and achievable targets can have on road safety over the long run, while incorporating random variability. Examining the parameters that underlie expected collision rates will aid policymakers in determining the effectiveness of implemented policies.