  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
(95% accuracy). 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.
