A Predictor-Corrector Method for Drift-Diffusion Asset Price Models

By defining a back-test residual for an empirical short-term drift-diffusion model, we are able to use a distribution of these residuals from long term historical back-tests to adjust or correct the drift and diffusion parameters of the short-term model for improved back-tests. In other words, we can use drift-diffusion predict steps into withheld historical data regions to then compute corrections of the drift-diffusion models themselves. Corrections may be of drift only, diffusion only, or both, and corrections can be additive or multiplicative, depending on modeler judgement or post-corrected back-test quality metrics. These adjustments by definition correct poor back-tests often seen in drift-diffusion models, especially over longer time ranges (e.g. the corrections make the models more historically realistic) and may yield improved price- probability forecasts ex ante. While this predictor-corrector method does not replace other model calibration methods, it provides a quick way to provide information feedback from long term back-tests and get models into the ballpark of historical accuracy.