We Did Not Rest and We Will Not Rest
In a workshop, Andreas found that an assymptotic mathematics approach, used in blast furnace automation, will do the job. A method based on Green's functions and an adaptive gridding and time-stepping. Adaptive Integration. An accurate, robust and ultra-fast solver that we in UnRisk (2000) applied for generalized Black-Scholes models and solving one-factor short-rate models.
The coal-faced mathematicians and lumberjack nickname come from that time.
In the following we transferred more sophisticated methods from technical problem solving into finance, including clever calibration techniques, derived from our in-depth knowledge of inverse problems.
It has been a remarkable journey so far and this year (2010) we entered into another radical innovation.
The in-time and robust calibration of the most sophisticated option valuation models (Heston, Bates, ..). A Hercules task in numerics.