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.
The motivation: "Valuation and risk management, two sides of the quant business, must be treated with equal sophistication, with equal respect, and equal suspicion" (Paul Wilmott). And those complex option valuation models with stochastic volatilities and jumps were criticized, because they are difficult to calibrate.
Andreas and his team again applied solvers from modeling the "fire" process and implemented them in a CUDA framework (nvidia FERMI architecture).
Again, a-wild-thing-that-makes-my-heart-sing. Reducing hours to seconds, without giving up accuracy and robustness - was the challenge.
Unlike others, we are emphasizing not only on making Montecarlo simulation and PDE solving faster, but do things that cannot be done without.
