OK... For newbies like me, this is what I mean: http://en.wikipedia.org/wiki/Numerical_analysis So let's talk about anything within it... Optimization. Inter(Extra)polation / Regression Analysis. Nonlinear Programming. Stochastic Programming. Etc. Etc. Of course, considering this being a ATS forum, maybe it can extend to the utilizing them using AIs. Oh... and I use both QuantLib and IMSL lib in my tester... ......................................................................................................
Autoregressive conditional heteroscedacity. It's sort of like AR models, but for variance. ARMA models => residuals/error terms are weak stationary -- i.e., same mean and variance. ARCH model improves on this by allowing the variance to be conditioned on other variables. ARCH/GARCH is useful for modeling the evolution of volatility (sigma). There's other applications, like widening stops, conditioning mean-scaling laws based on the volatility, etc. Useful for options pricing too, since in Black-Scholes-Merton you are assuming a fixed volatility when you price the option at time t. So if you are going to make a bet on a call moving in a particular direction at a future time-step, you can forecast the volatility with a n-step ahead prediction operator based on an ARCH/GARCH model. It seems as if we both have similar interests. We should discuss strategies and ideas. I could use some assistance going independent as it is. Seems like you are already there.