QuoteOriginally posted by: tthriftQuoteOriginally posted by: CuchulainnNice title (3+1 Muskateers)I suppose your goal is robust, accurate and fast iv solvers. Already, a number of candidate methods has been proposed. A data set for stress testing would be nice to have if you could provide it.// One devil's advocate remark is: the nonlinear equation may _not_ have a solution (e.g. give a ridiculous market price) in which case no numerical method will work. We want to distinguish this case from the one that the parameters are OK but the numerical method breaks down. And ... if there is a solution, is it always unique? e.g.r = 0.08, T = 0.25, K = 65, S = 60Market price = 333Vol = ??I like that goal (ie., robust, accurate and fast iv solvers). Data to stress solvers seems necessary.You have a good point about solvers being fragile with respect to ridiculous inputs.If left to my own devices, the monkey in me might want to generate combinations of inputs that cover the ranges of the individual inputs' data types.This would undoubtedly lead to some ridiculous inputs.An industrial grade solver might protect itself from combinations of inputs that don't make sense.However, some people's solvers may be called such that little or no protective pre-filtering is needed.From a robustness to inputs point of view, perhaps solvers should be stressed at several levels to characterize how they respond."ridiculous input" leads to no solution. This is really a pure maths problem as I posted:C/F = (N(d) - N(-d)] (2)will not always be solvable for depending on C/F(e.g. F = 1, C = 2000, find d, _never_ IMO because N(d) - N(-d)] <= N(d) <= 1) // Heuristic: if Aitken does not converge after +- 8 iterations, it will never converge and hence no solution. (?)
Last edited by Cuchulainn
on December 1st, 2014, 11:00 pm, edited 1 time in total.