hey,I calibrated several option pricing models (Heston-Stochastic-Volatility, Merton-Jump-Diffusion and Bates model) to a cross-section of implied volatilities on a daily basis. I find the parameters to vary significantly, especially in the Bates model (presumably a result of an overfitting). Therefore, I want to add a straightforward penalty function to the minimization problem. Most authors either use the (euclidian) distance to the parameter vector from the daiy before or some constant parameter vector (the prior).Now I have some issues implementing this stuff. The problem is that the parameters are not of the same magnitude (e.g. speed of mean-reversion is much larger than the long-run variance). If I simply take a non-weighted euclidian distance the algorithm will pay too much attention to staying close to e.g. the speed of mean-reversion.Do you agree?If yes, any elegant suggestions how to get rid of this problem?thanks, bernd

are you fitting data to "forward" data (i.e. current prices are fed as projections into future volatility) only? If, yes, I do not see how regularization can help ever...

QuoteOriginally posted by: BerndSchmitzhey,I calibrated several option pricing models (Heston-Stochastic-Volatility, Merton-Jump-Diffusion and Bates model) to a cross-section of implied volatilities on a daily basis. I find the parameters to vary significantly, especially in the Bates model (presumably a result of an overfitting). Therefore, I want to add a straightforward penalty function to the minimization problem. Most authors either use the (euclidian) distance to the parameter vector from the daiy before or some constant parameter vector (the prior).Now I have some issues implementing this stuff. The problem is that the parameters are not of the same magnitude (e.g. speed of mean-reversion is much larger than the long-run variance). If I simply take a non-weighted euclidian distance the algorithm will pay too much attention to staying close to e.g. the speed of mean-reversion.Do you agree?If yes, any elegant suggestions how to get rid of this problem?thanks, berndI have 2 suggestions:1. Set limits on the range over which the parameters may vary.2. Add a penality function as you suggest but renormalize the parameters so that they are comparable in range magnitude according to how you feel about them (this is equivalent to weighting them but more transparent as to why).

QuoteOriginally posted by: Fermion2. Add a penality function as you suggest but renormalize the parameters so that they are comparable in range magnitude according to how you feel about them (this is equivalent to weighting them but more transparent as to why).Yes, this is a very important point. Also, for efficiency/numerical reasons make sure that your optimizer works with variables which have the same order of magnitude (through normalization)To verify how good is the solution found by your optimizer you may also use a global optimizer, such as Differential Evolution

You should non-dimensionalize using a scale that's relevant to the problem and work with order 1 quantities. This is something that is kind of preached by everyone in applied math, etc. but never really written about very well anywhere. The only decent source to read about doing it properly that I'm aware of isMathematics Applied to Deterministic Problems in the Natural Sciences by Lin and Segel section 6.2