Why stability of a model for option pricing is so important? I think that parameters of a model give information about the market, so if the parameters change as effect of small changes in the set of option prices used to calibrate the model, then a trader that construct his strategy within such model needs to adjust his position. Is it right?

Yes, it is as you say...Relying on a model, means that you are assuming that the model captures the part of the market that you are interested in, and relatively to that, explains the price dynamics that you observe (and where it doesn't explain them, it's because the market is behaving in an anomalous way).So it is important to trust that the model is reasonably well behaved and explanatory of the part of the reality around which you are trading.Let's suppose that the model you are using is correct (ie. the data generating process of your real world is your model). From this lucky position, suppose you now observe that negligible changes in the market, produce vastly different set of values after recalibrating the model (or in other words the model is instable because too sensitive to the initial conditions).Because you know that the model is correct, the interpretation I'd have is to believe that the noise in the data can effect the model to a point that all the valid information it contains are obscured by little pertubation of your input parameters. Which makes the model useless, despite its correctness.In the real world, the model is never correct either, so as a trader you need the model to be relatively stable so that after enough time using it, you can start to trust it (and know when not to).Let now suppose that you use your model not for trading but for risk management. Common wisdom says that provide you price the instruments you buy, with the same model that you use to price the hedging instruments, you might still make the wrong deal, but at least the risk management is safe, and you are correctly controlling your risk.This is true, but if the model is unstable, it means that you need to adjust your hedges more often than you should, and re-hedging is expensive!gc

As an extreme illustration of why parameter stability is important,let's suppose I try to price an option on a stock, and I assume that the stock price is constantover time at its observed initial value. The risk free rate is assumed constant as well, so the the option is priced by the model at intrinsic value. Each day, I adjust the constant stock price to what I see on the screenThe delta is one or zero. Even if I use the delta to delta hedg when the model says I don't have to,there will be risk and replication wll not occur. We learn several things1) models which assume something is constant which are actually random will be biased when there is second order or higher senstiivity to the process2) the model provided hedges don't work, each day the hedge bleeds positively or negatively.3) It may be better to not hedge against events the (wrong) model says are impossible.

maybe concept of locality can well interpret it.AS a whole while,the stability of model is not important,that's to say model can be instable,but locally.is important,because we need to catch parameters as a constant.otherwise model is no means. comment it,thanks