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I'm optimizing 5 parameters for an option pricing model. Now I want to asses whether these parameters are stable over time (i.e., a year). For this I create about 12 subsamples and estimate the optimal parameters for each subsample (I do this by minimizing a cost function, i.e., chi-squared, under a certain threshold).

Now I'm not really sure what statistic quantifies those estimated parameters as stable. Is it a low standard deviation? What would be the best way to prove those parameters are stable over time?

EDIT: The model which I'm using is neither differentiable nor is it continuous.

Related question, without an answer: How to test stability/variability of statistic over time, using R

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jcfrei
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Google "parameter constancy test". There's a bunch of them, among most popular ones are Chow tests. There's a paper by Ericsson from FRB where he explains how they are used.

Aksakal
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  • thanks for the pointers. I have a follow up question: is a chow test also applicable if the optimization isn't based on a linear regression, but rather on a stochastic process which is then evaluated using Monte Carlo? – jcfrei Apr 25 '14 at 01:13
  • Show us an example. Estimation technique is not so important as the model specification – Aksakal Apr 25 '14 at 01:14
  • I'm following broadie and kaya: http://finmath.stanford.edu/seminars/documents/Broadie.pdf I'm basically using a euler discretization outlined in section 2.2. however I estimate the parameters with a differential evolution algorithm (by price & storn), using a chi squared goodness of fit test. – jcfrei Apr 25 '14 at 11:49