# How to statistically compare the pricing errors of various option pricing models?

I have three different option pricing models, for which I computed the in-sample and out-of-sample pricing errors.

Now I want to test the pricing performance of these three option pricing models against the Black-Scholes obtained prices. What is the most convenient way to do so?

When comparing the empirical predictive performance of various models, one usually uses the Diebold-Mariano test statistic. Would this be a valid approach for comparing the performance of the option models? I am concerned about the fact that the Diebold-Marino (DM) test-statistic is not following a standard normal distribution when using the pricing errors of the option models as input.

One paper (Andreou, Charalambous and Martzoukos, 2005) uses the matched-pair t-tests concerning the squared differences to compare the performance statistically. Here I am again concerned about the distribution of the t-statistic, as the inferences made are only valid in case of a standard normal distribution.

Or is bootstrapping the DM-statistic a solution? Let me know your thoughts...

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why doing it so complicated? You have three prices which you ought to track vs market prices. I would rather run a set of simple tracking statistics to express the average deviation (standard error/tracking error), min/max deviations, duration of deviations and such forth. A model such as DM forces you to accept whatever "scoring algorithm" they determine best whereas you may want to look at the whole picture. Just my 2 cents. – Matt Wolf Jun 20 '13 at 17:11
Makes sense, but I have some models which are quite close to each other and wanted to apply statistical tests to see how 'close' they really are significantly. Perhaps someday one will come with a solution to this. – JohnAndrews Jun 27 '13 at 13:38
What I presented is "a" solution, maybe not the one you are seeking, but I generally do not concern myself with general test statistics that output one "score". It may satisfy your curiosity which model scored higher but in the end it does not give you anything to further fine tune parameters because you will not know in what exact way your model results differed from, for example, market prices. – Matt Wolf Jun 27 '13 at 14:06