Statistical Tests for Comparing Option Pricing Model Errors

Summary

The document asks how to compare the predictive pricing errors of three option valuation models against Black–Scholes prices, using both in-sample and out-of-sample results. It raises the Diebold–Mariano test as a possible method and questions whether its usual reference distribution applies to pricing-error data. It also mentions a matched-pair t-test based on squared error differences, with a similar concern about the validity of standard distributional assumptions.

Bootstrapping the Diebold–Mariano statistic is raised as another possibility, but the document supplies no answer, data, or test results. Its contribution is framing the inference problem: model comparisons depend on the loss measure, dependence in the errors, and whether the test's assumptions support the claimed significance. It does not determine which test is appropriate or give implementation guidance, so the proposed methods require further statistical justification for the specific evaluation design.

Key ideas

• The document considers Diebold–Mariano tests for comparing option pricing errors.
• It also raises matched-pair tests based on differences in squared errors.
• The author questions whether standard reference distributions apply to the errors under study.
• Bootstrapping the Diebold–Mariano statistic is proposed as a possibility, not validated as a solution.
• The document provides no empirical comparison or definitive recommendation.

Tags

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


# 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.