Layman’s abstract for paper on goodness‐of‐fit for regime‐switching copula models with application to option pricing

Every few days, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

The article featured today is from the Canadian Journal of Statistics, with the full article now available to read here.

Nasri, B.R., Rémillard, B.N. and Thioub, M.Y. (2020), Goodness‐of‐fit for regime‐switching copula models with application to option pricing. Can J Statistics, 48: 79-96. doi:10.1002/cjs.11534

In finance, many instruments are based on several risky assets and their evaluation rest on the dependence of these assets. In fact, to determine this dependence structure, we must take into account the serial dependence in each asset (dependence between successive observations), as well as the dependence between the assets, i.e., the inter and the intra dependence. Underestimating the latter can have devastating financial and economic consequences, as exemplified by the 2008 financial crisis. We must also consider that the dependence may vary with time, potentially increasing in crisis periods. The traditional way of modeling dependence is to calculate the correlation between the data. Correlation can be defined as an indicator of the level of relationship between data. But it was noted that using correlation only underestimated the dependence in financial series, especially in times of crisis for reason that the correlation can only be good if the data follows should follow a Gaussian distribution. The other reason is that the relationship between assets seems to vary over time; it is stronger in times of crisis. To overcome these defects of the correlation, we often use more general models called copulas which can take into account more general forms of dependence. As said before, dependence can vary over time. For example, in a bad period (or regime), financial securities are more likely to fall together than during a good period. This is why copula models should also depend on these regimes. The models that we consider in this paper have precisely this property. In addition to showing how to estimate the parameters of these models, we propose a test of adequation to find out if the proposed model aligns well with the data. This test is also used to determine the correct number of regimes to use. Finally, to facilitate the future use of the proposed methodology, we have built a library of functions based on the free software R. This library of functions, available for free on CRAN, is entitled HMMcopula, and allows the user to choose between several dependence models and, for a fixed model, to make a test of adequation in order to select the right number of regimes.