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The Exponential Dispersion Family (EDF) Chain Ladder and Data Granularity

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  • Greg Taylor

    (School of Risk and Actuarial Studies, University of New South Wales, Randwick, NSW 2052, Australia)

Abstract

This paper is concerned with the choice of data granularity for application of the EDF (Exponential Dispersion Family) chain ladder model to forecast a loss reserve. As the duration of individual accident and development periods is decreased, the number of data points increases, but the volatility of each point increases. This leads to a question as to whether a decrease in time unit leads to an increase or decrease in the variance of the loss reserve estimate. Is there an optimal granularity with respect to the variance of the loss reserve? A preliminary question is that of whether an EDF chain ladder that is valid for one duration (here called mesh size) remains so for another. The conditions under which this is so are established. There are various ways in which the mesh size of a data triangle may be varied. The paper identifies two of particular interest. For each of these two types of variation, the effect on variance of loss reserve is studied. Subject to some technical qualifications, the conclusion is that an increase in mesh size always increases the variance. It follows that one should choose a very high degree of granularity in order to maximize efficiency of loss reserve forecasting.

Suggested Citation

  • Greg Taylor, 2025. "The Exponential Dispersion Family (EDF) Chain Ladder and Data Granularity," Risks, MDPI, vol. 13(4), pages 1-25, March.
    • Handle: RePEc:gam:jrisks:v:13:y:2025:i:4:p:65-:d:1622192
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    References listed on IDEAS

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    1. Peikun Li & Chaoqun Ma & Jing Ning & Yun Wang & Caihua Zhu, 2019. "Analysis of Prediction Accuracy under the Selection of Optimum Time Granularity in Different Metro Stations," Sustainability, MDPI, vol. 11(19), pages 1-19, September.
    2. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    3. Taylor, Greg, 2011. "Maximum Likelihood and Estimation Efficiency of the Chain Ladder," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 131-155, May.
    4. Taylor, Greg, 2017. "Existence And Uniqueness Of Chain Ladder Solutions," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 1-41, January.
    5. Elton, Edwin J. & Gruber, Martin J. & Blake, Christopher R. & Krasny, Yoel & Ozelge, Sadi O., 2010. "The effect of holdings data frequency on conclusions about mutual fund behavior," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 912-922, May.
    6. Edwin J. Elton & Martin J. Gruber & Christopher R. Blake & Yoel Krasny & Sadi O. Ozelge, 2010. "The effect of holdings data frequency on conclusions about mutual fund behavior," World Scientific Book Chapters, in: Edwin J Elton & Martin J Gruber (ed.), Investments And Portfolio Performance, chapter 10, pages 195-205, World Scientific Publishing Co. Pte. Ltd..
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