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Approximation of bivariate copulas by patched bivariate Fréchet copulas

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  • Zheng, Yanting
  • Yang, Jingping
  • Huang, Jianhua Z.

Abstract

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums.

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  • Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:246-256
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    Cited by:

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    2. Zheng, Yanting & Luan, Xin & Lu, Xin & Liu, Jiaming, 2023. "A new view of risk contagion by decomposition of dependence structure: Empirical analysis of Sino-US stock markets," International Review of Financial Analysis, Elsevier, vol. 90(C).
    3. Printechapat, Tanes & Sumetkijakan, Songkiat, 2018. "Factorizable non-atomic copulas," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 86-94.
    4. Sourabh Balgi & Jose M. Pe~na & Adel Daoud, 2022. "$\rho$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows," Papers 2209.07111, arXiv.org, revised Aug 2024.
    5. Durante, Fabrizio & Fernández Sánchez, Juan & Sempi, Carlo, 2013. "Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 897-905.
    6. Kamnitui Noppadon & Santiwipanont Tippawan & Sumetkijakan Songkiat, 2015. "Dependence Measuring from Conditional Variances," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-15, July.

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