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Stable approximation for call function via Stein’s method

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  • Chen, Peng
  • Qi, Tianyi
  • Zhang, Ting

Abstract

Let Sn be a sum of independent identically distribution random variables with finite first moment and hM be a call function defined by gM(x)=max{x−M,0} for x∈R, M>0. In this paper, we assume the random variables are in the domain Rα of normal attraction of a stable law of exponent α, then for α∈(1,2), we use the Stein’s method developed in Chen et al. (2024) to give uniform and non uniform bounds on α-stable approximation for the call function without additional moment assumptions. These results will make the approximation theory of call function applicable to the lower moment conditions, and greatly expand the scope of application of call function in many fields.

Suggested Citation

  • Chen, Peng & Qi, Tianyi & Zhang, Ting, 2025. "Stable approximation for call function via Stein’s method," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224002979
    DOI: 10.1016/j.spl.2024.110328
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    References listed on IDEAS

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    1. N. Yonghint & K. Neammanee, 2024. "Poisson approximation for the expectation of call function with application in collateralized debt obligation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(14), pages 5265-5279, April.
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    4. Peng Chen & Ivan Nourdin & Lihu Xu, 2021. "Stein’s Method for Asymmetric $$\alpha $$ α -stable Distributions, with Application to the Stable CLT," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1382-1407, September.
    5. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71(5), pages 421-421.
    6. Jagannathan, Ravi, 1984. "Call options and the risk of underlying securities," Journal of Financial Economics, Elsevier, vol. 13(3), pages 425-434, September.
    7. Chen, Shi & Zhao, Yonghong & Huang, Fu-Wei & Wang, Bin & Lin, Jyh-Horng, 2024. "Carbon leakage perspective: Unveiling policy dilemmas in emission trading and carbon tariffs under insurer green finance," Energy Economics, Elsevier, vol. 130(C).
    8. Nat Yonghint & Kritsana Neammanee & Nattakarn Chaidee, 2022. "Poisson approximation for locally dependent CDO," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(7), pages 2073-2081, April.
    9. Aurelio Vasquez & Xiao Xiao, 2024. "Default Risk and Option Returns," Management Science, INFORMS, vol. 70(4), pages 2144-2167, April.
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