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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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