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Poisson Approximation for Call Function via Stein–Chen Method

  • Kritsana Neammanee
  • Nat YonghintEmail author
Article

Abstract

Let V be a sums of independent nonnegative integer-valued random variables and \(h_z\) be a call function defined by \(h_{z}(v)=(v-z)^+\) for \(v\ge 0, z \ge 0\) where \((v-z)^+=\max \{v-z,0\}\). In this paper, we give bounds of Poisson approximation for \({E}[h_{z}(V)]\). These bounds improve the results of Jiao and Karoui (Finance Stoch 13(2):151–180, 2009). The technique used is Stein–Chen method with the zero bias transformation. One example of applications for a call function in finance is the standard collateralized debt obligation (CDO) tranche pricing. The CDO is a security backed by a diversified pool of debt obligation such as bounds, loans and credit default swaps.

Keywords

Call function CDO tranche pricing Poisson approximation Stein–Chen method 

Mathematics Subject Classification

60F05 

Notes

Acknowledgements

The authors are grateful to the referees for all valuable comments. The second author would like to thank the Development and Promotion of Science and Technology Talents Project (DPST).

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of ScienceChulalongkorn UniversityBangkokThailand

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